Next UCMS Lecture: How to Win at Blackjack

Posted on: November 1st, 2013 by Aaron Lauve

In this talk, the audience will see how calculus can inform your choice of strategy in gambling and other ‘investments.’ (Hint: “21” is an entertaining movie, but the best strategy isn’t learning how to count cards like Kevin Spacey.)

Tuesday, November 5th

Speaker: Jim Zhu (Western Michigan University – Dept. of Math)

Title: How to Win the Game of Blackjack

Lecture: 4:30 p.m., Cuneo Hall 311

Meet the Speaker: 4:00 p.m., Cuneo Hall 311
w/ tea & cookies


Counting cards, drinking beer and betting big, that is what the movie 21 tells us to do to win Blackjack in a casino. But masters beg to differ. Ed Thorp, the author of the classic “Beat the Dealer’’ emphasized that even when playing a favorable deck of cards one has to bet conservatively to avoid the gambler’s ruin. Thorp estimates the appropriate size of a bet by developing an early theory of John Kelly which was later dubbed “Fortune’s Formula’’ in Poundstone’s popular book of the same title.

It turns out that this is not the end of the story. Two important practical considerations were overlooked (for simplicity) in the derivation of the “Fortune’s Formula’’: players only play a finite number of times and they have to take risk into consideration. We will show in this talk how to use elementary calculus to address these practical considerations and arrive at the conclusion that in practice one has to be much more conservative than what the “Fortune’s Formula’’ suggests. Bright calculus students should bring a pen and a note pad so that they can discover the revised fortune’s formula during the talk on their own. We will also describe our computer simulation that validates those results in realistic settings. Implementing the simulation will be a good take home excise for those who love coding.

The analysis and methods discussed in this talk also apply to money management problems for investment as well as more general cumulative resource allocation considerations involving risks. This is joint research with Ralph Vince, the president of LSP Partners, LLC.

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