The term expected value, or EV for short, appears frequently in articles and game strategies. Video poker is a game of pure mathematics, making it possible to precisely determine the EV for every play. The concept of EV is cardinal to a successful strategy for any game. So just what is meant by EV?

To put it in as simple terms as possible, the EV of any chance event is the average of all possible outcomes. When most people hear the word average they usually think of what mathematicians call the mean; that is, you add up a bunch of numbers and divide by the number of numbers. To calculate the EV, however, we must use a weighted average, not just the mean.

For example, suppose you are playing common 9/6 jacks or better video poker, and you hold an ace and a jack of the same suit. The possible payoffs are a royal flush, which pays 800-for-1, four of a kind at 25-for-1, full house at 9-for-1, flush at 6-for-1, straight at 4-for-1, three of a kind at 3-for-1, two pair at 2-for-1, a high pair at 1-for-1, and zilch (no payoff) at 0-for-1.

The mean of these possible payoffs, which is (800+25+9+6+4+3+2+1+0)/9 = 94.44, tells us absolutely nothing of any useful value. To get the EV, we must take into account the probability of each payoff, as I show below.

If you multiply the amount of your bet by the EV of the play, the result is the expected return, which is the average that you can expect to get back if you made that same play many times. For example, an EV of 1.023 would mean that you have a 2.3% advantage, and you can expect to get back an average of $10.23 for each $10.00 bet. Conversely, an EV of 0.982 would mean that you could expect to get back an average of only $9.82 for each $10.00 bet, which translates to a 1.8% disadvantage. Obviously, we would like to place bets only on events with an EV greater than one.

Now let’s apply this to video poker. For any dealt five-card hand there are thirty two possible ways to play it, and for each of these thirty two ways of playing a hand there may be many possible outcomes. Assuming an honest video poker game, each unseen card has equal probability of appearing at any time. Assuming that you’re playing a consistent strategy, this makes it possible to calculate the probability of each possible payoff. The EV of any play can then be calculated by multiplying the probability of each possible outcome by its payoff and summing the products.

Another way to look at it is to multiply the number of ways each final hand can occur by its payoff, sum those products, and divide by the total number of possible outcomes. Using that method, let’s determine the EV of one video poker play.

Suppose we’re playing 9/6 jacks or better, and we want to know the best play when dealt: Kh Qs Jh 10h 4h.

Draw 1, hold K-Q-J-10, hoping for a straight. We are drawing one card from the remaining 47 unseen cards, so there are 47 equally likely possible outcomes, as follows. Any ace or nine will make a straight, which pays 4-for-1, and there are eight such cards in the deck. Also, any king, queen or jack will make a high pair, which pays 1-for-1, and there are a total of nine such cards remaining in the deck. Any of the other 30 remaining cards will yield zero payoff, so the expected value can be computed as:

(8×4+9 x1+30×0)/47 = 0.8723

Of course, the “30 x 0” term doesn’t contribute anything to the EV, it is purely for demonstration purposes.

Draw 2: Hold K-J-10-4 (all hearts), hoping for a flush. Any heart will make a flush, which pays 6-for-1, and there are nine such cards remaining in the deck. Also, any king or jack will make a high pair, which pays 1-for-1, and there are six such cards available. None of the other 32 cards yield a payoff, so this play has a total expected value of: (9×6+6×1)/47 = 1.2766

Draw 3: Hold K-J-10 (all hearts), hoping for a royal flush. This is more complicated because we are drawing two cards instead of one. Since there are (47*46)/2 = 1,081 possible outcomes instead of just 47, I’ll skip the mathematics and tell you that the expected value is 1.3506.

Therefore, if you were dealt this same hand many times and always drew for the straight, you could expect an average return of only a little over 87 cents for each dollar bet, so you would be losing money on the play. However, if you always drew for the flush you could expect an average return of $1.27, and if you always drew for the royal you could expect an average return of $1.35 for each dollar bet. Which way would you play the hand?

Note that in each case we are usually hoping for one particular final hand, which I call the primary payoff, but part of the expected value (sometimes most of it) comes from other possible outcomes, which I call secondary payoffs. In draw number three above, for example, nearly half of the expected value comes from secondary payoffs (i.e. final hands other than a royal flush). This is good because it reduces the volatility of the game. That is, it reduces our likely bankroll fluctuations.

There are 29 other ways to play this hand, but these three give the highest expected values. If we were building a hand rank table, we now know that a three-card royal flush (abbreviated RF 3) is generally higher than a four card flush (flush 4), which in turn is higher than an open-ended four card straight draw (straight 4).

By analyzing hundreds of different hands in this way, we can build a complete hand rank table, which can then be used as a playing strategy. Once you have an accurate hand rank table, it is no longer necessary to consider specific expected values. It is the job of analysts like myself to provide such tables, so that anyone can play optimum strategy without having to understand the math. For any given dealt hand, you simply scan down the table and hold the first available combination.

I am sure that most video poker players are familiar with the expressions ‘full pay,’ ’short pay’ and ‘partial pay’, but, others may ask what these mean. The explanation given below should be required reading before play on any VP machine: reading the pay schedule. The best place to start is with a basic ‘plain vanilla’ vp machine pay schedule for jacks or better (jacks+). This version is usually the choice of newbie VP players because of its simplicity, however many VP veterans nominate Jacks or Better as the best VP game. Following is a full-pay 9/6 regular VP pay schedule for jacks or better: (Multiply by 5 for maximum coin play.)

strategy tips for jacks+:

