Here's a concept I've posted before, but it got lost due to confusion/forum switch/lack of interest. The situation is this. You are faced with an awkward stack, opening from the SB. Your hand is probably too good to fold but shoving seems excessive.
$220+16 Turbo 6-max No Limit Holdem Tournament
Full Tilt Poker (pays 65/35)
Blinds: t50/t100
5 players
Stack sizes:
UTG: t1330
CO: t2705
Button: t1730
Hero: t1580
BB: t1655
Pre-flop: (
5 players) Hero is SB with A
9
3 folds,
Hero raises all-in t1580...
If you’re going to shove 15 BB with any hand from the SB, A9o isn’t a bad hand to pick. You’re sort of grudgingly calling a reraise anyway, but your hand doesn’t improve significantly by adding extra hands to his range where he would attempt a resteal. It’s profitable no matter what his calling range is. It’s just not any more profitable to have him re-stealing wide.
Push/fold is the limiting case when you call his push every time you open for a standard raise and he pushes. We can just look at the respective values of open-pushing to see how the hand responds to a wider range. Take three hands right next to each other in the S-C rankings: A9o, KQs, and 44. If he calls with a pretty standard calling range of 15%, they are pretty close to the same value for pushing. That’s about the only time they’re together. A9o doesn’t change much whereas KQs and 44 get worse against a wider range, meaning you have to be able to raise-fold at the right times or play a flop more profitably with 44 than A9o, which doesn’t seem terribly likely.
Against a LAGgy opponent who resteals very wide, say 45%, it’s much more profitable to raise/call 100% with KQs than open-push, but the opposite for 44. A9o again doesn’t really matter. This assumes opponents rank hands by S-C, which isn’t perfect but probably close enough for these sorts of patterns to hold up well for most people. I guess the next step is to characterize hands by the shapes of these plots to figure out the best sorts of hands for mixing in raise/call, raise/fold, and open-push lines in these spots.
The plot is the $EV of shoving vs. folding from the SB in that hand using all the stacks as they were, as output by SNGWhiz. I’ve plotted the $EV as a function of the BB’s calling range for four different hands. I picked these three hands for a few reasons. One is the actual hand, A9o. Two of the others, 44 and KQs, are right next to A9o in the Sklansky-Chubukov rankings. They also have about the same $EV for shoving against a calling range of about 10-15%, which is about what I think we can reasonably expect to get called with. That $EV of around +0.5% says shoving isn’t terrible with any of these hands. The question is can we play them more profitably by raising less, even if we plan on calling every time BB pushes.
I’m assuming that raising less, more like a standard 3 BB or so, would make BB push over with a wider range than he would use to call because he thinks he has some folding equity. So let’s say that all hands play equally well after the flop. That’s not exactly true, but if it were it would make looking at the preflop situation the defining value for the hand. Say BB pushes the top 25% of hands against a standard raise. If you call every time, making that play with A9o is still about +0.5%. It loses a little, but not much. Making that play with 44 loses a lot of value, now only +0.3%, because you add a lot of hands 44 is flipping with, and you just end up paying the ICM coinflip tax 25% of the time instead of 10-15%. With KQs, that extra hand range is even worse because now it adds a lot of hands that are actually beating you (weak aces) to the hands you face but only adds a few like KJo that you dominate. The point is, if you want to mix up your play with a hand, do it by varying what you do with A9o there and not KQs. Open-pushing KQs is much better than raise/calling with it, but with A9o it doesn’t really matter. It’s still profitable to raise/call with KQs. It’s just not the most profitable play unless you think you save a lot money on unfavorable flops. I think this is something people usually overestimate because they don’t like to think about all the times they end up folding the best A-high or K-high when no one connects and they have to play OOP.
I also put 99 on there. With those better hands, higher up on the S-C chart, they actually improve quite a bit as the opponent’s range opens up. That means it’s even more profitable to make a small raise to induce a push than it is to make a big one that drives worse hands off, even with the ICM tax, because those extra hands are absolutely crushed by 99. Conventional wisdom is "ZOMG protect 99 against stupid overpair hands," but in reality that falls apart unless your opponent pushes some really odd range that includes JTs but not 88. Overall, for as bad as open-shoving while still relatively deep can be, there are times when it works well, but more often the best play is a standard raise down to where raise/fold couldn't possibly be correct.
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