Years ago, a mathematician determined that it was possible to figure out the likelihood of a gambler either doubling his bankroll or going broke trying to do so. The formula is just a simple algebraic equation that takes into account the size of the gambler's bankroll in units, the size of his bets, and the advantage or disadvantage in the specific game being played. This concept has traditionally been called the Gambler's Ruin Formula.
Professional card counters more commonly call a variation of this formula specifically devised for blackjack games the "risk of ruin" (or RoR); it was discussed by Ed Thorp in Beat the Dealer, Allan Wilson wrote about it in his 1965 Casino Gambler's Guide, and it was further described by Ken Uston in Million Dollar Blackjack. Since then, the concept of risk has been analyzed to the nth degree by many of the major authors.
Personally, I'm not crazy about the idea of individual players determining their bet sizes solely based on Risk of Ruin. Uston discussed how some of the teams he was involved in based their bets on a 5% element of ruin. This sounds pretty good to most players; if you double your bank 95% of the time (19 out of 20 banks double) that's a huge win-expectation in the long run.
But Uston was involved in big teams of players, with multiple investors, and if the team went broke on a play, the investors could simply put together another bank and do it again. That's not an option easily available to a solo player. If you have a bank of $10,000, and you lose the whole bank on your first play, can you simply put together another $10,000 and do it again? You might argue that it's unlikely that you'll lose your bank on your first attempt to double it, but consider it from my perspective as an author whose advice is being followed by thousands of individual players: For every ten thousand players who go out and plays to a 5% RoR, 500 of them will go broke! How many of these players can quickly put together another bank? How many have lost their life savings? How many will write nasty letters to me blaming me for their new poverty?
Basing your bet sizes on a 5% (or any!) risk of ruin should be left to those who can afford to put together another bank easily if the first one fails. This is for big teams supported by investors, and solo players who have the capability of forming another playing bank through easily accessible outside sources of funding. A better method for bet-sizing for most players is…
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