Quote:
Originally Posted by whosnext
TomC is correct.
Using the Kelly criterion is equivalent to wanting to maximize your expected log stack. So the concept of "risk-aversion" is built into Kelly.
When choosing between running it once, twice, four times, or ten times, you are not changing the total amount of your "exposure" (or bet). So the principles underlying Kelly would suggest that you would choose running it as many times as you can.
As TomC points out, under the Kelly framework a sure thing is worth more than any gamble with equal expected value but positive variance.
(The confusion may stem from Kelly being used to choose how much to wager on a positive-EV bet. This is not really what is going on in run-it-twice decisions.)
Edit: I suppose it could be pointed out that when you choose to run-it-twice, this is essentially making two simultaneous half-size bets. The simultaneous-bet Kelly criterion is slightly different from the single-bet Kelly criterion. But I am quite sure that this subtlety is irrelevant to this discussion. There is another thread in this forum on simultaneous kelly you may want to look at.
Ok, in the simultaneous bet thread, you proved that making two bets simultaneously is only slightly different than making them one at a time, such that a gambler who is dealing in estimates of edges should not really take notice at all.
But in those cases, the bettor is allowed to choose the size of each bet.
Here, our exposure is locked and we are presented with the option to move down from Kelly in two separate bets. The bets are only quasi independent such that the total overall EV is 57.2 percent.
Poker bets are (apparently) usually way below full Kelly as a consequence of heuristics of poker bank roll management.
The curve as Kelly maximizes growth is gradual, and humans experience less variance and better enjoyment by fudging below Kelly and allowing for human error in edge calculation.
But here, the edge is rigged. Full Kelly should be implemented by an optimal Econ bettor.
Since the poker player is already at about 1/3 Kelly, that gradual curve is now actually quite noticable.
Moving farther down away from Kelly has to be a mistake right?
OR...
Is Kelly no longer applicable because we are past the "bet sizing" decision?