The kelly criterion in blackjack sports
The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate. The Kelly Criterion is to bet a predetermined fraction of assets, and it can seem counterintuitive as it . The criterion is known to economists and financial theorists by names such as the “geometric mean maximizing portfolio strategy”, maximizing logarithmic utility, the growth-optimal strategy, the capital growth criterion, etc. The author initiated the practical application of the Kelly criterion by using it for card counting in blackjack.
This investment system specific option pricing interval is compatible with option valuation methods of using a replicating portfolio or a risk neutrality argument. DOI: This approximation leads to results that are robust and offer similar results as the original criterion. In the first part of the paper, we study the trade triggering algorithm using either an Ito process model, or real data from indexes and ETFs. The Trans Times 4 1 , February.
The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market
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Learn more. DOI: Edward O. The central problem for gamblers is to find positive expectation bets. But the gambler also needs to know how to manage his money, i. In the stock market more inclusively, the securities markets , the problem is similar but more complex. The gambler, who is now an "investor", looks for "excess risk adjusted return". In both these settings, this chapter explores the use of the Kelly criterion, which is to maximize the expected value of the logarithm of wealth "maximize expected logarithmic utility".
The criterion is known to economists and financial theorists by names such as the "geometric mean maximizing portfolio strategy", maximizing logarithmic utility, the growth-optimal strategy, and the capital growth criterion.
In probability theory and intertemporal portfolio choice , the Kelly criterion or Kelly strategy , Kelly bet , The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate.
The Kelly Criterion is to bet a predetermined fraction of assets, and it can seem counterintuitive. It was described by J. Kelly, Jr , a researcher at Bell Labs , in For an even money bet, the Kelly criterion computes the wager size percentage by multiplying the percent chance to win by two, then subtracting one. In recent years, Kelly-style analysis has become a part of mainstream investment theory  and the claim has been made that well-known successful investors including Warren Buffett  and Bill Gross  use Kelly methods.
William Poundstone wrote an extensive popular account of the history of Kelly betting. The behavior of the test subjects was far from optimal:.
If losing, the size of the next bet gets cut; if winning, the stake increases. For simple bets with two outcomes, one involving losing the entire amount bet, and the other involving winning the bet amount multiplied by the payoff odds , the Kelly bet is:. If the gambler has zero edge, i. There is no explicit anti-red bet offered with comparable odds in roulette, so the best a Kelly gambler can do is bet nothing.
For even-money bets i. In this case, as is proved in the next section, the Kelly criterion turns out to be the relatively simple expression. Thus, using too much margin is not a good investment strategy when the cost of capital is high, even when the opportunity appears promising. Heuristic proofs of the Kelly criterion are straightforward. This gives:. For a rigorous and general proof, see Kelly's original paper  or some of the other references listed below.
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