$2/$5 MGM National Harbor
UTG1 opens to 20. Hero ($925) calls A9ss in the HJ. BB calls (covers).
Flop ($60) Ac9cTs
BB checks. UTG1 bets $40. Hero calls. BB calls.
Turn ($180) 3c
Checks to hero who bets $100. BB calls. UTG1 folds.
River ($380) Td
BB checks. Hero?
I thought it would be interesting to look at the profitability of Jon’s play given different assumptions about the villain. I ended up assigning villain this range by the river in my first scenario. The range is somewhat tight and conservative, as that was Jon’s read on BB at the time.
On the podcast Jack and Jon mentioned that it could be a “chop block” however, I don’t see much of any Ax below A9 calling on the turn with UTG1 left to act. The best possible hand BB could call with on the turn that would be chopping with Jon’s hand is Ah8c or Ad8c and I think those hands are pretty unlikely to call turn and may not even call the flop bet from UTG1 after Jon calls. However, because BB may have all suited Ax in his preflop range I decided to account for it in the range. I think it’s possible for BB to be stubborn and get to the river with Ax combos a small frequency of perhaps, 4% of the time. Because there are 54 total combos of suited and offsuit Aces below Ace-Ten, I will represent this by including two combos of Ax8c. Another hand that Jon bets off a chop are the suited and offsuit varieties of A9, which are somewhat likely to get to the river this way as played.
The offsuit hands I assigned were KcQx and KcJx. I thought it would be most reasonable for the villain to call gutshots with the backdoor nut flush draw. If the villain has more of these kinds of hands that Jon beats, then checking back has a greater expected value. Furthermore, as the expected value of checking becomes greater it means Jon’s shove needs a higher EV to become the superior choice.
I thought it would be useful and practical to weight combos equally in the initial analysis, with the exception of the low frequency of Ax that is represented in grey as the Ax8c combos. While I think Jon’s correct in assuming that the villain would raise flushes at a significant frequency on the turn, there are also arguments for the villain playing the other hands in his range differently. Both suited and offsuit versions of AQ and AJ could be 3bet preflop at a low frequency and they could find a tight fold on the turn after Jon bets and UTG1 is left to act. Similarly, the offsuit KcQx and KcJx could raise as a semi-bluff on the turn sometimes. As for the low flushes, perhaps some of them are folded preflop and on the flop, or they could be raised on the turn. T9o might not be in the villain’s preflop range, but if it is I think it’s likely to be played in this manner once it is called preflop. In conclusion, because nearly all the hands could take a different line at some frequency, I think it’s most useful to look at the hand as if they are equally weighted and perhaps adjust afterward.
In this analysis I assume villain calls with the second nut flush, the nut flush, T9, and flushes with the Tc. Flushes with the Tc make good calls because they block full houses. Against the hands the villain folds in pink, blue, and grey (better, worse, and chops), Jon makes $380 which happens 73.4% of the time given this range (+$278.92). However, 26.5% of the time Jon loses $765 when he shoves, making the overall EV of his play +$76. So while shoving seems to be plus EV given these assumptions, it remains to be seen if it is better than checking. When Jon checks he makes $380 the 12.2% of the villain has a worse hand (blue) and he makes $190 the 12.2% of the time the villain has a chop (grey), which comes to an overall EV of $70 for checking. So given this villain’s river range and his calls the EV of betting all-in is $6 more than checking, so the decision is quite close.
We could also look at what hands the villain might call with if Jon bet $300 on the river (pictured above). I will start by assuming that the villain will call all his flushes and full houses for this size, while folding all of his worse hands. This has the villain folding 59% of the time and calling 41%, such that the overall EV of the bet is $123, which is somewhat higher than the EV of Jon’s all-in bet. I also don’t think it’s out of the question that the villain would hero his worse flushes (45c, 56c, 75c) some of the time for $300, which would make the bet even better. What would make the bet worse is if villain lands on the river with fewer Ax hands, or if he decides to get sticky with the Ax hands. Given Jon’s read of the villain as a tight player, I don’t think that the latter is very likely.
I think one takeaway from this is that opponents are less elastic in their calling ranges than they should be in many situations. When confronted with these situations in which opponents are less sensitive to bet size it can become higher EV to bet larger with value hands and smaller with bluffs.