- Raise All-in
A#33: When I first read this question, I thought the answer was an obvious shove. We flopped a set, so we’re getting it in, right?
Not so fast. To be certain that shoving is correct, let’s go through the hand systematically, and verify that it's correct to go with the hand. As usual, let’s start with RED-i.
Read (Preflop): The big blind got to see a free flop, so he could have just about any hand. Well, that’s not quite true. He’s a “reasonable” player; more than likely he would have squeezed with his bigger hands here, so we can probably rule out TT+, AQ+, and perhaps KQs. Almost all other hands are in his range preflop. He saw us limp behind the opener preflop, so he probably is putting us on small and medium pairs, and maybe larger suited connectors.
Read (Flop): The flop of 4d-5h-7c is semi-wet, with straight possibilities. The big blind leads out on the flop. He’s “not aggressive, not passive” when he shows aggression on the flop. To me, this means he’s playing ABC, betting his strong hands strong and not betting his weaker hands. His lead indicates strength. When you reraise, he certainly has to read you also for serious strength (as this flop hits your perceived range pretty hard), and yet he still 3bets to $400. This bet commits him, and combined with the demonstrated strength should scream huge hand or at least a monster draw. He got a big-blind special preflop, so hands like sets, made straights, and one pair + straight draws are solidly in his range. Call it definitely 55, 77, 36, 86, and possibly 45, 47, 46, 56, 57, 67 are all in his range here.
Estimate (Flop). The pot is currently ~$530. This means you’re getting direct expressed odds of $530: 300 to make this call, or 1.76:1. This means we have to be good 36% of the time. Your implied odds are more like $1000: 300, or 3.33:1. This means (assuming you would get paid off), your hand needs to be good ~23% of the time to make it worth continuing here. Sometimes he'll call with worse hands, and sometimes he'll fold, so I think the real equity we have is somewhere between the direct and implied odds. The median required equity between these two numbers is ~30%, so let's use that as our target.
Hmmmm. You’ve flopped bottom set, so 30% sure "feels" like this is an automatic shove. But let’s run ‘stove to be certain.
Per pokerstove, our equity is in this situation is ~50%. Sounds good. If we really tighten his range up to just sets and made straights (55, 77, 63, and 86), however, our equity is considerably lower at 30.5%. This is still at or above the required equity, so we're probably OK. Maybe.
We have no idea what, if any fold equity we have in this hand. Chances are he's only going to fold worse hands if we shove (which is not what we want) and call with better hands (which is REALLY not what we want). Therefore I don't think we've got any meaningful fold equity.
Decide: We’ve got at least 30% equity, which is marginally enough to continue. We're not thrilled to get it in here, but we shouldn't be terrified either. We have zero fold equity, so raising here to fold out worse hands is useless.
Ergo, a slowdown SDV line is what we would probably choose. We might also (gasp) choose a fold line and not really lose much EV.
Implement: Calling the raise here to let him fire again on the turn is probably the best implementation of an SDV line. Unfortunately, our only options in the answer set are raise, raise all-in, or fold.
Raising should be ruled out, as the only hands he’s going to call with (or reship) are those that beat us (namely 55 or 77). Worse, raising pretty much any amount above his $400 commits us.
Shoving all-in also (obviously) commits us, but we have very little if any fold equity. I actually think it's not horrible to shove here, but I am not really in love with it either....
... which leaves us with one possible multiple choice answer: Folding. Wow, this isn't what I expected when I started the hand. But the more I think about it, the more I think folding actually isn’t that terrible. We're not pot committed yet, and we're only barely getting enough odds to continue on an SDV line. Folding is zero EV at this point, so it's not a terrible choice.
All-in for now…
*I believe a MUCH better line is to call and then check-call the next two streets, letting him fire into us and turning our hand into a bluff catcher. As stated, however, the answer to this problem--given the limited possible answers--is actually fold. Weird, huh?