Skip to main content Accessibility help
×
Home

Explicit Optimal Strategy for the Vardi Casino with Limited Playing Time

  • Yi-Ching Yao (a1)

Abstract

The Vardi casino with parameter 0 < c < 1 consists of infinitely many tables indexed by their odds, each of which returns the same (negative) expected winnings -c per dollar. A gambler seeks to maximize the probability of reaching a fixed fortune by gambling repeatedly with suitably chosen stakes and tables (odds). The optimal strategy is derived explicitly subject to the constraint that the gambler is allowed to play only a given finite number of times. Some properties of the optimal strategy are also discussed.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Explicit Optimal Strategy for the Vardi Casino with Limited Playing Time
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Explicit Optimal Strategy for the Vardi Casino with Limited Playing Time
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Explicit Optimal Strategy for the Vardi Casino with Limited Playing Time
      Available formats
      ×

Copyright

Corresponding author

Postal address: Institute of Statistical Science, Academia Sinica, Taipei, 115, Taiwan, ROC. Email address: yao@stat.sinica.edu.tw

References

Hide All
[1] Chen, M.-R. and Hsiau, S.-R. (2006). Two-person red-and-black games with bet-dependent win probability functions. J. Appl. Prob. 43, 905915.
[2] Chen, R. W., Shepp, L. A. and Zame, A. (2004). A bold strategy is not always optimal in the presence of inflation. J. Appl. Prob. 41, 587592.
[3] Chen, R. W., Shepp, L. A., Yao, Y.-C. and Zhang, C.-H. (2005). On optimality of bold play for primitive casinos in the presence of inflation. J. Appl. Prob. 42, 121137.
[4] Dubins, L. E. and Savage, L. J. (1976). Inequalities for Stochastic Processes (How to Gamble if You Must). Dover, New York.
[5] Grigorescu, I., Chen, R. and Shepp, L. (2007). Optimal strategy for the Vardi casino with interest payments. J. Appl. Prob. 44, 199211.
[6] Schweinsberg, J. (2005). Improving on bold play when the gambler is restricted. J. Appl. Prob. 42, 321333.
[7] Shepp, L. A. (2006). Bold play and the optimal policy for Vardi's casino. In Random Walk, Sequential Analysis and Related Topics, eds Hsiung, A. C., Ying, Z. and Zhang, C.-H., World Scientific, Singapore, pp. 150156.
[8] Yao, Y.-C. (2007). On optimality of bold play for discounted Dubins–Savage gambling problems with limited playing times. J. Appl. Prob. 44, 212225.

Keywords

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed