Originally Posted by CTS
Let's do some of the math behind preflop 4-bet shoving. I will be using PokerStove for most of the analysis. It's really nice free software, I'd highly recommend checking it out. Consider a 3/6NL game with $600 effective stacks. I open from middle position with A5 for $21. The button, an aggressive 22/17 player, reraises me to $77. I shove all-in for $600. Let's assume he will call me with { QQ+, AKs, AKo }. Against this range my equity is right at 30%. Actually, against just about any sane calling range I have around 30% equity with a suited ace.
equity (%) win (%) tie (%)
Hand 1: 30.1525 % 28.99% 01.16% { A5s }
Hand 2: 69.8475 % 68.69% 01.16% { QQ+, AKs, AKo }
So when my 4-bet shove is called my expectation is
0.30 * (600 + 21 + 6 + 3) - 0.70 * (600 - 21) = -$216
When he folds to my 4-bet shove, I win
77 + 21 + 6 + 3 = $107
Then if he folds to my 4-bet shove 2/3 of the time, the play is roughly neutral EV with A5 in this situation (2*107 - 216 = -$2 in EV). His calling range of queens or beter and ace-king is precisely the top 2.6% of hands. So for him to fold to my 4-bet shove more than 2/3 of the time and make my shove profitable, he needs to be reraising me with more than 7.8% of his hands. The top 7.8% of hands is the range { 88+, ATs+, KTs+, QJs, AQo+ }. When I have a loose, wild image, players are 3-betting me light with all sorts of stuff, including suited connectors and small pairs, most of which they will have to fold to a push so the shove shows an immediate positive expectation.
My opponents see that I am 4-bet shoving with a loose range and they may try to adjust and start calling me more frequently. The problem for them is that I'm also shoving with my monsters (aces, kings, and ace-king), so by calling me with say TT they will be a huge dog a significant portion of the time. This style of play is difficult to adjust to and I frequently got absurd amounts of action when I shouldn't have:
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