The math for my previous post, vs the best-case range that I posted earlier, i.e. at the turn we are 47% vs the range:
AA,TT,77,AdKd,AdQd,AJs-ATs,KQs,98s,AJo,KQo
We get check-raised at turn. We have put in 60 + 80 + 220 = 360 at that point. If we fold, our EV = -360.
If we continue, calling his raise, we have invested 900. The pot is now 1800. We can the put him in for another 1800 right now, or wait until river and decide what to do when he shoves another 1800. If there is a showdown, the pot is 5400.
If we shove turn, we have put in a total of 2700, and win 0.47 * 5400 = 2538, for a net of -162 EV.
If we flat the turn, we have put in 900. We now reevaluate with 46 possible rivers.
River: A
T
7
J
??
There are 46 possible river cards:
15 - Scare cards as in previous post (non-pair diamond, 4-to-broadway)
We fold. EV -900
1 - J
We call and win with the nuts. EV +2700
1 - A
We call and are 0.84 vs his range. EV +1836
2 - A
, A
We call and are 0.875 vs his range. EV +1836
3 - T
, T
, T
We call and are 0.88 vs his range. EV +2052
3 - 7
, 7
, 7
We call and are 0.88 vs his range. EV +2052
21 - Blanks
We call and are 0.36 vs his range. EV -756
(Surprised? I was. We catch a blank and STILL lose 2/3 times vs a wide range.)
Multiply the number of cards by each EV, add them up, divide by 46... river is -184 EV.
Note the EV for some isn't exact... depending on what exactly the blank is, or even the suit of a card, our EV is slightly different as it affect which cards are in his range. See the difference between the Ace rivers, for example. To do it exact you'd have to stove every single river card. But I think this is close.
Summary
--------------------
Fold at turn: -360 EV
Shove at turn: -162 EV
Re-eval river: -184 EV
So if you buy the logic and I didn't screw the math... shoving turn is our best play by a nose over calling. Either is better than folding. From a chip EV perspective.
Of course we're going busto a lot as well in a tourney which presumably we think we're a favorite, so is that a good spot? Or should we fold (which costs us 200 chips in the long run over shoving) and wait?
And of course, we are losing money with second set no matter what we do. That sucks!
Which begs the question... could we play this differently, or did we just get coolered?
Once we get check-raised at turn we wish we had checked behind, because now we have basically thrown away the value of position, and our skill, with the stacks so shallow relative to the now-bloated pot.
If we check behind we can suck out free vs KQ, or at least keep the pot small enough to prevent villain from shoving river with impunity when a scare card comes. But is checking behind something we should 'know' in advance on this board, or not?
I think it would also be interesting to re-do the math vs one of the tighter villain ranges as well. My guess is those bode even worse for our JJ, probably in large part because we still fold to scare cards even though that's incorrect more often.
Last edited by chalupa; 05-20-2010 at 11:41 PM.