The hand from yesterday's sit and go that stuck in my mind was the 99 hand from the button, three handed. I had a few comments about it from
Fuel, and I also posted a thread on
2+2 which (amazingly) generated some sensible replies. So, here it is again, together with some summaries and further thoughts.
PokerStars No-Limit Hold'em Tourney, Big Blind is t200 (3 handed)
Hand History Converter Tool from
FlopTurnRiver.com (Format: 2+2 Forums)
Hero (t3600)
SB (t4853)
BB (t6547)
Preflop: Hero is Button with 9
♦9♠.
Hero raises to t600, SB calls t500,
1 fold.
Flop: (t1400) K♣, 6♣, 5♠
(2 players)SB checks,
Hero bets t800,
SB raises to t1600, Hero ???
As playedThis is a difficult decision -- a simple call is out of the question, so it's fold or all in. Fold leaves 2200 chips behind, and of course all in has me playing for my tournament life (I can assume that the SB won't fold getting better than 3:1 odds). For geeks like me, at this stage of a sit and go you need to think about more than just chip equity -- you need to use the
independent chip model. Fortunately (after the fact) there are
handy calculators for this, and, using one of them, I can work out that we'd need to be winning the pot about 35% of the time for a shove at this point to be a break even move. As all my estimates are going to be rough ones, I'll take that as a guideline, possibly padding it a bit on the high side since I feel I have a bit of a skill advantage over my opponents (always!) so there's a premium on staying in the game.
If I'm already behind at this point (to a king, a pair tens or higher, or a set of 6's or 5's) I'm basically drawing to 2 outs and have 8% equity in the pot. If I'm ahead, my opponent likely has at least six outs (two overcards or underpair plus overcard), and possibly many more (flush draws, combo draws etc.) So my equity, if ahead, is something between 50% and 75%. Call it 70% for optimism.
Basically that suggests that I need to believe that I'm ahead a little less than 1/2 the time (if my estimates are correct and I'm ahead 1/2 the time then I have a 39% chance of winning).
As we know, at the time I folded, and I'm relatively happy with that. I don't think that my opponent's raise
in this game, and under these circumstances, is a bluff or semi-bluff (or underpair) half the time.
ReflectionThe main difficulty in the decision is caused by the fact that the bet sizing to this point left me in an all in or fold situation. There are two ways around this: bet more (i.e. everything) preflop; or bet less.
Shoving certainly merits consideration. If I assume a relatively tight calling range (true at the table I believe) of something like TT+, AJ+, KQ then I'll only get called about 1 time in 14 by either blind individually, so 1 time in 7 collectively. When I'm called my equity against that range is 33%. So, 18 times in 21 I'll gain 300 chips, 1 time in 21 gain a bit more than 3600, and 2 times in 21 lose 3600. The gains certainly outnumber the losses but ICM might have a bit to say about this (in fact it seems to suggest that pushing is about the same as folding preflop). But, the wider we make the opponents' calling range the happier we are.
What about the other approach? Limp and give up on all but the best of flops (containing a 9 or three low cards)? That seems a bit peculiar but perhaps worth considering if only to vary our play.
Finally, I think the winner is a smaller preflop raise. For the sake of argument let's look at a raise to 400 i.e. 2BB and suppose the hand plays out similarly to the original example. The SB calls, then checks. I bet 500 into a 900 pot and he raises to 1000. The pot is now 2400, and I still have 2700 behind. A push at this point actually leaves me in effectively the same position we discussed originally but
probably has some fairly significant fold equity -- including folding a number of hands that beat us at present (e.g. TT, JJ, KQ, possibly KJ). Furthermore, some drawing hands that would have been able to call correctly originally are now not getting the correct odds.
ConclusionIn short handed games with an intermediate stack (15-20 BB) and a decent, but not premium hand on the button, consider a smaller than normal preflop raise.
Labels: math, sng