# Don’t Let the Gambler’s Fallacy Hook You

Don’t ever let yourself get sucked in by idea behind the “gambler’s fallacy,” whether it’s online craps, roulette, or any casino game of chance.  If you do, you’ll fall right into the casino’s trap.  People who don’t understand statistics generally don’t understand the concept.  If that’s you, then you must accept the facts as presented in this article, even if the only math class you ever took was second-grade addition and subtraction.  This article doesn’t try to earn you a PhD in statistics, so don’t think you won’t understand it because you were terrible at math.  We explain the concept using real-life situations so it’s easy to understand.  If you want to be a consistent winner in the casino, whether live or online, you must never let yourself be influenced by this phenomenon.

The idea behind the “gambler’s fallacy” is that you mistakenly believe recent outcomes in a game with fixed odds can influence future outcomes.  In other words, you believe a certain outcome is “due” to hit.  You see it all the time in a casino.  A husband says to his wife, “Honey, let’s hurry to the roulette table and bet a high number because only low numbers have come up the last ten times.”  At the craps table, the guy next to you takes down his Pass Line Odds bet because a 7 hasn’t shown in 20 rolls and he believes it’s “due.”  In both cases, their actions are just plain bad.

Let’s look at this concept in its simplest form by flipping a coin.  Assume the coin and the flip are fair (i.e., the coin isn’t weighted so it lands on one side more than the other, and the flip isn’t manipulated in some way to make one side show more than the other).  When flipping a coin, there are two possible outcomes, either heads or tails.  That means, for each flip, there’s a 50% chance that heads will show and a 50% chance that tails will show.  The 50/50 odds are “fixed,” they won’t ever change, assuming the coin and flip remain fair.  Now, suppose you flip the coin and there’s a short-term distribution variance that favors heads.  (Read our article on how to calculate the house advantage to learn and understand distribution variance at casinos.)  Suppose heads shows 10 times in a row.  Since heads has shown 10 times in a row, then surely tails is “due,” right?  Wrong!  If you believe tails is due, then you’ve fallen for the gambler’s fallacy.

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In this example, if you believe tails is due, then what you actually believe is that the odds of tails appearing on the next roll has increased to better than 50/50.  For example, if tails is due because it hasn’t shown in 10 flips, then you think maybe the odds of it showing are 10 times greater than 50/50.  That’s just not true.  For the next flip, there are still only two possible outcomes, heads or tails.  The odds are still 50/50 on the next flip.  Nothing about any of the previous 10 flips has any influence on the next flip.  Therefore, even after 10 flips that all showed heads, the chance of a tails showing on the next flip is still 50/50.

Indeed, there are things in life where past occurrences do influence the outcome of future outcomes.  For example, suppose you play a game of guessing which color marble will be randomly pulled from a bag of 100 marbles.  Suppose at the start of the game, 50 marbles are red and 50 are blue.  Suppose each time you pull a marble from the bag, you set it aside (i.e., you do not put it back into the bag).  For your first try, the odds of pulling a red or blue marble are 50/50 because there are an equal number of red and blue marbles in the bag.  Now, suppose you pull out a red marble on your first try and set it aside.  Because you didn’t put the marble back into the bag, the odds of pulling a blue marble on your next try have increased because now there are more blue marbles in the bag (i.e., 50) than there are red ones (i.e., 49).  So, in this example, previous occurrences do, indeed, influence the outcome of future events.

This just isn’t true in casino games such as craps and roulette.  For example, when the shooter rolls a 5 on her first roll, the casino doesn’t change the dice so that rolling a 5 is impossible on the next roll.  Instead, the dice remain exactly the same for all rolls.  Therefore, the odds of making any of the numbers 2 through 12 are exactly the same on the next roll as they were for all previous rolls.  Remember, we call this “fixed odds” where the odds don’t change from one event to the next.

In other words, the dice don’t have a memory.  The dice don’t think, “Well, I showed a 5 on the last roll, so the next roll I ought to influence myself so I don’t land on 5 again.”  Instead, the odds of any number showing remain constant on each and every roll.

