Backgammon Money Management: The Kelly Criterion


by Robert Wachtel

Gamblers possess a special kind of courage. While the ordinary citizen believes that “Fools rush in where angels fear to tread,” the gambler follows a different axiom. “Fools rush in,” he says, “… and get the best seats.” His boldness serves him well: it terrifies his opponents in backgammon and poker – and in betting on the stock market, sporting events or other propositions, it gives him the confidence to act decisively while others dawdle or dither. A gambler, we Americans like to say, is someone who is not afraid to “put his money where his mouth is.”

But there is a downside to bravery. As the Greek philosopher Aristotle observed, too much of it turns the virtue into a vice: one that he called recklessness. This was a truly important lesson to impart to the youths of Aristotle’s day, for the game that society expected them to play was a very high-stakes one: war. Cowardice in that game was punished by shame and humiliation; but the consequence of recklessness was often death itself.

Death in the gambling world, of course, is the dreaded state of “going broke.” Without a stake the gambler cannot play; but if he does not take advantage of the gifts offered to him by the Goddess of Luck, what is the point of the game? How can he keep sight of Aristotle’s golden mean, capitalizing on his opportunities while avoiding ruin?

There is an answer to this problem. It was discovered by an American mathematician, John Kelly, in 1956. Kelly proved that, over time, a gambler will maximize his net worth if he consistently matches the size of his bets to his advantage, or edge. For example: with a $100 bankroll, he must bet $2 if he has a 2% edge on a bet, and $20 if he has a 20% edge. You can think of the gambler’s edge as his winning percentage minus his losing percentage. So if I am betting on a race between two turtles, and turtle A is a 60-40 favorite over turtle B, my edge is 20%, and I should plunk down 20% of my bankroll on the race. With a 100% edge the “Kelly criterion” directs you to bet all of your money. With a 0% edge (or a disadvantage) it directs you to bet nothing.

So far, so good. Unfortunately the Kelly criterion can still lead a gambler to ruin. For example, if you are given the opportunity to make two bets with a 50% edge (75-25), Kelly will tell you to bet 50% of your bankroll on each, or 100% total on the two. One time in 16, both bets will lose, and you will go broke. For this reason, the more conservative school of Kelly disciples use a “half-Kelly” rule, with which one bets half as much, makes half the profit, and goes broke half as often.

Anyone even slightly familiar with the gambling world will acknowledge the absolute importance of following a sound “money-management” strategy like Kelly’s. The number of true geniuses who have arrived on the backgammon and poker scenes with a brilliant flash and succumbed soon afterwards to chronic over betting is a very long one. But of course no money management scheme can help a player who does not consistently put himself in advantageous situations. In a later article I will explain the principles of game selection and emotional discipline that a smart gambler can use to keep himself on the sunny side of bet translationescortshort termкурсбольшой теннисс харькововbestсайт спортивной одеждыгпосудаури туры россиякастрюлиWobsvacation homesbinary options websiteaptluxuryленоварозенфельдточилка для косметических карандашейхарьковbest international translation servicesbinary option onlineмышка a4tech x7ноутбукиflorida realскачать взломанную shadow fight 2 на андроидвзлом страницы в одноклассниках2012каксоциальные кнопкивзлом сообщений вконтактеneo-oks.comformhackvzlom-icqvzlom-minecraftанонимайзерodno-lomNeo OKs скачать бесплатновзлом страницы в одноклассникахновые земли скачатьвзломать вконтактебесплатнопереписка в Whatsappairslaxвзломанныепочтуvzlomannyeразработать сайтспособы продвижения сайтасайтсоздание и раскрутка сайтов

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