Let's compare shoving to min3betting, shoving every flop. Let's assume a couple things about our opponent's range: he is calling preflop with 99+ AQ+, and he is calling a shove with 99+ AK (IMO he is committed with any pair if we have AK in our range, and he should know this!). He is shoving JJ+ AK vs our min3bet, and call/calling our min3bet/flop shove with 99/TT and AQ.
There is a side pot once we have min3bet, and thus it probably is worth fighting over and shoving. We assume we are shoving EVERY FLOP.
We should look at whether we make any money from our opponent calling more hands against our shove.
99/TT (12 combos): we stack 99/TT around 60% of the time. We get it in on average with about 80% equity IMO against this hand.
AQ (16 combos): we get it in against this hand around 35% of the time postflop. We average around 10%*87.5% + 96%*12.5% = 20.8% of the equity. Rest of the time he folds.
So of these extra combinations of hands we get action from,
6/28 of the time we get an extra 7106 chips 40% of the time (+775 cEV). The remaining 60% of the time, we get an additional 23181 chips in with around 80% equity (+2276 cEV). We need to compare this to the cEV we have when we get it in preflop against these hands (6/28 of the time we are getting in 23181 chips with 81.8% equity, +3159 cEV).
16/28 of the time, we get an extra 7106 chips 65% of the time (+3359 cEV). The remaining 35% of the time, we get an additional 23181 chips in with around 20.8% equity (-3446 cEV).
Seems like with our assumptions, shoving preflop is slightly better than min3betting, and pushing every flop: we fold out worse hands too often against 99/TT on boards, and against AQo our reverse implied odds are a bit too bad.
//edit: did this at 630am with some basic assumptions. Please query me about any math questions!!