• Always keep a five-card winning ‘pat’ hand unless you can draw one card to a royal flush, or a straight flush
• Break a high pair only for a 4-card royal or any 4-card straight flush including an inside draw
• Break a low pair for any 3-card royal flush or any 4-card flush or straight flush
• Break a 4-card flush or open-ended straight for a 3-card royal
• If you have both a 4-flush and 4-straight, go for the flush, the better paying hand.
• An inside straight is completed with one card only, (e.g. dealt 6, 7, 9, 10). Here only the eight can produce a winning hand. This is a good bet to complete a straight flush or royal.
• An outside straight is completed with two possible cards, (e.g. dealt 6, 7, 8, 9). Here a ten or five can produce a winning hand. This hand should always be held for a possible win.
• Ace is not the most important card, especially if not suited with another high card. The jack is, because you have more opportunities to develop winning hands around a jack than around an ace. To form a sequence, a jack has two possibilities: a queen on one side and a 10 on the other. The ace however, has only one possible sequence partner: the king. In addition, when dealt two face cards and an ace, not suited, keep the two face cards only and discard the ace allowing three opportunities, rather than two, to either match the face card(s) or form a straight.
• Never keep a kicker. That’s an additional face card with any pair; this reduces your return by 5%. Hold only the pair and draw three cards. Approximately 1/3 of all hands dealt will have no value other than high card(s) and 20% will be paying hands.

Jacks+ 9/6 strategy is easy to learn and that is the beauty of this VP version. Note: These strategy tips are for Jacks+ 9/6 version only. All other VP versions with varying pay tables require specific strategies for each. I have included a Jacks+ Strategy Card below for your convenience.

Jacks+ VP strategy card draw to the hand higher on the list high card is a jack or better.

Keep in mind that in a grouping of video poker machines, known as banks or carousels, some casinos will ‘mix-in’ several VP machines with inferior pay programs (short/partial pay). This means that the educated player, on the full-pay Jacks+ 9/6 machine, will be winning more for the same hands than the other players will.

Many strategists say optimum play when they really mean perfect play; that is, every play would be made for the highest possible expected value, even if the cost of a simplified play is miniscule. For all attractive video poker games, only a computer would be able to make the absolute best play in every situation.

For some games, we can come very close to the maximum payback with just a few strategy rules. For others, it requires a hand rank table as shown elsewhere in this site for Double Bonus Poker at about 100.15% and All American Poker at about 100.7% payback. Such games seduce some strategists into generating a very detailed strategy with lots of penalty card situations (penalty cards will also be discussed in an upcoming article).

Some “experts” are so concerned about perfection that they generate penalty card situations ad nauseam. I do play video poker quite a bit, and I could learn those complex rules if I wanted to, but it would be a wasted effort. With my strategies I can come within a couple of hundredths of a percent of perfect play, and I can play about 500 to 700 hands per hour. Adding the complexity of all those penalty cards would slow me down, cutting into my expected win rate much more than the potential gain of the better strategy and greatly reducing the fun of playing. For any endeavor, there is a point of diminishing returns.

In the case of a complex video poker game such as All American Poker, you can use a very simplified strategy and play very fast, but you will be giving up a significant part of your potential win rate. Learning a somewhat more accurate strategy will increase your expected per-play gain with little loss of speed, resulting in an increase in your hourly win rate.

A strategy might be developed that would yield very close to the maximum payback, but it would necessarily by quite complicated. Following such a strategy faithfully would increase your per-play expected gain, but considering those penalty card situations would probably slow you down.

Worse, you might make more errors through inadvertent deviations from the strategy and thus have a lower net win rate. Because of the wide difference in the various games and various people, I feel that the term optimum play should be defined as ‘the strategy that will yield the highest per-hour expected win rate for a particular player.’ Note, especially the reference to a particular player.

I don’t know anything about your ability and dedication to be a winning player, so I don’t know exactly what your optimum strategy would be, so let’s examine what I do know. I know that the industry-wide average hold on all video poker games in Nevada is about two percent more than it would be if everyone played perfectly, and the reason is that the vast majority of players play by guesses and hunches instead of learning a good strategy.

Is this due to lack of ability? No, nearly everyone has the ability to learn to be a winner, but most either don’t try because they are in a casino just for fun, knowing that they will most likely loose the money they have brought along to gamble, or they believe that it doesn’t matter how they play because the machines are set to a specific payback.

Contrary to common myth, the machines are random, and in most jurisdictions they are honest, so you can be a winner if you want to. In the previous column I presented simplified versions of my Precision Play rules for Jacks-or-Better Draw Poker and Deuces Wild. While these greatly simplified strategies obviously will not yield the full potential payback of the games, they do come within one or two tenths of one percent.

For games with widely ranging payoffs and probabilities, such as video poker, it has been very difficult to determine bankroll requirements. Until recently, we relied mostly on computer simulations for an approximation, but Russian mathematician Evgeny Sorokin has shown that the risk of ruin (the probability of losing one’s entire starting bankroll) can be calculated precisely as a root of equation 1 below.

The formula may look complicated, but don’t let that stop you from reading this article, even if you’re not mathematically inclined. As a serious player, you will find this information very valuable. For several of the most attractive games, you can skip the math altogether by using a table published in Video Poker Times. Take a few minutes to look at the equation.

Simply stated, the risk of losing a one-bet bankroll is equal to the summation of a function of all the possible payoffs and their probabilities. Although the rebate is not actually paid immediately on each play as implied by adding C to W, the result is very close, since you can go to the slot club booth and make the cash any time it reaches the club’s minimum transaction level. As a starting point, this formula assumes that your entire gambling bankroll consists of exactly one betting unit (five coins for a typical video poker game), but it’s easy to extend that to a real bankroll. You place your one bet, and if you lose, you’re done. If you win or get a push, you continue playing indefinitely until you either lose that starting bet and all winnings, or have amassed a fortune.

Let’s apply this to a specific game. Suppose you play full pay double bonus poker very accurately in a casino that pays 0.25% cash rebate on the slot card, and you want to know your risk of ruin (RoR). The per-coin payoff (assuming five coins played) and the probability of each final hand type (assuming perfect play) are shown in the double bonus poker strategy section, and C will be 0.0025 for all cases. The Zilch (no payoff) entry is never shown on the machine’s payoff schedule, but its probability is given by the game analysis program, and it must be included in this calculation as the i=0 case.

Since R(1) is the summation of a series involving a function of itself, it can be found only by an iterative procedure; that is, make a guess, try it, use the result as the new guess, and repeat until the result is as accurate as desired. The series will converge faster if we start with a reasonable guess such as 0.99 and then average each result with the previous guess for use as the next guess. Using final hand probabilities and payoffs for standard full pay double bonus poker plus 0.25% slot club rebate, we find that the risk of losing a one-unit bankroll is R(1) = 0.99970164. (With real human play, the risk is a bit higher, typically in the fifth or sixth decimal place with skillful play)

Subtracting from one, we see that the probability of building a single 5-coin bet into a vast fortune with perfect play on this game is 0.0002984, or about one chance in 3,350. That may not seem like a very good prospect, yet it’s a lot better than any state lottery. Also, your starting bankroll is presumably at least a little bigger than just one 5-coin bet. What we really want to know is the risk of losing that real gambling bankroll. The probability of losing an entire starting bankroll of B betting units is given by equation 2. Since R(1) is less than one for a positive expectation game, a bigger starting bankroll results in an exponential reduction in the risk as follows:

For example, if you start out with 1,000 betting units (e.g., $5,000 on a 5-coin $1 double bonus machine) and play at a casino with a 0.25% cash rebate slot club until you either lose it all or amass a vast fortune, you have almost a 26% chance of becoming very rich (although at an expected average win rate of only 0.4% of your action, it’s going to take a very long time).

As a more practical concern, you probably want to know how big a starting bankroll you need for a specific risk of ruin that you consider acceptable. For example, suppose you decide that you can live with one chance in ten of losing your entire bankroll. You could interpolate from the above table and estimate that you need about 8,000 betting units for RoR = 0.1, but why not calculate it exactly? Solving equation 2 for B, we get equation 3. Plugging in 0.1 for R(B) and 0.99970164 as determined above for R(1) we get B = 7,715 betting units. Multiplying by $1.25, we find that we need to start with at least $9,644 to limit our RoR on a quarter Double Bonus game to ten percent.

Now let’s look at another game. For standard full pay deuces wild, R(1) computes to 0.9993469 (with no slot club rebate). This doesn’t seem much different from the figure for double bonus poker, but the third column above shows what happens when we raise it to large powers of B to compute RoR. Note how much lower the risk is with any reasonable bankroll. Combine that with up to five times the average win rate and a much more straightforward strategy, and you see why I recommend deuces wild for beginners in Las Vegas. On a quarter deuces wild we would need only $4,406 for that same 10% RoR, and that is even without a slot club rebate!

As you can see, the risk of ruin when playing video poker can now be determined precisely. You can do the calculation yourself, or Video Poker Times issue 7.5 presents a table giving the necessary bankroll for whatever you consider to be an acceptable risk of ruin for a dozen attractive games. (Note: There is a typographical error in the cash rebate for Sam’s Town in that table. It should say 0.093%. The RoR numbers for bonus deuces are correct for that rebate.)

There are always two roots of Sorokin’s equation; one, and the result we are seeking, which we are hoping is less than one. (If the root is greater than one then the game offers less than 100% total payback, and ruin is certain if you play long enough.)

equation 1:
equation 2:
equation 3:

Key: R(1) is the risk of ruin with a one-unit starting bankroll, n is the number of entries in the game’s payoff table, i identifies one entry in the payoff table, P is the probability of final hand type number i, W is the per-unit-bet win (payoff) for hand type i, C is the cash rebate from the slot club as a decimal fraction, B is the number of betting units in your starting bankroll, and R(B) is the risk of ruin with a starting bankroll of B bets. Note: One betting unit is typically five coins for video poker.

We know that a video poker player generally can hold the casino edge to less than one half of one percent, and in many cases we can even turn it into a player advantage with only a modicum of effort. But can we still get the comps and cash rebates even if we are playing with the advantage?

Note what I said above; the comp system is based not upon today’s actual losses (or winnings) but upon the casino’s perception of your expected losses. Since the vast majority of video poker players play at about two percent less than maximum payback, the casino generally sees video poker players as losers just like all other gamblers. (Otherwise, why would they have the machines in the first place?) Therefore, it is usually possible to collect comps and other benefits even if you are a winner.

Most casinos now reward slot and video players by means of a slot club. Membership is free, and when you join they issue you a card. Although the card appears very similar to a credit card, its use is quite different. Before you start to play, you insert the card into a reader on the machine. This identifies you so that the computer can track your play. In some casinos they only keep track of your action (total money wagered), but most also record your wins and losses.

The rewards may come in one or more forms, as follows:

• cash rebates: Usually figured as a fixed percentage of your action, typically ranging from 0.05% to 1%. Many casinos do not offer cash rebates.
• comps: Most often complimentary meals or accommodation. These may be in addition to or in lieu of cash rebates.
• intangibles: Actually another form of comp, but may include show tickets, use of the limo, etc.
• mailings: Joining the slot club puts you on their mailing list, and most casinos mail out monthly flyers. Often they include vouchers for discounts at restaurants, match plays, or even free money when you buy in. Often these vouchers are related to your level of action. They usually keep track of your action in the form of points. The most straightforward clubs award one point per dollar played. Others want to claim that their points are worth more. Of course they do this by requiring more action for each point earned, so the advertising can be very deceptive. The important thing for you is to figure out the actual total return as a percentage of your action.

Let’s look at a rather broad example. Suppose the casino gives one point per nine quarters played. Thus, each point requires $2.25 of action. When you have accumulated enough points you can get:

• $5.00 cash for each 1,000 points redeemed
• a buffet (regular $8.95 plus .65 tax) for each 1,250 points earned
• a show ticket (regular price $49.95 plus 3.62 tax) for each 5,000 points earned.

Note that you have to redeem points for the cash rebate, but in this club the other rewards are granted for points earned without having to cash your points in. To make the calculation easy, let’s assume you have earned 10,000 points. Doing this required 10,000 x $2.25 = $22,500.00 action. On a quarter video poker this would require $22,500.00/$1.25 = 18,000 plays, or about 30 hours of play for most players. For that 10,000 points, you can get 10,000/1,000 x $5.00 = $50.00 cash. Dividing by the $22,500 action indicates a 0.222% cash rebate.

That’s not bad by itself, but remember that you also get 10,000/1,250 x $9.60 = $76.80 worth of buffets, plus two show tickets worth $107.14, for a total return of $233.94 in values. Assuming that those comps have full value to you, that’s a total of 1.04% returned to you. Even if the best game available offers only a little over 99% payback, the potential total expected return is over 100%. The slot club has turned a negative situation into a positive one.

How can the casino return this much?
First of all, remember that most players are going to get less than 98% return from the game, so the casino still has its edge. But more importantly, note that the biggest part of the rewards are what are called soft comps. The buffet probably costs them quite a bit less than $8.95, and it keeps players coming back into the casino to eat those ‘free’ meals and play some more. The show tickets may be for nights that the show is never sold out, to their actual cost is negligible.

What does this return mean to you?
Suppose you’re playing full pay Jacks or Better at about 99.52% return. Adding the slot club benefits, you find that you have a positive expectation at over 100.5% total payback. Not a big profit situation, but what if the casino has a double points day? Doubling the slot club benefits boosts your total payback nearly 101.6%. Of course, that’s assuming you can use all those buffets and show tickets. Well, if you can’t use them all yourself, why not treat your friends or business associates to a meal or show?

The point is that the slot club rewards can make up a significant portion of your expectation. When choosing a casino, try to weigh all the factors. Advertising can alert you to promotions and changes in the slot clubs, but now you know how to evaluate them for yourself. Doing so is an important step in choosing a casino.

If you want a get rich quick scheme video poker is not your game. If you are looking for a way to overcome the house edge that is built in to nearly all casino games, again you will be disappointed. If you want to know how to find a hot machine, you will be depressed to know that there is no such thing. But if you want to learn how to achieve a small but real advantage on certain video poker games (and have fun doing it) then read on.

My publications show you how to keep the house edge to a minimum, and, in some casinos, to even gain a real mathematical advantage over the house. My strategies are computer-generated and proven by professional players, yet they are easy for a novice to begin using immediately. You can become a favourite to be a winner in the long run and have fun at the same time.

For more than two decades, casino visitors have been intrigued by video poker. They may have heard that the payback is higher than reel slots (which is generally true), perhaps they like the challenge of making decisions instead of just pulling a handle, or maybe it’s just to try something new. After a short try, however, many move back to the one armed bandits. Why do they give up so quickly? Is video poker too difficult? Are they losing even more than they did on the reel slots? Is it the five coin requirement to qualify for the royal flush jackpot? Or is it just that they have a very small budget for gambling and there are too few nickel video poker machines available?

This article delves into the whys and wherefores of video poker for the novice, especially one whose gambling has been limited mostly to nickel or quarter slots. By seeking out the good machines and following a few simple playing rules, you can cut the house edge to one half of one percent or less, and in some cases you can even gain an edge over the casino, even on some nickel machines.

Already I hear you say, “I don’t want to be bothered with rules. I’m on holiday, and just want to have some fun.” But isn’t it more fun if your limited bankroll lasts longer, and even more fun when you’re winning? The big advantage of video poker over the no brainer reel slots is that the maximum payback can be determined from the payoff schedule on the front of every machine. No, you don’t have to do any maths; just compare the payoff schedule with my tables. Most players’ intuitive decisions will yield about 1% to 5% less than a game’s maximum payback. Statistics from Nevada casinos show an average payback on video poker of about 2% less than what it would be if everyone played perfectly.

This is why the casinos are able to offer games with over 100% payback potential, thus making it possible for us to gain a small but real edge on some games. Most video poker experts assume computer-perfect play when rating a game’s payback. Such accurate play is impossible for most of us, yet you can easily get within a few hundredths of one percent of the rated payback with my simplified strategies. Even in a casino that doesn’t offer 100% plus games, video poker generally offers a higher return than any other low stakes game.

In this article, we look at how to pit your wits against the machine using purely brain power; once engaged, you have a 50-50 chance to overcome the house advantage.

It’s a common tip that to play a video poker game without the advantage is in the vicinity of insane. But what does that imply? That there are people out there taking advantage of some stupid mistakes by the casinos? Yeah right, and a blackjack pays 5 to 1.

In reality, (and possibly new to you since noone cuts through the bull) - nobody ever walks into a casino anywhere, sits down at full pay deuces wild, 10/7 DB poker, or 9/6 JB with creative comps, and plays with a mathematical advantage of any kind. Why? Simply because those advantages are theoretical over an infinite amount of time with absolutely unattainable computer-perfect play, and even the most addicted players pound away less than 8 hours a day, which is nothing more than a disconnected series of short-term attempts.

The casinos know this - why don’t they? The math never lies, but playing to the math is impossible. Where this all started that the casinos would actually allow people to play their machines, who so blatantly announced their superiority over certain games with any kind of credibility, I’ll never know. Name one casino in Nevada that worries about such stuff. They certainly allow them to play all right - to the tune of taking their money.

Now let’s use our heads some more. Who said the human mind is limited to never figuring out ways to overcome odds of any kind? Based on our history we already know this is untrue. When it comes to games of chance, the mathematicians always seem to have the last word. Not any more. Up until 4 years ago, while I played optimal strategy, I had less than a 15% rate of leaving casinos a winner. Since then I’ve had a greater than 98% success rate, and it is dead on target to the expectation that took me nearly 3 years to develop with the help of several consultants in many countries. It is loaded with special manoeuvers and inconsistencies, but is simple in its premise of setting pre-determined win and loss goals, and never deviating from them.

