The Kelly Criterion in Blackjack Sports Betting, and the Stock Market

  title={The Kelly Criterion in Blackjack Sports Betting, and the Stock Market},
  author={Edward O. Thorp},
The central problem for gamblers is to find positive expectation bets. But the gambler also needs to know how to manage his money, i.e., how much to bet. 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, we explore the use of the Kelly criterion, which is to maximize the expected value of the logarithm of wealth (“maximize expected… Expand

Figures and Tables from this paper

When a bet with a positive expected return is available, the Kelly criterion can be used to determine the fraction of wealth to wager so as to maximize the expected logarithmic return on investment.Expand
Since the Betfair betting exchange launched in 2000, sports gamblers have had a gambling forum quite different from the traditional bookmaker. Three features of betting exchanges in particularExpand
Nash Bargaining Over Margin Loans to Kelly Gamblers
I derive practical formulas for optimal arrangements between sophisticated stock market investors (continuous-time Kelly gamblers or, more generally, CRRA investors) and the brokers who lend themExpand
Practical Implementation of the Kelly Criterion: Optimal Growth Rate, Number of Trades, and Rebalancing Frequency for Equity Portfolios
Under few conditions, using Monte Carlo simulations with different scenarios, it is proved that the Kelly criterion beats any other approach in many aspects and has the best performance in the long run. Expand
Bet doubling in gambling and investing
Purpose - The purpose of this paper is to analyze strategies for gamblers/investors to increase their chances of reaching certain monetary and/or survival goals while facing a losing proposition.Expand
Nash Bargaining Over Margin Loans to Kelly Gamblers
I derive practical formulas for optimal arrangements between sophisticated stock market investors (namely, continuous-time Kelly gamblers or, more generally, CRRA investors) and the brokers who lendExpand
Rebalancing Frequency Considerations for Kelly-Optimal Stock Portfolios in a Control-Theoretic Framework
It is shown that if there is an asset satisfying a certain dominance condition, then an optimal portfolio consists of this asset alone; i.e., if the trader puts “all eggs in one basket,” performance becomes a constant function of rebalancing frequency, and the problem ofRebalancing is rendered moot. Expand
On inefficiency of markowitz-style investment strategies when drawdown is important
The focal point of this paper is the issue of “drawdown” which arises in recursive betting scenarios and related applications in the stock market and a new investment strategy which involves a time-varying linear feedback block K (k), called the drawdown modulator, which results in classical Markowitz-style strategies are inefficient. Expand
Multilinear Superhedging of Lookback Options
In a pathbreaking paper, Cover and Ordentlich (1998) solved a max-min portfolio game between a trader (who picks an entire trading algorithm, $\theta(\cdot)$) and "nature," who picks the matrix $X$Expand
Money management.
This note reviews the literature on money management and shows that in order to achieve maximum growth of wealth, at every bet a gambler should maximize the expected value of the logarithm of his capital. Expand


The Return on Investment from Proportional Portfolio Strategies
Dynamic asset allocation strategies that are continuously rebalanced so as to always keep a xed constant proportion of wealth invested in the various assets at each point in time play a fundamentalExpand
Reaching Goals by a Deadline: Digital Options and Continuous-Time Active Portfolio Management
We study a variety of optimal investment problems for objectives related to attaining goals by a fixed terminal time. We start by finding the policy that maximizes the probability of reaching a givenExpand
A Favorable Side Bet in Nevada Baccarat
Abstract A winning strategy is developed for the nine to one side bet on a Banker natural nine. Let n be the number of cards that remain for play. Let t be the number of nines that remain for play.Expand
Beat The Market
Speculation in asset market is modelled as a stochastic betting game played by finite number of players and repeated infinite times. With stochastic asset return and unkown quality of public signal,Expand
The Pricing of Options and Corporate Liabilities
If options are correctly priced in the market, it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks. Using thisExpand
Portfolio Choice and the Kelly Criterion
The following sections are included:IntroductionSamuelson's objections to logarithmic utilityAn outline of the theory of logarithmic utility as applied to portfolio selectionRelation to the MarkowitzExpand
A new interpretation of information rate
  • J. L. Kelly
  • Mathematics, Computer Science
  • IRE Trans. Inf. Theory
  • 1956
The maximum exponential rate of growth of the gambler's capital is equal to the rate of transmission of information over the channel, generalized to include the case of arbitrary odds. Expand
Optimal Gambling Systems for Favorable Games
The following sections are included:IntroductionThe nature of Λ*The asymptotic time minimization problemAsymptotic magnitude problemProblems with finite goals in coin tossingREFERENCES
Of Permanent Value: The Story of Warren Buffett
The author also includes a complete chapter detailing his remarkable investing record - quarter by quarter - that reveals the incredible investment performance of this compelling and enigmatic figure.
The Theory of Stochastic Processes