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Poker players start with a fixed bankroll (bankroll) and play with a win-rate winRate (say measured in dollars per hour) and standard deviation of win-rate (sd).

How can I use the Wolfram Language to graph/simulate a poker player starting with bankroll and playing for, say, 100 hours (t = 100)?

If the total winnings ever dip below bankroll, the simulation result should just be $0 since the player has no ability to keep playing anymore!

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  • 1
    $\begingroup$ Look at RandomProcess, using WienerProcess. That should get you started. $\endgroup$ – ciao Nov 7 '19 at 1:49
  • $\begingroup$ You may want to incorporate the Kelly criterion , which maximizes the expected value of the logarithm of wealth (the expectation value of a function is given by the sum, over all possible outcomes, of the probability of each particular outcome multiplied by the value of the function in the event of that outcome). $\endgroup$ – Jagra Nov 7 '19 at 12:12
  • $\begingroup$ Applying the Kelly bet sizing methodology (a proportional bet, sized relative to bankroll, risk, and signal noise at each sequence of play) protects a player from their bankroll ever going to 0. $\endgroup$ – Jagra Nov 7 '19 at 15:00
  • $\begingroup$ what about buyins? $\endgroup$ – morbo Nov 8 '19 at 9:52
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ListPlot[
 NestList[# RandomVariate[NormalDistribution[1.05, .1]] &, 100, 50],
 Joined -> True,
 AxesLabel -> {"Games played", "return (dollars)"}]

enter image description here

Or...

ListPlot[
 Table[
 NestList[# RandomVariate[NormalDistribution[1.05, .1]] &, 100, 50], 
 10],
 Joined -> True, 
 AxesLabel -> {"Games played", "return (dollars)"}]

enter image description here

The bankroll constraint is easily incorporated:

ListPlot[
 NestList[
  If[# > 60, # RandomVariate[NormalDistribution[1.05, .1]], 0] &, 100,
   50],
 Joined -> True,
 AxesLabel -> {"Games played", "return (dollars)"}]

Here the "bankroll constraint" is 60 (even though you start with 100). If your game ends if you ever go beneath your starting money, you will often stop fairly quickly.

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  • $\begingroup$ What has this to do with the poker, or the bankroll constraint? $\endgroup$ – wolfies Nov 10 '19 at 4:08

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