Progressive in nature - after losses and wins - it is far from the dangerous Martingale system, which plays a minor role in the overall methodology. Willpower, determination, bankroll, and the ability to always do what you say you are going to do - a feat almost impossible to perform while involved in casino action - are the ultimate keys. It is the true test of a gambler who has entered the arena for the purpose of gambling to win, and not simply to have his performance rated.

This is Part 2 of article about the load of crap (pun intended) some websites try to feed you to separate you from your money. Don’t fall for it. Be smart. Play smart. Let’s continue with more excerpts that are even more ridiculous than those in Part 1.

Excerpt: “Now for the first time, I’ll show you how you can turn $40 into $50,000 in as little as 87 days with a new system of playing and winning at craps! What the casinos hope you will never find out about playing this elusive game, now it’s possible to win 78% of the time. Using my system, you can win about three times out of four (up to 78% of the time, to be more specific). With my strategies, which are really a combination of the systems of the best pros that I’ve gambled with and learned from over the years, you can pick up everything you need to know to win at craps every time you play. You probably already know that craps is hands downs the best casino game based on the odds. What you may not know is that by using my ten-step system, you can actually turn the odds in your favor! That’s right, using my craps strategies, which I’ve detailed in a brand new report called [name redacted] you can actually beat the house!”

Analysis: This claim seems to me to be as ridiculous as those that promise you can learn dice control. If you learn nothing else from reading my website, my free sample chapter, and my articles, you must understand and accept one important fact: the game is designed for you to lose. It’s mathematically impossible for the player to gain an advantage over the house. Say it out loud, slowly, and let it sink into your brain—it’s mathematically impossible for the player to gain an edge over the house no matter what combination of bets or bet amounts are used. Therefore, the guy’s statement about his system, “—you can actually turn the odds in your favor,” is total crap. Period. If the guy’s system relies on dice control to gain the advantage, then run for the hills as quick as you can because you might get run over by another flood of bull manure. After reading my free sample chapter, you know what I think of dice control and dice setting. The phenomenon called “distribution variance” is what allows players to win in the short-term. Nothing else. No fancy system, no silly dice-setting technique, nothing. Got it? The house always wins in the long-term. No player can beat the house over time. You must understand and accept that fact. The truly knowledgeable player plays for the fun, excitement, and the occasional short-term win, not because of any silly belief that he can actually beat the house consistently over time. You must not yield to your strong desire to win an easy buck. Instead, you must be smart, you must play smart, and you must learn the secret to craps. In the excerpt above, the guy states, “—you can win about three times out of four (up to 78% of the time, to be more specific).” Then, he proudly states, “—everything you need to know to win at craps every time you play.” This guy can’t even keep his apparent lies straight! In one breath, he says you’ll win three out of four times, and then in his next breath he says you’ll win every time you play. So, which is it? Do you win only 78% of the time that you play or do you win every time you play (i.e., 100%)? LOL (laugh out loud). Remember, don’t be a sucker.

Excerpt: “[Name redacted], the author of [name redacted] system has developed a unique a way to win at the dice table. He is talking about walking away with a handsome win, not breaking the table. The [name redacted] system is a Place bet system designed for a conservative approach to the game of craps. It has an exact play for every roll of the dice. Each and every hit in the [name redacted] system pays you a profit. Each hit puts more money in your pocket. The game of craps was created to make money for the casino. The [name redacted] system makes money for the player. If you’re willing to put in a little bit of time to learn, and apply the rules in a responsible, controlled way you WILL make a profit! You cannot lose in [name redacted]. Order the [name redacted] beginner’s system for $120, delivered by e-mail, or $125 for a printout sent by first class mail.”

Analysis: First of all, if this guy gets $120 for his eBook, then I must be charging way too little for mine! LOL. This guy’s system can’t possibly be a consistent long-term winner because he states that it involves Place bets, all of which have built-in house advantages that you can’t overcome no matter what combinations or amounts of Place bets you make. Because it’s a mathematical fact that no combination of bets (including Place bets) can result in a player advantage, the obvious question you should ask is whether this guy is a total idiot or lying through his teeth to rip you off when he states, “You cannot lose—.” I still can’t get over the fact that he gets $120 for his eBook. I wonder how many he’s actually sold. You better hurry up and buy my eBook for a measly $9.95 before I jack up the price to a hundred bucks!

Before reading the next excerpt, ensure your Hip Waders are pulled up as high as they can go. Disclaimer: I cannot be held liable in any way if you drown in this guy’s bull manure. Continue reading at your own risk!

Excerpt: “Earn a living playing craps, can it be done? The answer is yes. To date, all of our students average $1,000 to $3,000 a day playing craps and I can show you how you can join the club. Average $100 to $325 per hour every day you play craps using our [name redacted] craps system/strategy. We guarantee it! Even if you have never played the game of craps before, you can learn our [name redacted] system quickly and easily. In fact, we provide the only effective craps system that is capable of winning long term and it is not complicated at all. Fact: Our craps system is so good, that you will make a bare minimum of $1000 the very first day you use it, or you are entitled to a 100% money back guarantee. Please note, we did not say ‘might be able to make $1000,’ we said ‘every single person who has used our system makes an average of $1000 or $3000 per day, every day that they choose to play.’ Our most advanced players average from $900 to $1500 per hour!”

Analysis: I think this guy’s load of crap is hysterical. Let’s see if I understand it correctly: it’s the only effective system capable of winning long-term, it’s not complicated, you can learn it quickly and easily, it’s guaranteed, the beginner can win up to $3,000 per day every day, and the advanced player can win up $1,500 per hour every day (which equates to $15,000 per 10-hour day). Woohoo! This is a get-rich-quick sucker’s dream come true. It’s easy to learn (no effort or energy needed) and as a beginner you can win up to $3,000 per day every day, which means you can make more than $1,000,000 per year with minimal effort, minimal skill, and minimal knowledge. Well, golly gee wilickers! We better run out and buy this system right now because every hour we wait, we lose $325. No analysis of this excerpt is needed. If it doesn’t seem absurd to you, then you deserve to lose your shirt.

