Kelly Criterion deduced from ROI & Prize Structure.
 

Hi, I wrote a small piece of software to calculate kelly criterion for multiple different outcomes, and applied it to tournament prizestructure and ROI to get some hopefully usefull results.

1616 player tournament, top 261 itm.

return on investment : 100.0%
kelly criterion : 2.85%

return on investment : 50.0%
kelly criterion : 0.89%

return on investment : 25.0%
kelly criterion : 0.32%


315 player tournament, top 36 itm.

return on investment : 100.0%
kelly criterion : 3.45%

return on investment : 50.0%
kelly criterion : 1.39%

return on investment : 25.0%
kelly criterion : 0.73%


90 player SnG, top 18 itm.

return on investment : 100.0%
kelly criterion : 14.51%

return on investment : 50.0%
kelly criterion : 6.27%

return on investment : 25.0%
kelly criterion : 2.85%


9 player SnG, top 3 itm.

return on investment : 15.0%
kelly criterion : 6.49%

return on investment : 10.0%
kelly criterion : 4.16%

return on investment : 5.0%
kelly criterion : 2.3%


2 player SnG, top 1 itm.

return on investment : 15.0%
kelly criterion : 15.79%

return on investment : 10.0%
kelly criterion : 10.33%

return on investment : 5.0%
kelly criterion : 5.22%


The ROI is calculated after the rake obviously, with rake being 10% for all but HUP where it is 5%. If your prize distribution is skewed your kelly criterion may differ, as an example if you often lose HUP in a SnG or a tournament but still somehow manage to have a positive ROI. Here is an example of assumed position distribution in 9 player SnG with ROI 15%.

1st 14.2%
2nd 13.7%
3rd 13.1%

I can calculate it for other prizestructures & ROIs, post them here (include the entire prize structure, not just ITM) and I'll run it trough the program, also include the rake and ROI(s) you want.

Re: Kelly Criterion deduced from ROI & Prize Structure.
 

THIS IS GENIOUS

Re: Kelly Criterion deduced from ROI & Prize Structure.
 

For those unfamiliar with kelly criterion, Kelly criterion is...

Re: Kelly Criterion deduced from ROI & Prize Structure.
 

Re: Kelly Criterion deduced from ROI & Prize Structure.
 

From the Wikipedia article...

[ QUOTE ]
The optimum bet for the greatest growth of bankroll is making the full bet suggested by the Kelly criterion, but this produces a volatile result. There is a 1/3 chance of halving the bankroll before it is doubled. A popular alternative is to bet only half the amount suggested which gives three-quarters of the investment return with much less volatility. Where money would accumulate at 9.06% compound interest with full bets, it still accumulates at 7.5% for half-bets.

Over-betting beyond that suggested by Kelly is counter-productive as the long run growth rate will fall, dropping to zero when the Kelly bet is approximately doubled. Using half-Kelly bets also safeguards against being ruined by unknowingly overbetting, as it can be easy to over-estimate the true odds by a factor of two.

[/ QUOTE ]

So, not much point buy into anything outside 0.25 - 1.0 times what Kelly Criterion says you should.

Re: Kelly Criterion deduced from ROI & Prize Structure.
 

basically your chart shows that in large field MTT's even the best players need 50+ buyins and even to low ROI players need upwards of 200 to 300 buyins.

Re: Kelly Criterion deduced from ROI & Prize Structure.
 

[ QUOTE ]
From the Wikipedia article...

[ QUOTE ]
The optimum bet for the greatest growth of bankroll is making the full bet suggested by the Kelly criterion, but this produces a volatile result. There is a 1/3 chance of halving the bankroll before it is doubled. A popular alternative is to bet only half the amount suggested which gives three-quarters of the investment return with much less volatility. Where money would accumulate at 9.06% compound interest with full bets, it still accumulates at 7.5% for half-bets.

Over-betting beyond that suggested by Kelly is counter-productive as the long run growth rate will fall, dropping to zero when the Kelly bet is approximately doubled. Using half-Kelly bets also safeguards against being ruined by unknowingly overbetting, as it can be easy to over-estimate the true odds by a factor of two.

[/ QUOTE ]

So, not much point buy into anything outside 0.25 - 1.0 times what Kelly Criterion says you should.

[/ QUOTE ]I think that's assuming you can only make one bet at a time. I play $3rs and $109s at the same time even though a $3r is well under what my roll can handle.

Re: Kelly Criterion deduced from ROI & Prize Structure.
 

OK, Let's see if I understand this correctly:

I play the $2.20 sat's into the Sunday $100K (Flat $11 T$ payout to top 20%)

That tournament is closely approx'd by this table:

[ QUOTE ]
90 player SnG, top 18 itm.

return on investment : 100.0%
kelly criterion : 14.51%

return on investment : 50.0%
kelly criterion : 6.27%

return on investment : 25.0%
kelly criterion : 2.85%


[/ QUOTE ]

My ROI is around 25%, so my bankroll should be $2.20/2.85% or $77 for optimal growth or $154 for a more conservative approach.

My gut says that no way will a 25% ROI player bust a $77 bankroll 1/3 the time playing the $2.20 sats... The variance is too small. I put the likelyhood closer to 1 in 50... (or smaller)

Where am I going wrong?

Re: Kelly Criterion deduced from ROI & Prize Structure.
 

A 25% roi MTTer should probably be quite a bit higher in that sat if you play a good bubble game.

Edit: Very nice work OP

Re: Kelly Criterion deduced from ROI & Prize Structure.
 

this is an outstanding piece of work quantifying br requirements, which is greatest reason gamblers end up busto.

maybe op could run more tourney requirements and the mods might sticky this.

i don't know if op is aware , there is a program called blackjack risk manager that quantifies roi for all fractions of kelly based on win rates and bankroll over a varying number of hands. it is an absolute must for any serious advantage player.