What’s Your Play? Jacks With Heavy Action in Front Results

Edit: As usual, my attempts to perform a complicated equity calculation in under an hour resulted in a mistake. I don’t have time to fix it at the moment – the Borgata Main Event starts shortly – but any calc involving UTG+2 is wrong because his actual calling range is KK+, since I have him shoving AK and QQ pre-flop. I’ll fix this when I have the chance.

Thanks for all the comments on What’s Your Play? Jacks With Heavy Action in Front. This is going to be a little less thorough than usual because I’m posting in between sessions at the Borgata, but I’ll make two general statements with regard to the comments received. The first is that a lot of people ask good questions about how these guys have played in previous hands. The answers would indeed provide helpful context in interpreting these stats, and while I don’t have them, it’s good that you’re thinking about them. The second is that this is both a hand reading and a math problem. If your response didn’t include a discussion of ranges and a calculation of equity, then you’re doing it wrong.

The way I’d think through this is first to decide what my play would be if I had 100% confidence in the stats I gave for these players. As many of you point out, $5 MTT players don’t tend to be this tight, so there’s reason to doubt them. If it turns out that even against tight players we have a shove, then our work is done. Otherwise, we can figure out how close it is and decide how much of a margin of error we want to allow for in the stats.

Sorry for the cyberlingo, by the way. For those who don’t know, VPIP = Voluntarily Put Money in Pot, a measure of how many hands a player plays. PFR = Pre-Flop Raise, a measure of how often the player raises pre-flop.

The UTG raiser has an 8% overall PFR, which means he’s probably tighter than that UTG. Let’s give him {88+,AJs+,KQs,AQo+}

UTG+2’s play is the strangest, as he’s cold calling an UTG raise for a large percentage of his stack. This should be a monster hand, but as Prabhat points out it could easily be something weaker than he doesn’t feel comfortable getting in pre. I’m going to assume he jams strong but vulnerable hands like AQ/AK and TT – QQ and calls with the biggest pairs and with more marginal hands he doesn’t want to get in pre. This is a rough estimate, but if turns out he sometimes flats QQ and jams KK, that’s not going to make much difference. I’ll give him {KK+,99-77,AQs-AJs,KQs,AQo}.

The player doing the shoving isn’t quite as intrinsically tight as UTG, but he also can’t expect to win without a showdown here. I’ll give him {88+,AQs+,AQo+}.

For the sake of simplicity, I’m going to assume that if we jam, everyone with live cards will get it in with QQ+ or AK and fold everything else. If you disagree, that will change the result dramatically. That’s 3% of hands.

UTG folds roughly have the time. UTG+2 folds roughly 75% 78% of the time. There’s also roughly a 10% chance of one of the other four players yet to act waking up with a hand in that range.

(The following calculations ignore card removal, which is complicated but not insignificant here. )

That means you’ll get it heads up with UTG+3 about 34% 35% of the time (.9 * .5 * .75 .78 to find the odds of everyone else folding). You have 53% equity against his range, and there will be 8605 in the pot, so your EV from that is 1550 1596.

Another 34%35%, you’ll race against UTG and UTG+3, with 28% equity in the main pot of 10945 and 36% in the sidepot of 2654. That’s .34 .35(3064.6 + 955.4) = 1367 1407.

If the action folds back to UTG+2, he’ll call just 11% of the time. The other numbers are the same as in the previous case, so .11(3064.6 + 955.4) = 470 Since I’m assuming UTG+2 shoves AK and QQ the first time around, he calls with just AA and KK, which is 22% of his range. There’s a 45% chance of the action folding around to UTG+2, and if he calls, then there’s the same 10945 in the main pot and 2654 on the side. So .45(.22(.17(10945) + .19(2654))) = 234.

About 4% of the time, you’ll race against UTG+3 and someone who came in cold. Then the main pot is 11545 but the sidepot stays the same. .04(.28(11545) + .36(2654)) = 144. Edit: Actually this is further complicated because the pot will be a touch smaller if it’s the BB or SB who comes in cold. Since this is already a rare scenario and it’s a small difference, I’m not going to bother calculating it.

There’s about a 15% chance that you’ll have to race against two others plus UTG+3. That gives you 26% equity in your side pot of 3981 and 22% equity in the main pot of 13245. These numbers change slightly if it’s someone who hasn’t acted yet who gets in there with you, but not enough to be worth calculating. .15(.26(3981) + .22(13245)) = 592

 

There’s a 1% chance of getting it in with a cold caller and UTG+ 2. That makes a main pot of 13085 and a sidepot of 3981. .01(.16(13085) + .17(3981)) = 28.

4% of the time, you’ll get it in with a cold caller and UTG. .04(.22(13085) + .26(3981)) = 156.

10% of the time, you’ll get it in with UTG, UTG+2, and UTG+3. .1 (.16(12485) + .17 (3981) = 268

Notice that 35% + 35% + 10% + 4% + 1% + 4% + 10% adds to just 95%. This is due to rounding and the <1% chance that you have to race against three or more players. We’ll want to round our result up a bit to account for this, but I don’t feel like writing out even more equations. So 1596+ 1407 + 234 + +144 + 28 + 156 + 268 = 3833 compared to the 4267 you’d have in your stack if you folded. Even accounting for those missing 2% of cases, this is too close to warrant getting in in a tournament where Hero expects to be a significant favorite against the field. Edit: That’s a money loser even after rounding up, and even if we slightly loosen certain assumptions. 

Remember, though, that these calculations assume those statistics are accurate. Although VPIP and PFR converge relatively quickly, meaning that you don’t need a huge sample size to be decently confident about them, we’re dealing with very few hands and have good reason to think, given the average player in a $5 MTT, that they are skewing low and these players aren’t as tight as they seem. So in this case, I’d put the money in but not feel overly excited about it.

Edit: One thing we can learn from my initial error and recalculation is that the strength of UTG+2’s calling range makes a big difference – Hero’s EV dropped by nearly 10% when I adjusted it, turning a close fold into a clear fold if my assumptions are accurate. This makes sense, because if he calls just KK and AA, then you’ve absolutely smashed, and if his initial cold calling range is narrow, he’ll have those hands often. So a lot comes down to just how confident you are putting UTG+2 on a narrow range. As several commenters point out, it probably isn’t a good idea with a small sample size in a $5 tournament, and I’d jam in Andre’s shoes, but if UTG+2 is a known good player, I think this is a fold. 

Another thing that will make a big difference to your equity is shoehorning TT or AJ into anyone’s calling range. Once you get to the point where you think you could actually get it in ahead sometimes, this becomes a clear shove. Again, that may be possible in a $5 MTT, but perhaps not against very good players.