# Kelly Criterion Extension: Advanced Gambling Strategy

## Abstract

**:**

## 1. Introduction

## 2. Kelly Criterion Basics

#### 2.1. Optimizing Blackjack Betting

#### 2.2. Optimizing Winning Reward Rate

## 3. Kelly Criterion Extension

#### Gambling the Mutual Fund Investment

## 4. Conclusions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Kelly, J.L. A New Interpretation of Information Rate. Bell Syst. Tech. J.
**1956**, 35, 917–926. [Google Scholar] [CrossRef] - Shannon, C.E. A Mathematical Theory of Communication. Bell Syst. Tech. J.
**1948**, 27, 379–423, 623–656. [Google Scholar] [CrossRef] - Nekrasov, V. Kelly Criterion for Multivariate Portfolios: A Model-Free Approach. 2014. Available online: https://ssrn.com/abstract=2259133 (accessed on 16 November 2023).
- Bellman, R.; Kalaba, R. On the role of dynamic programming in statistical communication theory. IRE Trans. Inf. Theory
**1957**, 3, 197–203. [Google Scholar] [CrossRef] - Mossin, J. Optimal multiperiod portfolio policies. J. Bus.
**1968**, 41, 215–229. [Google Scholar] [CrossRef] - Cover, T.M. An algorithm for maximizing expected log investment return. IEEE Trans. Inf. Theory
**1984**, 30, 369–373. [Google Scholar] [CrossRef] - Browne, S. Risk-constrained dynamic active portfolio management. Manag. Sci.
**2000**, 46, 1188–1199. [Google Scholar] [CrossRef] - Wu, M.E.; Hung, P.J. A Framework of Option Buy-Side Strategy with Simple Index Futures Trading Based on Kelly Criterion. In Proceedings of the 2018 5th International Conference on Behavioral, Economic, and Socio-Cultural Computing (BESC), Kaohsiung, Taiwan, 12–14 November 2018; pp. 210–212. [Google Scholar]
- Wu, M.E.; Wang, C.H.; Chung, W.H.; Tso, R.; Yang, I.H. An Empirical Comparison between Kelly Criterion and Vince’s Optimal F. In Proceedings of the 2015 IEEE International Conference on Smart City/SocialCom/SustainCom (SmartCity), Chengdu, China, 19–21 December 2015; pp. 806–810. [Google Scholar]
- Park, C.H.; Irwin, S.H. What do we know about the profitability of techincal analysis? J. Econ. Surv.
**2007**, 21, 786–826. [Google Scholar] [CrossRef] - Basu, S. Investment Performance of Common Stocks in Relation To Their Price-earnings Ratios: A Test of The Efficeint Market Hypothesis. J. Financ.
**1977**, 32, 663–682. [Google Scholar] - Thorp, E.O. Chaper 9—The kelly criterion in blackjack sports betting, and the stock market. In Handbook of Asset and Liability Management; Zenios, S., Ziemba, W., Eds.; North-Holland: San Diego, CA, USA, 2008; pp. 385–428. [Google Scholar]
- Hsieh, C.H.; Barmish, B.R. On Kelly Betting: Some Limitations. arXiv
**2017**, arXiv:1710.01787. [Google Scholar] - Hsieh, C.H.; Barmish, B.R.; Gubner, J.A. Kelly betting can be too conservative. In Proceedings of the 2016 IEEE 55th Conference on Decision and Control (CDC), Las Vegas, NV, USA, 12–14 December 2016; pp. 3695–3701. [Google Scholar]
- Hsieh, C.H.; Barmish, B.R. On Drawdown-Modulated Feedback Control in Stock Trading. IFAC-PapersOnLine
**2017**, 50, 952–958. [Google Scholar] [CrossRef] - Vince, R. The Leverage Space Trading Model: Reconciling Portfolio Management Strategies and Economic Theory, 1st ed.; Wiley: Hoboken, NJ, USA, 2009. [Google Scholar]
- Ansari, V.A.; Khan, S. Momentum anomaly: Evidence from India. Manag. Financ.
**2012**, 38, 206–223. [Google Scholar] [CrossRef] - Brown, B.M. Martingale Central Limit Theorems. Ann. Math. Stat.
**1971**, 42, 59–66. [Google Scholar] [CrossRef] - Cover, T.M.; Thomas, J.A. Elements of Information Theory; John Wiley and Sons: Hoboken, NJ, USA, 1991. [Google Scholar]
- Thorp, E.O. Optimal Gambling Systems for Favorable Games. Rev. Int. Stat. Inst.
**1969**, 37, 273–293. [Google Scholar] [CrossRef] - Peter Smoczynski, D.T. An Explicit Solution of the Problem of Optimizing the Allocations of a Bettor’s Wealth when Wagering on Horse Races. Math. Sci.
**2010**, 35, 10–17. [Google Scholar] - Weide, J.; Peterson, D.W.; Maier, S.F. A Strategy Which Maximizes the Geometric Mean Return on Portfolio Investments. Manag. Sci.
**2010**, 23, 1117–1123. [Google Scholar] [CrossRef] - Securities, U.; Commission, E. Mutual Funds and ETFs: A Guide for Investors. 2017. Available online: https://www.sec.gov/investor/pubs/sec-guide-to-mutual-funds.pdf (accessed on 16 November 2023).
- Fernando, D.; Klapper, L.F.; Sulla, V.; Vittas, D. World Bank Policy Research Working Paper; World Bank Group: Washington, DC, USA, 2003; p. 3055. [Google Scholar]

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**MDPI and ACS Style**

Kim, S.-K.
Kelly Criterion Extension: Advanced Gambling Strategy. *Mathematics* **2024**, *12*, 1725.
https://doi.org/10.3390/math12111725

**AMA Style**

Kim S-K.
Kelly Criterion Extension: Advanced Gambling Strategy. *Mathematics*. 2024; 12(11):1725.
https://doi.org/10.3390/math12111725

**Chicago/Turabian Style**

Kim, Song-Kyoo (Amang).
2024. "Kelly Criterion Extension: Advanced Gambling Strategy" *Mathematics* 12, no. 11: 1725.
https://doi.org/10.3390/math12111725