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Is my math correct (OK to call 3-way AIPF if needed but I must fold the flop?)

$50 max BI (25c-50c) full ring PLO on WSOP.com is down to 5 handed at midnight. No maniacs or fish at the table. I had a nice run and am at $175. V1 UTG HJ ($65) opens $1.75, I call CO w Kh, Qs, Th, 8c. Folds to BB ($60) who 3bets to $7.25. HJ 4 bets pot to $23.75 (always AA). Despite not closing the action I call given I have several ways to crack AA. BB calls, so 3 ways to flop ($69 after rake). Given how short the 2 Vs are, this seems like 2 clear calls PF (the initial raise and then cold calling the 4 bet knowing BB would at least call as well).

Note I considered the risk that the BB would 5 bet shove when I overcalled the 4 bet PF. Had he pushed the HJ clearly calls, so last to act I would have needed to call another $40 for a total pot of 190-8 rake = $182, which requires 22% equity to call. I believe I have that much equity vs. AA and the BB's strong but wider range (a lot of smooth rundowns, double paired/double suited, etc.).

Question 1: Is my analysis correct on calling the 4 bet, committing me to call a push 5 bet from the BB? In other words does my had have more than 22% equity (a strong broadway rundown plus the 2nd NFD) vs. the hand ranges I described?

Flop = 3J7r (no H). As expected, BB pushes his last $35 and HJ pushes his last $40 so pot now $144. With the J as my Broadway pivot card I see nut potential and get (too) excited. Since the math here = the AIPF math, I still need 22% to call. I have a gutter 9 to the nuts and several other ways to get the nuts by the river so getting almost 5-1 it seemed a no brainer call during the game.

However, in analyzing it after the fact, I think I had a clear fold after the flop. The immediate gutter to the nuts could be rivered by whatever BDFD will become available on any turn, and if I miss the 9 on the turn I will need runner-runner B/Way cards to hit the nut Str8 (assuming I dodge the BDFD). Remembering HJ likely has AA, on the turn I had 4 9's to the current nuts, plus 2 (NOT 4) Aces and 3 each of K,Q,T that would leave me with a 11 card wrap to the nuts on the river. Thus on the turn I have 15 cards/45 = 33%. If I hit one of those 15 cards on the turn, then I probably lose 5 outs to whatever BDFD hits on the turn, leaving me only 10/44 = 23% on the river. 33% * 23% =7.5%, so I had nowhere near the odds needed to call the flop. Despite what looked like a clear call getting almost 5 to 1 it looks like I needed over 13-1.

Q2: Is my math here accurate or am I forgetting something?

Q3: If the math is right, that means I should call AIPF but I need to fold to the flop bets as I only have a gutter to the nuts or runner-runner A,K,Q,T for B/Way (which could end up 2nd best if we go R-R BDFD). So I should call the PF action even if its AI, but save $40 (almost 1 full buy-in) by folding after the flop?

Thanks for the help as I try to develop the skill of doing these essential calculations quickly AND ACCURATELY during a live hand.


  • FreeLunchFreeLunch Posts: 1,311Pro
    You are forgetting to think what the SPR is going to be after 3 calls and how your hand plays at that spr. You also are missing the goal of poker which is to profit from other mistakes. What kind of mistakes are people going to make on what flops at a low SPR?
    Thanked by 1CycleV
  • CycleVCycleV Posts: 1,196Subscriber
    I want to start by saying that I'm certain you have a much better command of equities and such than I do. Also, I only play live full ring, so shorthanded online is certainly different. But you have a double gapped, single non-nut suited hand, facing a 3! and a 4! when you don't even close the action, at a table with no obv fish or maniacs. I have no idea how we didn't fold after the 4!.
    Thanked by 1FreeLunch
  • High__RollaHigh__Rolla Posts: 798Subscriber
    edited May 2019
    The math for a preflop Allin or flop all-in can be easily answered by assigning ranges with propokertools. For example,you need 22% equity to call- off OTF as you identified. If you give one player AAxx and another player a top 10% range without aces then you are short of the 22% equity needed to call on the flop.

    Your first question is much more difficult to answer because there are several potential outcomes:
    1. You call, BB ships, HJ ships
    2. You and BB call, BB ships flop, HJ fold
    3. You and BB call, BB checks flop, HJ ships
    4. You and BB call, BB ships flop, HJ ships flop
    5. You and BB call, both players check to you.

    So, the math on calling the 4bet preflop is too difficult without a solver program. I tend to agree with the others that you should just fold to the 4bet. At best, it is a high variance marginal EV spot; stacks aren’t deep enough for your position to really matter.

    Thanked by 1FreeLunch
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