I guess it's time to break out the maths
We will use fairly simple assumptions based off poker stove and
http://www.flopturnriver.com/poker-s...lop-odds-19147
Assumption #1: Hero will only continue post flop if he hits the flop
Assumption #2: In the case of hero hitting the flop he shoves and villains fold
Assumption #3: In the case of the flop having no A or K, villains shove and hero folds
Assumption #4: In the case of preflop all-in action, Poker Stove equity applies.
Assumption #5: V1 has a range of AJ+, TT+, V3 has a range of AQ+, TT-QQ
Assumption #6: Hero will hit the flop (one pair or better) 30% of the time and miss 70% of the time
Poker stove equity
Quote:
Text results appended to pokerstove.txt
2,788,113,636 games 2.458 secs 1,134,301,723 games/sec
equity win
Hand 0: 32.080% { AcKd }
Hand 1: 34.069% { TT+, AJs+, AJo+ }
Hand 2: 33.851% { QQ-99, AQs+, AQo+ }
Scenario #1 Hero flats 3-bet: Pot is $135 when action gets back to Hero. Hero needs to call $45. Hero hits the flop 30% of the time and wins, otherwise hero folds. We can construct the situation just focusing on the 30%.
EV1 = ($135 + $45) x 30% - $45 = $185 x 30% - $45 = $55.5 - $45 =
EV1 = $9.5
So with assumptions, EV of just flatting preflop is $9.5
EV of folding preflop when action gets back to Hero is 0.
Therefore, EV of flatting preflop is greater than EV of folding preflop, therefore flatting preflop is better than folding preflop (I stand corrected Daniel
).
Scenario #2 Hero shoves preflop. Poker stove equity applies based on above ranges.
Scenario 2A: Hero shoves and both villains fold: I don't think it's too much of a stretch to say that this will happen "
at least" 10% of the time: pot is $135 when action gets to hero
EV2a = $135 x 10% = $13.5
Scenario 2B: Hero shoves and both villains call: V1 has $125 behind, V3 has $165 behind: Pot is $135 when it reaches hero, in order to put both players all-in Hero needs to bet $165
EV2b = ($135 + $125 + $165 +$165) x .32% - $165 = ($590 x .32%) - $165 = $188.8 - $165
EV2b = $23.8
EV2 = EV2a + EV2b
EV2 = $13.5 + $23.8 = $37.3
EV for folding = $0
EV for flatting = $9.5
EV for shoving = $37.3
I kept the shoving EV simple as I didn't feel like going through the rigor of V1 folding but V3 calling vs V3 folding and V1 calling and what happens on flop if we hit our A but they flop a set yada yada yada. The above assumptions are good enough to get a ballpark feel with confidence which line is optimal. OBviously, you can play around with ranges and equity will rise or fall depending on what ranges you use, but I felt the above was reasonable given the info presented.
Last edited by dgiharris; 06-05-2014 at 11:53 PM.