When do you have to push with a big stack?

[Madd]

I'm just using pen and paper (and maybe sometimes Excel).

E.g., if you fold 34s, you have 6400 chips = 80% of all chips left. HU there is a linear relation between the chip ratio and the likelihood to win the HU duell, i.e. with 80% of all chips you will win in 80% of all cases.

On the other hand, 34s wins in 38% of all cases against a random hand. So, by calling against random two you win in
38% + 62% * 70% = 81,4% of all cases.

Though I'm not able to calculate these numbers accurately in the given time at the table, I would have called in this spot. However, I agree that by sometimes folding marginal hands you might increase your folding equity later.

[poincaraux]

ah .. right! i was trying to think about skill, but if you ignore skill, chip value has to be linear here. I'm not sure exactly how to factor skill in, but this is certainly a good start. I re-did the calculations myself just to check and here's what I got:

First hand: A4o with 7700 in the BB
Fold: 91.25%, $48.25
All-In: 96.75%, $49.35

Second hand: 52o with 7400 in the sb
Fold: 90.00%, $48.00
All-In: 90.14%, $48.03

Third hand: 34s with 6800 in the BB
Fold: 80.00%, $46.00
All-In: 81.59%, $46.32

Fourth hand: 33 with 5600 in the sb
Fold: 67.50%, $43.50
All-In: 72.22%, $44.44

Fifth hand: A2o with 3200 in the BB
Fold: 35.00%, $37.00
All-In: 43.94%, $38.79

(the differences between our numbers are rounding errors .. I used PokerStove to get my numbers)

So, all of these were pretty close. The last hand is pretty interesting: If I put him on a slightly smaller range like any ace, any suited cards, any two broadway cards and pairs 55 or better, i'm 48.039%, but the blinds make it worth it:


Fifth hand: A2o with 3200 in the BB
Any ace, any suited cards, any two broadway cards, pairs 55 or better
Fold: 35.00%, $37.00
All-In: 38.43%, $37.69

If I give him any two broadway cards, pairs 55 or better, any suited ace, any suited king, A9o-A7o, then I should fold

Fifth hand: A2o with 3200 in the BB
two broadway, 55+, Axs, Kxs, A9o-A7o
Fold: 35.00%, $37.00
All-In: 33.62%, $36.72

But again, it's not huge.

It's good to work this stuff out beforehand. I have a better idea of what's a close decision and what's not. I think this also points out how much big blinds suck. The A2o vs. a random hand case in particular .. A2o has a 9% advantage over a random hand but that only translates into a $2 difference in expected value (2.5% of the $80 prize pool) even when you're all-in.

Hmmn .. it's obviously a good idea to work this out beforehand .. I'll work it out for a random opponent and then for a couple of distributions .. anyone have any suggestions for good opponent distributions to use (either on the calling or pushing end)?

[poincaraux]

Ok, I did some more work on this. Andrew Prock was nice enough to host it for me, so you can see the results at Heads-Up Jam or Fold Calculator. You can plug in tournament structure, blind levels, stack sizes and rough opponent distributions and it will show you the equity of each hand.

There's a lot of interesting stuff there (I think). Most of it tells me to be more aggressive, but I learned some things in the other direction as well. For instance, you can fold totally worthless hands when you have a very small stack (e.g. small blind, 8000 total chips, opponent will call with anything, blinds 200/400, you have 800 chips has you folding 13 hands).

I think this is useful, but I'm obviously a bit biased. Any thoughts?