How much dead money do you need in a pot to make shoving profitable?

by ~ October 11th, 2009. Filed under: Fold equity, aggression and bluffing, Instructional posts, Philosophy and approach, Poker theory.

In two hands in my Daily Grind I 4 bet on the small side, indicating that I want action. In one case I have AA, in the other AK. In the AK one I say that the other reason for 4 betting small is to be able to fold to a shove.

But this may be incorrect depending on the dead money in the pot. I looked at the effect of dead money with a hand on the flop, but it’s relevant preflop against short stacks and relevant in 3 bet or 4 bet pots preflop as well.

Start with effective stack sizes of 100 bbs, I raise from early/mid position, get 3 bet from behind, (not in the blinds, therefore adding the blinds to the dead money), I 4 bet.

You can play around with the bet sizing, but the pot is around 34 bbs and we have 75 bbs remaining in our stack. First he has to call our bet, meaning the pot goes to 51.5, and if he shoves we have to put in 75 to win 51.5 + his added 75 = 126.5. The 51.5 is dead money.

We have to put in 75 to potentially win 126.5, which is 59.3%, meaning if we have better than a 40.7% chance of winning, we have to call. Against various 4 bet or shoving ranges:

The green shaded areas are winning percentages above 30%, which is what I had originally miscalculated the pot odds to be, but oh well. It still highlights the stronger situations. Don’t pay too much attention to the green, in other words.

Probably the most common scenario is AK against QQ+,AK which is 38.8%. There are certain levels and games where you will find players who won’t shove anything less that AA/KK, but not often. And as soon as QQ comes into their possible range, AK’s chances improves dramatically.

And once AK comes into their possible range, AK/JJ/TT, even 22 starts to fare well. Combinatorially, there are 6 AAs, 6 KKs, 6 QQs, 4 AKs and 12 AKo so 18 overpairs and 16 overcard-connectors in this range, and it’s the underpair-vrs-overcards coinflip situation that helps out any pair from JJ down to 22.

I guess that’s one of the reasons for 3 betting larger, like 3.5x the previous raise. Using the starting stacks from above,

now if he shoves we get a pot of 49.5 + 90 = 139.5 and we have 62 left. We’re getting better than 2 – 1 on our money so anything above 31% is +EV. This gets AK into a nil EV situation against QQ+, so open raising larger and 4 betting larger gets us into a better situation with AK.

And if he does this with AK at all, then any pair fairs well, though the more his hand range swings towards allowing more big pairs, the poorer old 22 does. This is something that tournament players know intrinsically when the stacks get short. I guess you could view it as a tourney situation with the stacks at 4 bbs, though any Ace would be a good hand in that situation. Maybe a better comparison would be around 10 bbs, when you get to the shove/fold preflop situation.

On the other hand, AQ doesn’t fare well unless the range of your opponent is heavily skewed toward pocket pairs only, or is so wide as to include other big Ace hands.

It’s not always this simple, of course. Often one player will have less than 100bbs, or you might both have over 100bbs. Or there might be a third player involved, and if all 3 players have different stack sizes, it gets more complicated.

Whew. Okay, this is not an area of my expertise, so if any reader sees any miscalculations or has questions, please leave a comment or send me an email.

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