[ilya]

[ QUOTE ]
ilya, telling us that an SNG is clearly superior to a push based on the math and not actually posting the math isnt gonna help prove your point.

you're basically asking everyone here to go and do the math by themselves rather than you just posting it here...

[/ QUOTE ]

ok fine you win, here's the math. first we have to give him a range wide enough that pushing preflop is +$EV at all. so, let's put him on 22+/A2+/K4+/Q6+/J7+/T7+/97+/87. Notice that I made this range relatively heavy in dominated hands.
Then:

22+, A2+, K4+, Q6+, J7+, T7+, 97+, 87

SHOVE:

+0.3

stop and go:

on the flop he will fold non-pairs whenever he doens't make a pair

and he will fold pairs never


so, pairs make up 72 combos, he always calls: 35% when he does this

J7+....87 make up 160 combos: 30% when he does have a pair

6 outs 3 times, will get a pair 33% of the time, 55 combos pair 105 combos no pair

Q6+ makes up 72 combos: 40% when he does have a pair

5 outs 3 times, will get a pair 30% of the time, 22 times pair 50 times no pair

K4+ makes up 140 combos: 30% when he does have a pair

6 outs 3 times, pair 33% of the time, 50 pair, 90 no pair

A2+ makes up 141 combos: 40% when he does have a pair

5 outs 3 times, 30% pair, 41 pair 100 no pair


so altogether he has 585 combos

on flop he folds 345 combos

on flop he calls 240 combos

when he calls we have

72*35 + 55*30 + 22*40 + 50*30 + 41*40 = 2520 + 1650 + 880 + 1500 + 1640 = 8190

8190/240 = 34% chance of winning

so 159 times we lose it all

81 times we double up


when we lose it all: 0 equity

when we double up: 31.6% equity

when we take it down: 27.6% equity

159*0 + 31.6*81 + 27.6*345 = 2559.6 + 9522 = 12081.6

12081.6/585 = 20.6%, I.E. +1.6%

vs

EV shove preflop 19.3%, I.E. +0.3%

And this despite the fact that I deliberately made all of my rough equity estimates err on the side that would favor pushing preflop. E.g., I underestimate our equity when opponent flops a pair & overestimate how often he will call on the flop with a pair in the hole.

Note also that BB is short enough that whether we shove or coldcall preflop will have little to no effect on his overpushing range.