Open Access Open Access  Restricted Access Subscription or Fee Access

A COMPARISON OF SIMULTANEOUS KELLY BETTING STRATEGIES

Andrew Grant, Peter W Buchen

Abstract


In this paper we consider the problem of Kelly betting on simultaneous games, and the relative performance of betting strategies that use multibets compared to those that do not. We develop a simulation model based on the Dirichlet distribution to test the performance of three Kelly betting strategies using the empirical odds distribution from the 2007-08 English Premier League Season. This model allows us to control for the size of a bettor’s edge and the noise of this edge. The simulation results suggest that the Kelly using multibets of all levels outperforms the portfolio optimisation approach of betting on single game outcomes only. We also provide a discussion regarding the practicalities of implementing the strategies.


Keywords


Kelly Criterion, Gambling, Numerical Optimization, Asset Allocation

Full Text:

PDF

References


Ali, M. M. (1979), ‘Some Evidence on the Efficiency of a Speculative Market’, Econometrica 47, 387–392.

Breiman, L. (1961), ‘Optimal Gambling Systems for Favorable Games’, Fourth Berkeley Symposium on Probability and Statistics 1, 65–78.

Cain, M. and Peel, D. (2004), ‘The Utility of Gambling and the Favourite-Longshot Bias’, The European Journal of Finance 10, 379–390.

Deschamps, B. and Gergaud, O. (2007), ‘Efficiency in Betting Markets: Evidence from English Football’, Journal of Prediction Markets 1, 61–74.

Dixon, M. J. and Pope, P. F. (2004), ‘The Value of Statistical Forecasts in the UK Association Football Betting Market’, International Journal of Forecasting 20, 697–711.

Forrest, D., Goddard, J. and Simmons, R. (2005), ‘Odds-Setters as Forecasters: The Case of English Football’, International Journal of Forecasting 21, 551–564.

Forrest, D. and McHale, I. (2007), ‘Anyone for Tennis (Betting)?’ European Journal of Finance 13, 751–758.

Gneiting, T., Balabdaoui, F. and Raftery, A. E. (2007), ‘Probabilistic Forecasts, Calibration and Sharpness’, Journal of the Royal Statistical Society, Series B 69, 243–268.

Golec, J. and Tamarkin, M. (1998), ‘Bettors Love Skewness, Not Risk, at the Horse Track’, Journal of Political Economy 106, 205–225.

Grant, A., Johnstone, D. and Kwon, O. K. (2008), ‘Optimal Betting Strategies for Simultaneous Games’, Decision Analysis 5, 10–18.

Hakansson, N. H. (1970), ‘Optimal Investment and Consumption Strategies Under Risk for a Class of Utility Functions’, Econometrica 38, 587–607.

Hakansson, N. H. and Ziemba, W. T. (1995), Capital Growth Theory, in R. A. Jarrow, V. Maksimovic and W. T. Ziemba, eds, ‘Handbooks in Operations Research and Management Science: Finance’, Vol. 9, North-Holland, Amsterdam, pp. 65–86.

Insley, R., Mok, L. and Swartz, T. (2004), ‘Issues Related to Sports Gambling’, Australian and New Zealand Journal of Statistics 46, 219–232.

Kelly, J. L. (1956), ‘A New Interpretation of Information Rate’, Bell Systems Technical Journal 35, 917–926.

Kuypers, T. (2000), ‘Information and Efficiency: An Empirical Study of a Fixed Odds Betting Market’, Applied Economics 32, 1353–1363.

MacLean, L. C., Ziemba, W. T. and Blazenko, G. (1992), ‘Growth Versus Security in Dynamic Investment Analysis’, Management Science 38, 1562–1585.

MacLean, L. C., Ziemba, W. T. and Li, Y. (2005), ‘Time to Wealth Goals in Capital Accumulation’, Quantitative Finance 5, 343–355.

Medo, M., Pis’mak, Y. M. and Zhang, Y.-C. (2008), ‘Diversification and Limited Information in the Kelly Game’, Physica A 387, 6151–6158.

Mossin, J. (1968), ‘Optimal Multiperiod Portfolio Policies’, Journal of Business 41, 215–229.

Paton, D., Siegel, D. and Vaughan Williams, L. (2002), ‘A Policy Response to the E-Commerce Revolution: The Case of Betting Taxation in the U.K.’, The Economic Journal 112, 296–314.

Smith, J. (2000), ‘Gambling Taxation: Public Equity in the Gambling Business’, Australian Economic Review 33, 120–144.

Thorp, E. O. (2000), The Kelly Criterion in Blackjack, Sports Betting and the Stock Market, in O. Vancura, J. A. Cornelius and W. R. Eadington, eds, ‘Finding The Edge: Mathematical Analysis of Casino Games’, Institute For the Study of Gambling and Commercial Gaming, Reno, NV, pp. 163–213.

Vaughan Williams, L. (2005), Information Efficiency in Financial and Betting Markets, Cambridge University Press, Cambridge, U.K.

Vlastakis, N., Dotsis, G. and Markellos, R. N. (2009), ‘How Efficient is the European Football Betting Market?

Evidence from Arbitrage and Trading Strategies’, Journal of Forecasting 28, 426–444.

Whitrow, C. (2007), ‘Algorithms for Optimal Allocation of Bets on Many Simultaneous Events’, Journal of the Royal Statistical Society, Series C (Applied) 56, 607–623.




DOI: http://dx.doi.org/10.5750/jgbe.v6i2.579

Refbacks

  • There are currently no refbacks.