Let’s look at another popular casino game that blatantly uses the gambler’s fallacy to hook its customers.  People walk by the roulette tables every minute of every day and never realize the casino is trying to take advantage of them.  Each roulette table has a “tote board” sticking up into the air that shows the outcomes of the most recent spins.  The next time you’re in the casino, notice that not only do these tote boards show the numbers that were rolled, but they also show the color (i.e., red or black).  Do you know why they show the color?  It’s to hook you into making a bet that you normally wouldn’t make by taking advantage of your belief in the gambler’s fallacy.  The key to remember is that the gambler’s fallacy hooks you into making a bet that you would not normally make otherwise.

Suppose you and your wife stroll through the casino, enjoying the sights and sounds, on your way to the lounge for a cocktail.  In the distance, you see the roulette tables and you notice that one of the tote boards shows nothing but red numbers.  Your initial reaction is that it seems odd that only red numbers have shown.  Then your brain loses control and you start thinking maybe a black number is surely due to hit.  Your excitement builds.  You think, “Black has got to show, it can’t possibly be red again.”  Your pace quickens.  You begin dragging your wife hurrying to get to the table before the dealer gives the sign for no more bets.  Your wife says, “Honey, what are you doing, slow down!”  You respond, “Hurry up, I want to put twenty dollars on black at that table over there.”

In this case, the tote board accomplished its goal exactly as planned.  It hooked the husband into making a bet that he wouldn’t have made otherwise.  He was having a leisurely walk with his wife with no intention of making any bets on the way to the lounge.  But when he saw nothing but red numbers had shown the last 15 rolls, he was sure black was due to show on the next roll.  This “sure thing” influenced him to make a bet that he normally wouldn’t have made.

As with craps dice, the roulette ball doesn’t have a memory.  It doesn’t remember what color it landed on the last few rolls.  It doesn’t think, “Well, I landed on red the last fifteen times, so I ought to change it up and land on black this time.”  In roulette, as in craps, the odds are fixed.  There are always 36 numbers (excluding 0 and 00) with 18 red numbers and 18 black numbers.  They never change; therefore, the odds of hitting red or black never change, regardless of what happened on past rolls.  Even if red showed 20 times in a row, the chance of black showing on the next roll is exactly the same as it always is.

Let’s go back to the example of the husband and wife in the casino on their way to the lounge.  Suppose they step out of the elevator and the husband says, “I’ve never played roulette and I want to try it.  I have five dollars leftover from the Blackjack table, so is it okay if we make a quick stop to make a bet?”  She responds, “Yes, dear.”  As they approach the table, the tote board catches his attention and he sees nothing but red numbers.  He says, “Look, honey, black is due, I’m gonna bet black.”

In this example, the tote board’s influence on the husband is harmless because he had already intended to make a bet and the odds of betting red or black are the same.  No matter what bet he makes, the house advantage is about 5%.  Although the tote board influenced him to bet on black, it did not influence him to make a bet that he normally wouldn’t have made.

So, how does the gambler’s fallacy hurt us as craps players?  Remember, the key is that the concept influences us to make bets that we normally would not make.  After learning all the lessons in our articles, you have developed into a solid player, a rock.  You make only smart bets with low house advantages.  No matter how much the drunks at the table try to talk you into making proposition bets, you maintain discipline and stick to your plan.  So far during your Vegas vacation, your plan has made you a consistent winner; therefore, there’s no way you’re going to deviate from your plan.  Now, suppose your plan does not include betting the number 4 (for some reason you hate the number 4, and your plan does not call for betting it under any circumstances).  Suppose you’ve been at the table for 30 minutes and the 4 seems to show every five or six rolls.  Suppose five rolls have gone by since the last time 4 showed.  You think, “Based on what I’ve seen the last half hour, the four is due.  Should I bet it?  I hate the four, but it’s due.  Yes, do it, put \$25 on the four.”

Loser!  Sure enough, the 7 shows on the very next roll and you lose the \$25 bet on the 4.  In this case, your emotions took over your brain and you lost your discipline.  You gave in to the gambler’s fallacy and you paid the price.  Thinking that an outcome is due based on past outcomes compelled you to make a bet that you normally wouldn’t have made, which resulted in you adding to the casino’s profits.

Don’t fall for the gambler’s fallacy, see some scenarios explaining gambler’s fallacy.  Don’t let it influence your bets.  Always remember, in casino games of chance, the odds are fixed.  The odds of rolling any number are exactly the same on each roll no matter what happened in the past.  Stay strong, stay solid, and maintain your discipline.

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Written by John Nelsen in partnership with the team of craps pros at Crapspit.org