How to Win at Craps: The Gambler's Fallacy
The "gambler's fallacy" is the false belief that fixed odds increase or decrease depending on past occurrences. Let's use the
familiar coin-flip example to illustrate this concept. Assuming we use a fair coin and a fair flip, we expect a 50% chance that
tails will appear and a 50% chance that heads will appear. Those odds are fixed and will never change. Suppose heads
appears five times in a row. If you think tails has a better chance of appearing on the next flip because it hasn't shown for
the last five flips (i.e., you think tails is "due"), then you've fallen for the gambler's fallacy. The first step to becoming a
successful craps player is to understand that results of previous flips have no influence on the outcome of future flips. As a
craps player, you must understand that the results of past rolls have no affect on the outcome of future rolls. None! Got it?

When you play craps, the dice have no memory. The dice don't remember how they landed on the last roll. They don't care
if they haven't shown a 7 in the last 50 rolls or a ga-zillion rolls. The odds of any number showing remain constant and are
never influenced by what occurred previously.

Have you seen the big tote board by a roulette wheel showing the results of the last 10 or 15 rolls? It not only shows the
recent numbers that hit, but also the colors (i.e., red or black). Almost every roulette wheel in every casino on the planet
has a tote board. What purpose does that thing serve for either you or the casino?

It doesn't serve you any purpose at all except to sucker you into making a bet that you wouldn't otherwise make. It serves
the casino's ultimate purpose of taking advantage of the gambler's fallacy and getting more bets in play. The casino wants
as many bets in play as possible because the more bets in play, the more money the casino makes. The casino has one key
goal, which is to get you to make as many bets as possible. The casino knows its profits will go up as your number of bets
goes up. The sole purpose of the tote board is to get you to make a bet that you normally wouldn't make.

Let's look at an example. Suppose a husband and wife stroll through the casino on their way to dinner with no intention of
stopping to gamble or play casino craps. They approach the roulette area and see on a particular wheel's tote board that
the color red appeared on the last six rolls. The husband points to the wheel and says, "Look, dear, black is due. Let's try
it!" The tote board just did its job. It suckered the husband into making a bet that he wouldn't have made had he not
known that red appeared six times in a row. Yeah, sure, black is "due" all right. Wrong! The little ball doesn't know it
landed on red the last six times. It only knows that both red and black have an equal chance of appearing on the next roll.
The little ball doesn't influence itself to land on any particular number or color because of past occurrences. It doesn't have
a brain to think, "Gee, I landed on red the last six times so I better land on black this time."

Suppose your craps system tells you to Lay the 4 for $50 only after the number 4 hits three times in a row. Your system is
based on the belief, if the number 4 shows three times in a row, then chances are that a 7 will appear before another 4. Is
this a good, smart bet? Is this simple craps strategy good or bad?

Yes, it's definitely a good bet, and this strategy is an acceptable way to play if you don't mind getting bored to death. You
think about what I just said about the gambler's fallacy and then ask, "Huh? You're either nuts or full of crap because you
just finished saying the dice have no memory, and future outcomes aren't influenced by previous ones. Therefore, how can
that be a good, smart bet?" Calm down, let me explain.

In this example, you make a bet only after the number 4 has appeared three times in a row. You're a knowledgeable player,
a solid and disciplined rock, one who sticks to your strategy and doesn't allow emotion to cause you to deviate. Making a
Lay 4 bet under those specific conditions doesn't make your odds of winning or losing any different than making a Lay 4 bet
at any other random time. Regardless of when or under what circumstances you make the bet, the odds don't change. The
Lay 4 bet with a vig after a win always has a 1.64% casino advantage. It doesn't matter whether you make the bet only
after the number 4 has appeared three times in a row, or only when the shooter takes a swig of beer, or only when there's
a full moon. The odds never change.

However, although the Lay 4 bet with a vig after a win is considered a good bet because of its low casino advantage, it's
possible to regard it as bad under certain circumstances. Let's look at another example.

Suppose your craps strategy doesn't include the Lay 4 bet. Under no circumstances does it tell you to make a Lay 4 bet.
Suppose the number 4 appears eight times in a row. The hot babe next to you falling out of her halter top says, "There's no
way a four will hit again. We should bet against it. What do you think?" You respond, "No thanks, I'll stick to my strategy."
She wiggles a bit and says, "Oh, come on, I don't want to be the only one hoping for a seven." Her jiggling causes you to
lose focus, so you say, "Maybe you're right. Another four can't possibly hit again. Let's go for it!"

This is a situation where a good bet can be a bad thing. The key is that you allowed yourself to risk more money than you
had originally planned because of the gambler's fallacy (and partly because you couldn't say no to the bimbo next to you).
Remember, the more bets you make, the more the casino wins. So, adding more bets to your plan--even though they may
be considered good because of their low house advantages--can be hazardous to your bankroll.

Let's revisit the example of the couple strolling through the casino. Suppose the couple were in their hotel room before
going down to dinner. As the guy brushes his hair, he says to his wife, "Is it okay if we stop at the roulette wheel so I can
make a quick five-dollar bet?" His wife responds, "Sure, but we have reservations and we can't be late." They stroll through
the casino and approach the roulette wheel. The husband sees that red has appeared six times in a row and, as a result,
decides to bet $5 on black (he thinks black is "due").

Under these circumstances, using the tote board to influence his bet is harmless. Regardless of what bet he makes (black,
red, even, odd, etc.), the casino still has about a 5% advantage. The husband came to the table intending to make a $5
bet, so the results displayed on the tote board weren't the trigger that influenced his decision to make the bet. In this
example, although the husband's belief in the gambler's fallacy influenced him to bet on black, the gambler's fallacy didn't
trigger him into making the bet (he had already intended to make the bet before leaving his hotel room). The gambler's
fallacy does its job only when it influences you to make a bet that you normally wouldn't make.

The moral is, don't let the gambler's fallacy cause you to make craps bets that you normally wouldn't. If you still believe that
previous results influence future results and--here's the important part--if this belief causes you to risk more money than you
intended, then you're playing a dangerous game. Play smart. Be a rock. Don't fall for the gambler's fallacy. Don't let it
cause you to put more money at risk than you had planned or that you can afford to lose. Don't fall for bogus winning
systems or ridiculous dice control claims. Be smart. Play smart.