Kelly's rule says how much of your bankroll to bet: the fraction that maximises your bankroll's growth rate. For the +80 % / −50 % coin flip from video 01, that is 37.5 %. But Kelly is not your edge. An even-money bet with the same +15 % edge: 15 %. A real tournament with the same +15 %: 0.35 % of your roll.
The tournament is real: PokerStars WCOOP 114-L, $215 NLHE, 1,028 entries, 175 paid, prize pool $205,600. The payouts are real; your skill is the assumption: 24 % more likely than an average player to finish in every paid place, which makes your ROI +15 % after rake.
Because a buy-in is indivisible, your bankroll fixes the fraction you bet, so Kelly answers in buy-ins. Here: 287 buy-ins. Below 130 buy-ins your bankroll's growth is negative, with the same +15 % edge. That includes 100 buy-ins, the rule most players were taught: a thousand of these tournaments typically leave you with three quarters of your roll. At 50 buy-ins, about a tenth.
Two players with the same skill and the same finishes, 2,000 tournaments (the median run of 400): the one at Kelly ends at ×1.45, the one who always plays the biggest game, at 50 buy-ins, at ×0.0065. And you do not need to overbet all the time: one shot in 20 at 50 buy-ins costs over half of your growth. Breiman (1961) proved no strategy grows faster in the long run; Algoet and Cover (1988) extended it to any market. Under the line? Play smaller, don't play, or sell action. Selling is the next video.
In the video
0:00 Kelly: the fraction has a name
1:35 A tournament is an option
2:23 A real WCOOP payout table
3:20 Kelly for this tournament: 287 buy-ins
4:31 The catch: a buy-in is indivisible
5:20 The aggressive winner
6:39 The occasional shot
7:59 Why Kelly: Breiman, Algoet & Cover
8:42 Three ways out
Sources
John L. Kelly Jr. (1956), "A New Interpretation of Information Rate", Bell System Technical Journal 35(4), 917–926. https://doi.org/10.1002/j.1538-7305.1956.tb03809.x
Leo Breiman (1961), "Optimal Gambling Systems for Favorable Games", Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1. Reprinted in The Kelly Capital Growth Investment Criterion (World Scientific, 2011), 47–60. https://doi.org/10.1142/9789814293501_0005
Paul H. Algoet & Thomas M. Cover (1988), "Asymptotic Optimality and Asymptotic Equipartition Properties of Log-Optimum Investment", Annals of Probability 16(2), 876–898. https://doi.org/10.1214/aop/1176991793
Payout table: PokerStars WCOOP 2026 Event 114-L, $215 NLHE, 29 September 2026.
A note for readers of the paper: Part 3 says a +15 % tournament can have negative growth at every positive bet size. That is not right: at small enough stakes any positive edge grows. The correct statement, used in this video: growth is negative below a bankroll threshold, because a buy-in is indivisible and your bankroll fixes the fraction you bet. On this tournament the threshold is 130 buy-ins.
The series
Previous: "Maximise EV" is the wrong advice
Next, on 2026-11-03: Selling, and why selling below value can be right
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