Excerpt: “The preferred grip for you is the one that you feel the most comfortable with, has the least amount of friction and skin on the dice, and that produces the best results for you personally. You will need to practice as much as possible to produce the best results. Before you go to a casino for a session, practice on your practice box, or in the hotel drawer just for a warm up to see how your throw is today, before the session. This will save you a lot of units and help save your bankroll!”

Analysis: This excerpt addresses the wonderful world of dice-setting—a world, in my opinion, called Fantasyland. One short sentence should be enough for you to realize the bull manure this guy is feeding you. “Before you go to a casino for a session, practice on your practice box, or in the hotel drawer just for a warm up to see how your throw is today, before the session.” What? A hotel dresser drawer? Good grief. Even the dumbest moron should realize how stupid that is. A hotel dresser drawer doesn’t have the same bounce characteristics and friction coefficient as a craps table, and a dresser drawer doesn’t have the little pointy rubber pyramids (spikes) on the back wall that a craps table has. So, how could practicing in a three-foot-wide dresser drawer foretell anything about how your toss will be on a 12-foot craps table? In my opinion, this easily rates as one the dumbest statements I’ve ever read. When you read nonsense like that, it should raise a red flag for you to be cautious of the rest of the crap the guy is trying to sell you.

The following are several excerpts combined into one. I found them embedded throughout a well-liked and respected craps-related website. Personally, I don’t know why it’s so respected because, in my opinion, it has no legitimacy. It deals with dice setting. To understand my disdain for the idea of dice setting, please read the free sample chapter of my eBook that’s included on my website.

Excerpts from the dice-setting website: “Craps can be beaten—. There is only one way to beat craps in the long run and that is through precision shooting and dice control—. Craps can be beaten by changing the nature of the game from a mathematical and random contest, where the casino has built in the edge for itself, to a physical contest, where the person who shoots the dice can gain the edge by skill—. Dice control is a physical skill that can be learned by disciplined players who are willing to practice and perfect the techniques we teach them… Our teachers are the greatest dice control specialists in the world, many with books and major publications to their credit, all with years of winning casino experience behind them—. This craps strategy is called dice control, precision shooting, or rhythmic rolling—. There are no ‘board certified’ dice controllers yet. Everyone is self-certified; that is to say, you have to take them at their word—. The [name redacted] board of directors wanted [name redacted] to have the highest standards of excellence in the budding field of dice control. To do this, we set up tough criteria for our instructors and coaches to meet. They had to be skilled shooters and good teachers—. These criteria have been established to standardize and elevate the teaching of dice control by subjecting our teachers to a rigorous certification process that makes sure they understand, can demonstrate and can effectively teach all the essential areas of our curriculum.”

Analysis: For analysis of this claim, and all other claims about the merits of dice control, read the free sample chapter of my eBook on my website. In the sample chapter, I don’t go into detail about the certification of so-called dice-control specialists, so I’ll talk a bit about it here. I must admit, this guy’s website is well-written and I respect the writer, not because I agree with the message, but because I like the writing. The author did a particularly wonderful job dreaming up and explaining the certification process. The idea actually sounds legitimate. However, in my opinion, it’s simply a well-crafted and well-written part of an elaborate scheme to separate you from your money. The author goes into a lengthy excuse for the fact that the certification program for their dice-control instructors was developed, executed, and managed by the same people trying to sell you the product. The sophisticated excuse does a fantastic job of explaining why no independent authority exists that can administer the certification process. I suggest that you think twice about the validity of the explanation. Any certification process not developed, executed, and administered by an independent organization should immediately raise a red flag in your brain. If the certification authority is the same bunch who’s selling the product, it’s like sending the fox to guard the hen house. In my opinion, the reason an independent organization still doesn’t exist after so many years since the idea of dice setting was born is because dice setting can’t be proven to be legitimate over the long-term. (Read the free sample chapter to find out why I feel this way.) In the 30 or 40 years that so-called dice-control specialists have been around, surely some entrepreneur somewhere would have formed an independent organization to test and certify dice setters. However, according to the excerpt, no such independent organization exists. Makes you wonder doesn’t it?

As these excerpts show, the Internet (and many books, magazine articles, and other resources) is crammed full of ridiculous claims designed for one thing–to get your money. If you want to play craps, you must get over your blazing desire to make an easy buck. You must plant yourself in reality. You must learn to play smart. You must accept the fact that no craps system exists that allows you to gain an advantage over the casino. Don’t fall for bogus strategies and wacky dice-setting schemes that claim they can consistently win you tons of money. Be smart. Play smart. Learn the secret to craps. Armed with facts instead of false hope, you’ll be a strong weapon against the casino.

Now you know!

I got the idea for this article while writing about dice setting. (If you’ve read the free sample chapter from my eBook on my website, you’ll know what I think about dice setting.) I thought about the ridiculous things (and sometimes downright lies) people say to separate you from your money. I thought about the shysters who spread their misguided and oftentimes flat-out wrong advice for beating the house. Then, I thought about the unfortunate who fall for such bogus claims and advice.

This article gives a small sample of the load of crap (pun intended) from various craps-related websites, followed by brief analyses of the sheer stupidity or dubious nature of their claims. If it weren’t for the sad fact that people actually believe such crap, we’d find it entertaining. Learn from this article. Once and for all, get it through your head that craps is designed for you to lose. No system exists, has ever existed, or will ever exist that will produce long-term gains for the player. The player cannot in any way gain a long-term advantage over the house, and that includes the latest trends in get-rich schemes that focus on dice setting. Don’t be a sucker. Learn to play in reality, not in fantasyland.

I took the following excerpts directly from some of the websites I scanned for 10 minutes after searching for “learn craps.” These excerpts are not from blogs, forums, or discussion groups; they’re from sites that sell craps-related products. My analyses and criticisms are based on my opinion and deemed valid until proven otherwise by a qualified and independent body.

