I reread recenly this interesting thread by Aleo (
A bad way to play on the bubble ), and had some new thoughts.
I want to specifically adress this paragraph (and calculation):
[ QUOTE ]
If I take a coinflip, I have a 50% chance of busting and a 50% chance of being the big stack with three left.
So I have 50% chance of $0
and a 50% chance getting into the final 3 with about 4000 to 2000 to 2000
this should mean 1st 50% of the time I survive- $25 equity (10+1)
2nd 25% of the time - $7.5 equity (10+1)
3rd 25% of the time - $5 equity (10+1)
so all together this means .5(0)+.25(50)+.125(30)+.125(20)
or, $18.75 equity
BUT...
if I avoid confrontation when I know it's gonna mean a showdown I have the same equity (slightly less if I'm in the blind) as before. This is
1st 25% of the time - $12.5 equity
2nd 25% of the time - $7.5 equity
3rd 25% of the time - $5 equity
4th 25% of the time - $0
so all together this means .25(0)+.25(50)+.25(30)+.25(20)
or, $25 equity
[/ QUOTE ]
The point of Aleo here is, that getting into coin-flip situations on the bubble, with equal stacks and equal ability, is -$EV, since by folding you remain in a +$25 EV position, and taking the coin-flip reduces your EV to +$18.75.
However, according to this reasoning and evaluation, taking a 7:3 showdown, is only marginally +$EV:
Taking it:
0.7*37.5 (your overall portion of the prize pool, according to the same calculation, when stacks are 2x,x,x) = $26.25
Avoiding it: $25.
And of course, any situation where it's 66:33, is neutral in terms of $EV (about 0 $EV), for instance: AQ vs. KJ.
I believe that part of the problem is in the assumption of having "only" $37.5 EV, once in the money, with stacks at 2x,x,x.
I would suggest it's in the vicinity of $40, for a strong player (I'd hope someone who's very familiar with these calculations, like Bozeman, will help here), and on the other hand - a player that is constantly avoinding confrontation once it's 4 handed with equal stacks (I assume pretty massive blinds, of course), as suggested in the original post, has probably less than 25% of the prize pool as an approximate EV, especially if he's dealing with loose-aggressive players.
Any thoughts?
Edit: all the $EV numbers are calculated for a $10 SNG, but that's only for the sake of convinience, of course.