## Double or Nothing

A friend told me that when he first came to Australia in the 70s he had \$3000. He had an opportunity to buy a business but its price was \$6000. He needed to double his money. How could he do it? There was no time in which to get a job and save the additional \$3000. He needed it now. The only way he could see to get it was to gamble. The casino was the obvious place to try to double his money.

He chose to play roulette, betting on one of the even chances, red or black, odd or even, high or low; he chose red. He had the 18 red numbers against the casino's 18 black numbers. But the casino also had the zero. So, although he only had 18 numbers going for him against the casino's 19, the difference seemed small and his prospects appeared not too bad. All he needed was a little luck. And that is how it worked out for a while. In the first hour he had more wins than the casino and his bankroll grew to be more than \$4000. But then the casino had a run of luck and the casino's 19:18 mathematical advantage began to take its toll and he lost his winnings and began to lose his capital. Over the next few hours, despite occasional partial recoveries, he lost his entire \$3000.

I asked him how much he wagered each time. In the beginning he staked \$300 which he increased to \$400 when his bankroll reached \$4000. When he started to lose, he reduced his bet size but when his bankroll got down to \$1000 be attempted a desperate recovery by wagering \$300, \$300 and a final fling of \$400.

I made no comment about his betting system but noted that it was typical of casino gamblers. Many a gambler with \$100 in his pocket will wager \$10 on roulette, so my friend's 10% bet was nothing unusual. Casinos are particularly fond of such gamblers or even those who stake much smaller bets. Obviously, small bets take longer for a player's bankroll to be lost but the casino's mathematical edge eventually grinds it down. The casinos even refer to these small-stake gamblers as "the grinds".

I could have suggested an alternative betting plan to my friend but, as the clock could not be turned back, I chose to say nothing. If you had been faced with my friend's problem what would you have done?

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Because roulette odds favour the casino, and the person is trying to achieve a \$6000 target, then the best bet is a single wager of \$3000. For ordinary roulette players, the bet size they ought wager is not apparent. A typical wager, as stated above, is some small part, or unit, of the money in their pocket.

Repeat visits to the casino follow this same pattern, resulting in occasional winning sessions, but losing in the long run. The great Edward O Thorp put it this way, "If the player continues to bet it is almost certain that he will be a loser and stay a loser forever, and so never again break even and will eventually lose his entire bankroll, no matter how large it was."

No one ought to play roulette, or any gambling game, but if one insists on playing then he, and all such players, ought play as the player with \$3000 has been advised, namely, wager on one and only one game ever! Each player's bet size ought be the total amount he is prepared to risk and potentially lose in his entire life, and to bet that amount in a single game.

19 players in 37 will lose that game but had they bet their bankroll in any series of smaller bets they would ultimately have lost it anyway. The other 18 in 37 who also would have lost their bankroll in small bets, in fact, actually double their money.

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