Excerpt: “In my humble opinion, the pass line (and come) are the worst bets on the table. I understand about the 1.4% advantage and all, but has anyone actually calculated odds against, after the come out? I found two books a long time ago that stated the average against you, on the pass line after a point is established, is around 34-35%. That is to say, the odds against ‘repeating’ the point before a 7.”

Analysis: This excerpt was taken from an article intended to provide tips and strategies or playing craps. In justifying his opinion that the Flat Pass Line and Flat Come bets are the worst bets on the table, the writer removes the come-out roll from the equation. That seems absurd. The house advantage on these two bets is so low because of the player’s 2:1 advantage on the come-out roll. Indeed, the advantage shifts back to the house after the come-out, but that advantage can never shift without first going through the come-out, so trying to disregard it seems ridiculous.

Excerpt: “The only good bet is the place bets—and only for the 2 reasons, one they can be taken down at any time, and second you pick your numbers. The odds are much much much better when you try to throw one number instead of repeating it before a seven, and that is what people don’t understand. What they also don’t understand is that the seven should mathematically come up one out of every six rolls—and that is all rolls, not just box number rolls, but all of them. If someone walked up to a table and threw 2, 3, 12, 11, 2, 3, 11, 12, 2, 3, 11, 2, 12, 12, 2, his odds of throwing a seven are greater then the guy who throws 5, 6, 8, 9. How many times do people at a crap table stand there and not even pay attention.”

Analysis: This excerpt is from the same article as the first excerpt. Remember, this author supposedly knows the game and is passing his wisdom to you. Where do I start? The author’s reasoning is based on the silly–and completely false–notion that outcomes of previous rolls influence future rolls. The author apparently believes in the Gambler’s Fallacy. By the believing in the Gambler’s Fallacy, the author proves his ignorance. No matter how many times a player rolls the dice, the odds of a 7 appearing on the next roll never change. So, the player throwing 14 rolls without hitting a 7 has the same odds of rolling a 7 on the next roll as the player who throws only four rolls without hitting a 7. The odds of a 7 appearing on the next roll for both players are exactly the same. Even if you rolled a million times without a 7 appearing, the odds of a 7 appearing on the next roll are exactly the same as if you had rolled only once. Results of previous rolls have no influence whatsoever on the odds of future rolls. The guy in the excerpt wonders, “How many times do people at a crap table stand there and not even pay attention?” I can’t help but laugh and wonder how many screws this guy has loose. The truly sad thing is that people read this guy’s baloney, take it to be true, and then base their bets on it.

Excerpt: “This is a proven professional method, used by experts, that until now has been kept secret from the public. When applied according to the rules presented, it is the most consistent money making craps method you are going to find and can reduce your risk of loss to less than 6%.”

Analysis: You can play the Pass Line with Odds (or Don’t Pass with Odds) and give the house an advantage of only about 1%. Lots of craps bets have house advantages much less than 6%, so touting a 6% risk of loss seems silly to me. I chuckled at the statement, “This is a proven professional method, used by experts, that until now has been kept secret from the public.” Yeah, okay, sure. LOL (laugh out loud). The following excerpt is taken from the same website.

Excerpt: “—As with any educational or entertainment program, results may vary and [name redacted] and its owners assume no liability for its use or any loss that may result. Purchasers of the [name redacted] are encouraged to rigorously test and personally verify results before wagering on an outcome. All gambling involves risk no matter how good the method might be. Purchasers are advised to use the [name redacted] responsibly, implement a sound money management system, and wager only with funds that will not seriously affect their lifestyle or that of others closely associated with them.”

Analysis: Again, I laughed. The website cleverly hooks you with claims of having a “professional” and “most consistent money-making” craps system. It fills you with hopes and dreams of beating the crap out of the casino. Then, after suckering you in, they cover their rear ends by including a disclaimer stating, “—its owners assume no liability for its use or any loss that may result.” I suspect that buyers of that bogus system never make it to the bottom of the web page to read the disclaimer. They’re so hyped up on false hope of beating the casino for ga-zillions, they’ve already clicked the “Buy” button before getting anywhere near the disclaimer. If the system is so “professional” and if it truly is the “most consistent money-making craps method,” why do they need to cover their rear ends with a disclaimer? Makes you wonder, doesn’t it? Don’t get conned into buying bogus winning systems. Learn to recognize bull manure. Don’t get suckered into believing you can consistently beat the casino over time. You can’t and won’t. Be smart. Play smart. Learn the secret to craps.

The next excerpt is lengthy, but I included it because I’m sure it’ll entertain you as much as it did me.

Excerpt: “Here is a simple craps strategy that takes no skill and only two of the same bets each time you play. The writer of this method has never failed to make at least $200 per hour using this strategy. Now, with this report, you can do the same at any dice table anywhere in the world! This craps strategy has been kept within the inner circle of casino bangers for years - under a mutual gentlemen’s agreement. We tried the [name redacted] on randomized computer print-outs and couldn’t come close to losing through 8000 decisions! (Think how long you would have to stand at the tables for 8000 decisions.) We tried it at several casinos in Atlantic City, Vegas, Reno, and Tahoe. The damned thing just would not lose! With this system you won’t care if the tables are hot or cold—you still win with this super craps strategy! A new shooter can throw three or four or more craps in a row and you win! A new shooter can throw three or four or more sevens in a row and you still win! A new shooter rolls a point, and sevens out on the next roll. Shooter after shooter can do this, and you still win! A shooter can throw 14 passes, or more or less, in a row, and you still win! A bunch of players in a row, can seven out after any amount of numbers, and you still win! Read this report and you’ll find out that there is absolutely no roll of the dice that can hurt you with this system! Want to collect on every roll of the dice? Here is how to do it with four easy bets. Follow this method exactly and you’ll go home a winner everyday!”

