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The Unofficial Guide to Casino Gambling
by Basil Nestor
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Basil Nestor incorporates decades of gambling knowledge to give the reader insight into probability, common gambling mistakes, and winning strategies in his popular book, The Unofficial Guide to Casino Gambling.  Covering all the bases of casino gambling including machine games (slots and video poker), table games (blackjack, roulette, craps, baccarat, poker), and waiting games (keno and sports betting) the book also has sections on how to get casino comps, gambling systems, a history of gambling in the US, and much more.
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BJ MathBJ Math is a site dedicated to the exploration of mathematics in conjunction with blackjack. The editors have done a great job collecting all of the important articles relating to blackjack probability and card counting strategies. The site also provides a 'Novice Corner' for those new to the concepts of blackjack mathematics. There is a forum for deeper discussions.

Deconstructing the 'Gambler's Fallacy'

Let’s return to our humble quarter and flip it some more. Forget the payouts. Now we’re just interested in heads or tails. The coin is “designed” to deliver heads in about halfBasil NestorBasil Nestor is the author of the new Playboy Complete Guide to Casino Gambling. This wonderful book teaches players how to avoid sucker bets and win more when playing gambling games.  He is also the author of The Smarter Bet Guide series for video poker, slots, craps, and many other books about gambling.  Basil's website is  of the contests. Right? Okay, let’s flip. It’s tails. Will the coin now “force” heads on the next flip to even the score? No, the probability of seeing heads is still only 50 percent.

What if George hits a bad streak and loses five consecutive times. What’s the probability that the streak will extend to six? Should you bet for or against our former commander-in-chief?

Some folks would say that George is “due.” Is that right? Others would say that the eagle (or state symbol) is “on a rush,” and betting the trend is the way to go. Which choice is correct?

They’re both wrong. It’s still a coin toss. The odds are exactly the same for every flip, always 50-50. History doesn’t matter.

There are situations when history will affect the future, but in most casino games this is not the case. Here’s why:

Deal yourself one card from a deck of cards. You have a 1 in 52 chance of receiving any particular card. Let’s say you draw the jack of diamonds. The chance of someone else drawing the jack of diamonds has dropped to zero. In addition, the chance of drawing another diamond has dropped to 12 in 51. In this situation the first decision (history) will affect subsequent decisions (the future).

There’s no mathematic law that says both sides in a gambling game must eventually be exactly even at some particular point. On a 50/50 proposition, one side could get lucky and stay ahead practically forever.

Now put the card back and shuffle the deck. The chance of drawing the jack of diamonds is back to 1 in 52. The deck doesn’t remember your previous draw.

Spin a roulette ball. Let’s say red wins seven consecutive times. Is red now less likely to hit? No. The wheel has no memory. Dice are the same. Gambling devices are not sentient. They do not say to themselves, “Hey, it’s time to average things out and end the trend.” And they cannot think, “Whoa, let’s keep this streak alive.” They are inanimate and do not respond to history.

So your next spin of the reels is no more or less likely to win than the last spin. Your next hand of video poker is no more or less likely to be a royal flush than the last hand.

Misunderstanding this one truth has cost gamblers more money than all the unfavorable games and poor odds in the entire history of gambling. The error is known as gambler’s fallacy. Gambling systems based on this fallacy are doomed to fail. Why? Because they don’t accurately predict the probability of a win. Bets are increased or decreased for no valid reason.

Just remember that a pattern of wins or losses generally tells you nothing about what will happen on the next decision. The only thing that matters are the actual odds. Nobody is ever “due” for a win or a loss.

But if nobody is ever “due,” how can probability work?

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