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Hello! I was bored today so decided to write this thingie..Please give input and tell me if I got any wrong calculations or anything.
Stopn "call"?
Played and interesting hand today where at first I thought villain made a huge mistake after calling preflop, and not shoving or folding. http://www.pokerhand.org/?1805509
But after doing some calculations realised calling is just as good as pushing. Because when you shove 9s and get called youre opponent will have either a higher pair or a-x almost all the time. Meaning by just calling you can fold the a-x-x flops where you only have about 8% eq (vs my estimated range,).
Facts: 1. In general I will shove the flop every time after he calls my 3bet
2. Villain was running pretty tight at that time 18/15
3. Im playing 23/16
My estimated 3bet range: I picked out an tight range for me start with wich consists of 4.5% of my total hd. Qs+ aq+ ,(2) jacks, (1) Ts, (2) jts, (2) 910s, (2) 67s.
= 33% pairs that beats him
= 53% aq, aqs, ak, aks
= 13% mix of SC
His eq for pushing: His push would be 331.50 euro, If I call hes riskin that to win 778e. Meaning he needs 42.6% eq (if Im calling every time). If I fold he wins 217.50 euro
How often will I call his push? (in terms of my 3bet range not that I have ak) have to call 229 to win 778 =aprox 30% ,meaning I have to call with atleast all pairs and aq+. I should prob even call a hand like 6-7s cause that has 32% eq vs his likely aq+. Lets say I call jts a-q+ and all my pairs, Im folding 6-7s and 9-ts. Meaning Im calling 4.2/4.5 = 93% of my hands.
So 7% (when I fold) of the times he will win 217.50 euro
93% of the times he will get it in with 40% eq. 0.40x778=311 euro. (hes pushing 331.50 euro, he expect to win 311 euro longterm every time I call)
93% he looses 331.50-311=20.50 euro
7% he wins 217.50
Lets say he push 100 times: 217.50x7= 1522.5e profit when I fold
20.50x93=1906.5e loss when I call
1906.5-1522.5= 384/100= -3.84e
As you can see his push with 9s into my range is extremely close, if we however look into his expectation if he just calls.
After he just calls my 3bet: Eq he needs to call floppush: calling 229e to win 778 = aprox 30%. This means he can call my push everytime unless:
1. ace flops (where he only has 8% eq vs my range)
2. 2 broadway cards (Ts included) like q-k-4. except on t-j-x flop where he has almost 40% eq
The flop will come down with either an ace or 2 broadways cards (not included 10-j-x) about 40% of the time. Meaning that if villain is playing optimal he will call my floppush 60% of the times. So 40% of the times he have to fold, loosing the 102.50 euro he invested when he called my 3bet (remember Im comparing pushing vs calling).
His eq vs my range when he calls my floppush:
flopp= 1 broadwaycard and x-x for example k-4-7 (happens about 7/10)= 9s has 45% eq
flopp= 9-x-x (happens about 1/10= 9s has about 90% eq
flopp= all cards under 10 (happens about 2/10 = 9s has about 55% eq
Summary: He has a little bit over 50% eq with 9s once he calls my floppshove (51.5%)
This means that those 60% when he calls my flopshove he will have 51.5% eq. Remember pot is 778 euro when villain call. So he expects to win very close to 400 euro.
40% of times he looses 102.50 euro (by choosing to call preflop)
60% of times he gets 400 euro from the main pot when he had 331.50 euro after his raise preflop (before he decided weither to call, fold or push). This means he will on average win 68.50 euro everytime he gets a good enough flop that he can call my floppush with positive expectation.
0.40x102.50= 41 euro loss
0.60x68.50= 41.10 euro win
Meaning that its close to totally breakeven weither to the call/fold/push with 9s vs my range. This means that as soon as youre playing against someone with a wider 3bet range you can push with expected profit everytime (remember the range we gave me was very tight when he isolated the limpers, not including even ajs) and with standard 100bb stacks I can never call a 4bet with that). So in reality you shouldnt fold 9s that often as soon as someone has a 3bet range wider then 5% of his entire hd.
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