The Math of a push (Schwza's A8s final table push)

[A_PLUS]

I have been working on a tool to analyze open pushing in a MTT.

I of course make some simplifying assumptions, such as constant calling range, only one caller, etc. I dont think they are big enough problems that they take away from the usefullness of the analysis (the numbers arent exact, but probably give a correct push/fold signal 95% of the time).

So here it goes.

Schwza's original post

I assume (rather generously) that your opponents will only call you with hands in which that have at least 50% equity, i.e. A8+, 22+.


CEV Analysis

Steal the Blinds 2250
% of time 56.5%
subtotal 1271.082131

Showdown pot 21740
equity vs range 36.8%
EV of showdown -1969.68
% of time 43.5%
subtotal -856.957755

TOTAL CEV 414.1243757


$EV

Current stack 9970
$EV $837.48
Current pot 2250
Steal success 12220
$EV $1,026.48
% of time 56.5%

Showdown Pot 21740
equity 36.8%
expected stack 8000.32
$EV $672.03
% of time 43.5%

$ equity of push $872.27
$ equity of fold $837.48
$EV of push $34.79



So pushing this earns you 34$ over folding. To calculate $EV, I used a basic (% of total chips)*(money remainin).

Questions, thoughts?

[johnnybeef]

you mean like this?

[A_PLUS]

I wish, Eastbay's tool is much more advanced than mine.

I would have purchased his a while ago if I was a regular SNG player, it is worth its weight in gold. I am working more on MTT situations, and figured I would learn more working through this stuff myself rather than just using someone else's tool.

[locutus2002]

I think the model is interesting. Most players have a mental map that does a better calculation based on their perception of the situation at the table.

I think the calculation of $EV(expected chips after being called) is wrong.

I think $EV(Win stack) + $EV(0 chips) >> $EV(expected chips) in any tournament with most of the money going to the higher places.

Intuitively, if you have 15XBB versus 7XBB then you have choices: raising, folding, bluffing, calling.

If you have 7XBB you only have one choice.


If you have 15XBB you don't push a8suited.

[A_PLUS]

[ QUOTE ]
I think the model is interesting. Most players have a mental map that does a better calculation based on their perception of the situation at the table.

[/ QUOTE ]

Yes top pros. Your average online player does MUCH MUCH MUCH worse than an adequate structured model. I know very good players that make huge mistakes in open pushing situations. Sklansky wrote a while back, how most top pros play very far from optimal push or fold poker. I will be the first to admit that my model isnt perfect, but I will bet it is better than all but the very good players for push/fold situations.

[ QUOTE ]
I think the calculation of $EV(expected chips after being called) is wrong.

[/ QUOTE ]

ahhh...good point, let me change that. Thanks

[A_PLUS]

I took Locutus' advice, and it made it a 90$+ push

$EV

Current stack 9970
$EV $837.48
Current pot 2250
Steal success 12220
$EV $1,026.48
% of time 55.7%

Showdown Pot 21740
$EV(win) $1,826.16
$EV(loss) $230.00
equity 36.8%
$EV(called) $817.39
% of time 44.3%



$ equity of push $933.89
$ equity of fold $837.48
$EV of push $96.41