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One of the most "amusing" stories I heard about a team betting full-Kelly occured back in the mid-1980s. A small group of investors put together a $200,000 bankroll, with a group of a dozen known and trusted players to take on the casinos of Nevada. All players were to bet full-Kelly, and the team would distribute the profits when they had doubled the bank. They estimated that it would take three to six weeks with the talent they had, and the number of hours the players should be able to play per week. The investors would get half the profit—$100,000—and the players would divvy up the other $100K, or about $8,500 per player. Sounded like a good plan…
After numerous ups and downs, with more downs than ups, the team hit a major downswing about three months into play. They had already gone twice as long as they were expected to go, but now the total bank remaining was only about $60,000. They had lost $140,000. The investors, all veteran players, took it in stride. They contacted the players and told them that $60,000 was simply not a big enough bankroll to front a dozen players. The investors were going to have to bite the bullet and put together a new bankroll; then they'd start over. So, they called in the remaining funds from the players.
But a funny thing happened…there were no remaining funds! Or, at least, there wasn't nearly the $60,000 there was supposed to be. All funds combined, the players had only about $11,000 in their possession! Where did the money go?
As it turned out, the players had all been taking informal "advances" on their expected $8,500 payday. Twelve players. Three months. They all had to live, eat, pay rent, buy gas…$49,000 had been dwindled away in the players' day-to-day living expenses. All the missing money, in fact, was accounted for. Each player knew how much he had advanced himself. An average draw of about $4,000 per player was not really that much money for three months living expenses. None of the players had been living high on the hog.
In fact, if this team had been betting quarter-Kelly, that $140,000 loss would have been a $35,000 loss. No big deal on a $200,000 bank. And the initial estimated time for doubling the bank would have been five to ten weeks, instead of three to six. Obviously, with this initial downswing, the team would not have made the estimated time schedule for doubling, but the fact is that even with the players taking their living-expense advances, they would have still had a substantial bankroll after three months, and a good chance of eventually hitting their goal.
If you bet half-Kelly, you cut your flux in half, but your win rate is still 75% of what it would be with full-Kelly betting. Better yet, with quarter-Kelly betting, you cut your flux to one-quarter of what it would be with full-Kelly betting, but your win rate is still 56% of the full-Kelly haul. If you've got a bankroll of $50K or better, quarter-Kelly betting makes sense, but the problem with betting this way on a $10K bank is that the initial hourly expectation is so low you might consider getting a job that pays better to increase your bank before beginning your blackjack career. But on any size bank, I'd never advise betting greater than half-Kelly.Share on: