Friday, October 17, 2008

Beating on shorty

Edits to correct. See comments for details. Apologies for errors. Thanks spritpot.

Short stackers are annoying, but they don't have to be unprofitable.

You can beat them if you fold and call their 20 BB 3-bet all-ins accurately. You can pin down their range using the 3-bet percentage statistic in either Holdem Manager or PokerTracker3.

1) Against a shortstacker who 3-bets all-in 13 percent of the time, for a range of 55+,A8+,KQ, and I raise to 3 BB preflop and my shortstacking villain 3-bets all-in for 20 BB:

I have to call 17 BB to win 24.5 BB (including the blinds). That means I need to win the hand 41 percent of the time when I call [bet/(bet + pot)=17/(17+24.5)=.41].

So using PokerStove to find hands that wins more than 41 percent of the time, I would call with only:

44+, A9s+, ATo+, KQs

*Checking my work: (.41)(24.5) + (.59)(-17)=~0

2) Against a shortstacker who 3-bets all in 10 percent of the time, for a range of 99+,A9+,KQ:

I should call with 22+, ATs+,AJo+

3) Against a shortstacker who 3-bets all in only 8 percent of the time, for a range of 88+,AJ+,KQ:

I should call with 88+, AJs+, AQo+.

In general, the cutoff for calling is around AT and mid-pocket pairs.

Please read the comments and follow-up spritpot post on this topic.


spritpot said...

Dude, I think your thinking about this case has become very up tight. You don't need your calling RANGE to have 41% equity to call, you need your specific HAND to have 41% equity to call. So for instance, eliminate QJ in the second scenario (however, add 22-66). It only has 33% equity vs. that range.

The only thing to worry about then is whether the shorty is making money from you folding all the time. Here's a list of the hands that have 41% equity or better vs. the range you specified for the 10% shorty: 22+,ATs+,AJo+. That's 10% of hands. If you are pursuing this strategy, would it be profitable for him to deviate to shoving a wider range? He is risking 20 bbs to win 4.5 bbs (in your scenario where your open is to 3 bbs). Assuming he's raising from the button, his EV of raising is:

f(4.5) + (1-f)(-20*(1-e) + 23e)

where f is how often you fold and e is his equity when called. Vs. your range of 22+,ATo+,AJs, top 30% of hands has about 40% equity so e = .4. So the above expression reduces to:

4.5f + (1-f)(-6.48)

This is equal to zero when f equals 60%. So if 22+,ATo+,AJs is less than 40% of your range, he has a profitable deviation. If it's not, that doesn't mean there isn't SOME profitable deviation for the shorty, it just means that deviating to shoving top 30% isn't it. That said, I think most shorties play pretty formulaicly and don't adjust to exploit individual opponents very much. If a shorty reshoves 10%, that's probably staying fixed and you can just stick with the range I specified above which has more than 41% equity vs. top 10%.


Fuel55 said...

I agree that once a shortstacker has a strategy it is largely opponent independent.

Some solid thinking here.

Gnome said...

Post corrected. Previous post calculated calling ranges with 41 percent equity against a shorty's 3-bet shoving range, rather than calling hands with 41 percent equity against a shorty's shoving range.
I truly hate getting these kind of math posts wrong, and I'm glad you pointed out my mistakes.
Thanks spritpot!