Analysis: Woohoo! Is this the Holy Grail, the Fountain of Youth, the mother of all systems that has eluded mankind forever? Woohoo! LOL. Yeah, right. Let me get this straight—no skill required—only need to make two bets at a time—and no matter what happens, I can win $200 per hour? Woohoo! I better hurry up and buy this system before the “casino bangers” put it back in their “inner circle” under lock and key and stop offering it to the paying public. Do I really need to analyze this mumbo-jumbo? Does anyone actually believe this crapola? Sadly, people apparently do, or the website probably wouldn’t exist.

Excerpt: “I’m so positive that I can easily convert you from an inexperienced player into a master player with the skills of a pro that you may try all of my methods risk-free! I personally guarantee these craps systems will work at any casino you play! Take up to a full year to learn, practice, and profit. Just remember, if your average daily winnings don’t add up to several hundred dollars, don’t forget that I will give you a 100% refund. It’s that simple.”

Analysis: This is from the same website as the previous excerpt and is typical of the guarantee that comes with many so-called winning craps systems. Read the words carefully. Let’s analyze them. “—you may try all of my methods risk-free.” It’s risk-free because the seller offers a full refund, not because the system consistently wins over time. “I personally guarantee these craps systems will work at any casino you play.” Of course, they’ll work, but will they win? Anyone can use any crazy system and it’ll “work.” The word “work” in this context simply means the system is a legitimate method for playing the game whether you win or lose with it. In the excerpt, if the word “work” were replaced with the word “win,” then the seller would be at great risk because no system will consistently win over time. “—don’t forget that I will give you a 100% refund.” Remember, the guarantee is that you can get your money back, not that the system will consistently win. The problem with these kinds of guarantees is that many people either simply forget or don’t try to get the refund after losing their shirts, or they try but get delayed so long they get disgusted and give up. The moral is, be skeptical of craps systems that come with guarantees. Ensure you fully understand the guarantee before buying. Focus on whether the craps system is guaranteed to win, or whether you’re guaranteed to get to your money back after you lose your rear end. Note the carefully chosen words and understand their meanings, such as “can” instead of “will.” One small word can, and usually will, make a big difference in the meaning of a sentence or an entire paragraph.

Starting to get the picture? Scams are everywhere. Don’t be a sucker. Don’t let your dreams of winning big blind you. Be smart. Play smart. Learn the secret to craps. Read Part 2 of this article for even sillier claims and bigger laughs.

Now you know!

If the casino has such an advantage over the player, why on Earth does anyone play the game? My guess is that most people don’t have a clue they’re playing a losing game. Others are so arrogant they think they can outplay the casino and turn a negative expectation into a positive, even over the long term. Others know they’ll lose, but play anyway for fun and excitement. As a knowledgeable player, why should you even bother playing a game you know will beat you? As a knowledgeable player, is there any hope you can walk away a winner, at least once in a while, even though you’re at a statistical disadvantage?

Craps is a game of numbers and statistics, with the house having a built-in advantage. Since craps is based on statistics, let’s find a way to use statistics to our advantage. You’ll never beat the casino over the long haul, but you can, indeed, beat it in the moments of time when the distribution hiccups and things go your way.

Let’s talk about “variance,” which is the average squared deviation of each number from the mean of a data set. Huh? Don’t worry; we don’t need a Harvard math degree to understand this. It’s simply a measure of how spread out the data is. Let’s consider the familiar coin-flip example.

Suppose we flip a coin 10,000 times. We expect heads to appear about 5,000 times and tails to appear about 5,000 times. Suppose we bet $1 on heads for each flip. If these are even-money bets, we expect to break even–or close to it after those 10,000 flips. As illustrated in one of my other articles, the house doesn’t give us even money when it loses. In our coin-flip example, instead of paying us $1 for each loss, suppose they pay us only $0.96. With this built-in house advantage, our negative expectation is to lose about $200 after 10,000 flips. Here’s the math. If we expect about 5,000 heads and about 5,000 tails to appear, then we expect to lose 5000 x $1 = $5000; and win 5000 x $0.96 = $4800. $5000 - $4800 = $200. This is called “negative expectation.”

Now, of those 10,000 flips, suppose we focus on only 30 of them, and we continue betting on heads. Of those 30 flips, we might see heads 25 times and tails only 5 times. This data fluctuation shows that, for a limited number of flips over a short period of time, we can get lucky and experience Nirvana where things go our way. I call it a “Nirvana hiccup” in the distribution that causes a relatively high variance. In this example of only 30 flips, we win $24 for the 25 heads (i.e., 25 x $0.96 = $24), and lose $5 for the 5 tails (i.e., 5 x $1 = $5), which gives us a net win of $19. This short term variance temporarily removes the long-term negative expectation, which means there are, indeed, times when we can walk away a winner.

Although you’ll lose in the long-term, there are times when you’ll win because of variance. Suppose you take a three day vacation in Vegas once a year and play four one hour craps sessions each day (i.e., a total of 12 hours for the trip). You could conceivably get extremely lucky and hit that Nirvana hiccup during each session, and then go home a big winner. In that case, you go home thinking you’re a genius, a craps god, invincible, a world-class gambling stud. Yeah, sure, okay. I don’t recommend quitting your day job.

Now, suppose you’re a Vegas local who plays an hour every day after work. In this case, it’s clear that whatever few Nirvana hiccups you experience will be properly adjusted over time such that you’ll lose your shirt in the long-term.

Therefore, the infrequent craps player can, indeed, consistently win if she’s lucky enough to hit those Nirvana hiccups. However, the frequent long term player has no chance of coming out a winner at the end of his craps life. Part of the secret to craps is knowing how to be around for those occasional Nirvana hiccups where the dice fall your way.

If you don’t want to lose your shirt, you must learn the secret to craps. Don’t fall for bogus winning systems or ridiculous dice-setting claims. Distribution variance is the only thing that makes you a short-term winner. Nothing else. No silly dice setting technique. No bogus winning system. It’s the distribution variance and nothing else. Got it? Be smart. Play smart. Learn the secret to craps.

Now you know!