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#31
10-21-2007, 01:58 PM
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Re: Kelly Criterion deduced from ROI & Prize Structure.
[ QUOTE ]
[ QUOTE ] Well, obviously the reweighted positions total has to match the given ROI, as to how I do it.... I dont know what the technique is called, but I assume you have the best result (position) of X random positions. Then all I do is find an X that matches the ROI. [/ QUOTE ] I don't follow you here. [/ QUOTE ] This is the actual tournament payout for a given position multiplied by your ROI for the tournament. 
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#32
10-21-2007, 02:56 PM
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Re: Kelly Criterion deduced from ROI & Prize Structure.
[ QUOTE ]
[ QUOTE ] [ QUOTE ] Well, obviously the reweighted positions total has to match the given ROI, as to how I do it.... I dont know what the technique is called, but I assume you have the best result (position) of X random positions. Then all I do is find an X that matches the ROI. [/ QUOTE ] I don't follow you here. [/ QUOTE ] This is the actual tournament payout for a given position multiplied by your ROI for the tournament. [/ QUOTE ] Almost, as you can see by the example, better finishes have a somewhat higher distribution than merely an even distribution multiplied by the ROI, while worse finishes have slightly lower. One, this seems to correspond well with empirical evidence, as a almost any good player has slightly more first positions than second, slightly more second than third, etc, while a losing player has it reverse. The second is that if you merely multiply each position by the ROI then you can end up in a situation where the total odds of all itm positions exceed 100% which just doesnt make sense. As an example, a 10 player SnG, with 50-30-20 prize structure and ROI 400% (unrealistic yes) you would end up with.. 1st 10% * 400% = 40% 2nd 10% * 400% = 40% 3rd 10% * 400% = 40% so you end up with 120% ITM??!?! while the way its now calculated again with ROI 400% it would produce the following distribution... 1st 30.7% 2nd 23.3% 3rd 17.0% which has ITM 71% which makes sense (for ROI 400%).
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#33
10-21-2007, 04:05 PM
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Re: Kelly Criterion deduced from ROI & Prize Structure.
[ QUOTE ]
1st 30.7% 2nd 23.3% 3rd 17.0% which has ITM 71% which makes sense (for ROI 400%). [/ QUOTE ] Copy-pasted in the wrong numbers, the result is obviously.. 1st 100% 2nd 0% 3rd 0% which has ITM 100% and ROI 400%... so I picked a bad example, ohwell.
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#34
10-21-2007, 04:14 PM
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Re: Kelly Criterion deduced from ROI & Prize Structure.
[ QUOTE ]
[ QUOTE ] 1st 30.7% 2nd 23.3% 3rd 17.0% which has ITM 71% which makes sense (for ROI 400%). [/ QUOTE ] Copy-pasted in the wrong numbers, the result is obviously.. 1st 100% 2nd 0% 3rd 0% which has ITM 100% and ROI 400%... so I picked a bad example, ohwell. [/ QUOTE ] I see what you're saying... However, I don't have a feel for what that slope looks like. I doubt it's linear. Because of bubble and payoff effects etc.. But I bet it still works pretty well. Excellent point you bring up.
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Linear Mode
