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Old 12-09-2005, 02:35 PM
A_PLUS A_PLUS is offline
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Default ATs...J4o...What does it matter???

I tended to disagree with the consensus from this post
BillyJex presents "Deep in a Party $109"

So I decided to run through some numbers.

Here is the quick situation. 12 players remaining (300/600 Blinds) Somewhat active CO raises to 2000.

We are in the SB with ATs. CO has 23K Behind, We have 13,512 after posting.

So, before thinking about how CEV relates to $EV in this situation, I wanted to see if it was in fact +CEV to push here.

OP mentioned that the CO had been opening 1.5-2x per orbit.

Let's do some math...

Last few orbits, we figure to have had between 8-6 players at our table, if CO has been opening 1.5-2x per orbit, we assume he is opening about 25% of his hands.

Of these hands, lets assume he will call with 88+, AJ+, which is 5.8% of hands. So, after he has raised, we will assume he will call 23% of the time (5.8/25).

CEV CALCULATION
77% of the time, CO will fold
Our stack size will be
13,512 + 900 (blinds) + 2,000 (his bet) = 16,412

23% of the time, CO will call
Our stack size will be
29,624 (total pot) * .3321 (our equity vs range) = 9,834

So, our expected stack size is = (.77) x 16,412 + (.23) x 9,834 = 14,900

That is an EV of +2.5BB. But it got me thinking. Our equity vs his range doesnt really come into play much here (it only matters 23% of the time). It turns out, given the assumptions I have made. It is impossible to have a hand that makes this play -CEV.

We would need under 20% equity to have a negative EV for this push. No hand has <20% equity vs this range.

So...what does this mean???

well, for one. In a play like a resteal (which this isnt really a resteal, just plays like one), your read is much more important than your cards MUCH more important.

This is a few examples of how EV changes with your cards

ATs AA A6 76s 82o 32o
equity 33.2% 84.6% 26.5% 31.4% 0.228 .244
% raising 25.0% 25.0% 25.0% 25.0% 0.25 0.25
EV 1374 4907 916 1250 659 769

Taking out hands that are actually big favorites vs the range that will call (AA-KK), there is only a 1BB difference between any hand you can hold, and they are all +EV.

On the other hand, if you do have ATs, the estimate for how many pots the CO will open in this spot is very important

equity 32% 32% 32% 32% 32% 32% 32%
% raising 50% 40% 35% 30% 25% 20% 15%
EV 2096 1895 1751 1560 1292 890 220


If we are wrong, and the CO has only been opening 1x per 6 hands, this is a pretty much EV neurtral push, whereas, if he is opening 2x per 6 hands, we have +2BB EV.

It just shows, that we really need to concentrate on our table. Yes, having ATs in the SB buys you a little wiggle room as far as pushing back at a late position raiser. But we are much better off if we know that he will open X% of pots here, and fold to a push.


***BTW, I think CEV and $EV Diverge a great deal here, and even if we sure of his opening and calling range, I am not convinced this a good push from a $$ perspective.
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