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# Gambling Myths and Fallacies

Keep on doubling!

This is such a popular fallacy that it deserves a reasonable amount of space. It even has a name, the Martingale System.

In this seductive system, commonly used on roughly even money chances in games such as roulette, you keep raising your stake with each consecutive losing bet to somewhat more than double the previous bet, so that when you eventually win you cover all the losing bets and make a small profit.

The fallacy with this system is rather obvious, a resource barrier will be hit at some point. Either the casino has an upper limit on the betting which you can't exceed, or else you reach into your pocket only to find the scribbled telephone number of Gamblers Anonymous, rather than the \$16,000 worth of chips you expected to find there.

The system ultimately works only if you had an infinite bank and the casino had an infinite limit. In all other cases (i.e. in real life) you will win a small amount frequently and lose a lot of money occasionally. Your percentage return remains the same.

If you increase the frequency or amount which you win using the Martingale System at a given game, you increase proportionally the amount you lose when the system fails. There is no staking system that can change the fundamental percentage returns on a casino game of chance.

This is a point worth emphasising, as the foolproof mathematical 'system' is one of the most enduring myths believed by foolish punters. So let us stress again, no matter what the system, changing bet amounts according to some special mathematical formula cannot increase or decrease your returns. All it can do is change the variance of the outcome, the 'volatility' if you like, so that you may be more likely to win than otherwise, but lose more money when the system fails, and vice versa.

It goes without saying that being more likely to win doesn't mean that you'll win more overall. This is shown mathematically by a comparison of winning versus losing returns over a large number of bets. When a system has you winning 10% of your bank 90% of the time (which sounds attractive) then you will lose your entire bank 10% of the time (which isn't so good!)

Note that there are staking strategies in some games requiring skill such as blackjack that do affect your percentage returns, but these are dictated by 'inside information' gained from techniques such as card counting. The game is not genuinely random as in the spin of a roulette wheel or toss of a two-up coin. A card counter at blackjack knows whether the spread of cards left in the deck are statistically favourable to the player or the house, so their staking method is based on knowledge, not some magical mathematical formula.

If only it weren't for that player on the end!

This one is mainly observed in casino blackjack, but can occur in any game where turns are taken and someone's actions appear to have an effect on your result.

In blackjack, the last person on the table, sometimes referred to as the 'anchor man', makes choices about whether to stand or take cards that have an immediate impact on which cards the dealer gets. If the dealer ends up with a winning hand, some players are given to thinking, 'That player caused me to lose. If they'd made the decision you're supposed to make there, then the dealer would've busted and I would have won'. This is a stupid but disturbingly prevalent philosophy. Except for rare cases where the player has special information about the deck through card counting, the likelihood of the remaining cards in the deck being beneficial to the dealer is completely independent of what the last player does. Sometimes it will be good, other times bad.

To clarify this point, the 'anchor man' will play some hands badly and cause the dealer to win, some hands badly and cause the dealer to lose, some hands well and cause the dealer to win, and some hands well and cause the dealer to lose. Ultimately both the dealer's and players' fortunes are affected equally by the anchorman's decisions, whether they be perfect basic strategy or suicidally stupid. It's just easier to remember decisions that cost us money! Click for debate on this point.

As a general principle, retrospective analyses of chance events are a waste of perfectly good angst that could be spent on worrying about whether Santa Claus really exists.