Re: reducing variance: the sklansky bux swap
Pete,
I think that your concept would greatly benefit people who go all in before the river rather than those who try to hit their hand and then get paid off. Waiting until you hit your hand could be very beneficial in games where the opponent is loose-passive.
Consider the following example hand (this was done quickly, if the math is slightly off or if you debate the way that the 'hero' plays this hand then my bad, lets not that take away from the theory behind this argument)
Imagine a heads up 25/50 game where effective stacks are $7,500
Suppose that the villain is somewhat fishy does not like to ever fold TPNK+
SB raises to 150 and Hero makes it 450 with 6[img]/images/graemlins/club.gif[/img]7[img]/images/graemlins/club.gif[/img], villain calls.
Flop ($900) comes 5[img]/images/graemlins/heart.gif[/img] 6[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/club.gif[/img]
Hero bets 750, Villain calls
Turn ($2400) is the money card, the 4[img]/images/graemlins/club.gif[/img] earning you a ton of Sklansky bux. If someone was doing a variance swap it would benefit him to check-shove or bet-call the turn even if he thinks that the villain will call with all Ax. This is because your calculator would only kick into place in all in pots.
If someone was not doing a variance swap it would make sense to check call the turn (especially against a loose-passive player who might check behind with AJs here when he would be willing to get it all in if you bet out) and get the money in if he hits the river.
In the above example, doing a variance swap would make it so that -EV plays (or plays that are less +EV) are encouraged
if they allow the hero to get his money in and take advantage of the Sklansky bux equalizer.
In order to compensate for this you would have to create a really sophisticated Sklansky bux calculator that takes into account the times that you brick on the river and there is still money behind that you would have won had you hit. In my opinion, the absence of such a calculator would make it more profitable for players in the group swapping sklansky bux to become all-in monkeys even when they would normally take a more conservative and more profitable approach to their play.
-Steve
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