How to Exploit Human Mistakes
After a Flop Overbet

But just how strong does a hand need to be to make it into the value region of your polarized range? And how should you choose your bluffs? To answer these questions, we’ll investigate a few examples.

As in the previous article, these examples are all drawn from BTN vs BB SRP 100bb deep cash game scenarios. On AK6r, BTN bet 253% pot. On T95r, they bet 125% pot.

Now, we will look at how to follow through on those flop overbets after the BB called.

At the moment they saw the flop, before any action took place, BTN enjoyed a nice ~56% equity advantage (vs. BB’s 44% EQ) and also had more of the best hands in their range. This is what made overbetting an appealing play in the first place:

This dynamic changes drastically after BB calls the overbet. Here’s what it looks like on one of the blankest of turns, the 2♣:

BTN’s nuts advantage is slightly more pronounced, but their equity has plummeted from 56% to 34%!

The players have entered a classic polarized-versus-condensed range dynamic. Because the board is so static, this is a rare real-world, pre-river spot that can be modeled reasonably well by a toy game.

BTN, with a high degree of confidence, can look at their hand and conclude either “I will hold the best hand on the river” or “I will not hold the best hand on the river.” BB can likewise conclude that, with most of their range, they will win against BTN’s bluffs but not against their value bets.

The GTO strategy for BTN in this case is to value bet all their strongest hands and to balance those bets with an appropriate number of bluffs. They can optimize this by betting geometrically, sizing their bets so that they bet the same fraction of the pot on the turn and river. This is exactly what the solver does; betting the turn for 73% pot to set up a 73% pot-sized shove on the river.

The tricky parts are identifying just how strong a hand must be to value bet and which hands to bluff with.

At the top end, notice that there is no slow-playing. With any AQ or better hand, BTN purely bets.

The main reason to slow-play would be to keep very weak hands in BB’s range and give them an opportunity to improve or bluff later. But it’s too late for that: BTN has already caused those hands to fold by overbetting the flop. Checking now would incur the downside of slow-playing (i.e., failing to grow the pot) without the upside of keeping those weak hands around.

The strongest hands BTN checks are AJ and AT, which, if they further strengthen BB’s range by betting the turn, would not be strong enough to jam a blank river for value. Because BTN is not looking to play for stacks with these hands, they can choose whether to get their second (and final) value bet on the turn or the river. There are slight advantages and disadvantages to each, but it doesn’t matter terribly much which they choose. The important thing is to recognize that these hands are not strong enough to play for stacks, which is why checking the turn is an option worth considering.

Among BTN’s weak hands, there are hands that always bluff, hands that never bluff, and hands that sometimes bluff. It is important to recognize that this distinction is not based on equity.

BTN does not simply bluff the bottom of their range and check the middle.

After overbetting this flop, they have no middle. A hand like 86s has 19% equity, but it rarely realizes that equity unless it improves. BTN should not expect to check it down and win unimproved, because BB should bluff the river with anything that cannot beat 86s, and a pair of sixes will be too weak to call even a small river bet.

As on the flop, a pair of sixes is a pure bluff, not because of its equity but despite it. BTN does not bet these hands as thin value bets or semi-bluffs. They are pure bluffs that show a profit because they block sets and two pairs. The same is true of the few hands in BTN’s range that pair the 2 on the turn.

Conversely, the worst hands to bluff are those that block BB’s folding range. That means BTN is checking QJ not because they expect to realize their 15% equity at showdown but because when they bluff, they want BB to be holding QJ or QT, and that is less likely when those cards are in BTN’s hand.

The hands that are indifferent to bluffing are those with only minor blocking effects. A hand like 33, which blocks neither calls nor folds, sometimes bluffs and sometimes checks.

Again, the critical thing to recognize is that these decisions are based on blockers, not on equity or how high (or low) a hand is in BTN’s range. Whether they have 1% equity or 19% equity, these hands are all effectively worthless at showdown. The only question is whether they contain the right properties for bluffing.

Straight-Completing Turns

Things play out a bit differently on straight-completing turns, but only a bit. Here’s what the range dynamics look like after a flop overbet and a J♣ turn:

BTN has 38% rather than 34% equity, and their nuts advantage is a bit more pronounced. But it’s still a polarized-versus-condensed dynamic, and BTN still does best by betting a polar range for a geometric size.

The threshold for how strong a hand must be to value bet is higher on a card that interacts more with both players’ ranges.

Because both players turn straights and two pairs on this card, BTN can’t purely value bet their two pairs. In fact, on the J♣ turn, blockers play a role even in selecting value bets: BTN purely bets AQ, which blocks straights and the stronger two pairs in BB’s range, but mostly checks K6, which does not block straights or many combos of Aces Up.

A pair of Sixes is still a good bluffing hand, but on the J♣, it gets demoted from a pure bluff to a mix. This is because BTN turns a pair much more often when the turn is a Jack than when it is a 2, and those turned Jacks also make appealing bluffs, especially when they block the straight (which means they also have a chance to river a straight if called).

Small pocket pairs never bluff because, although they are relatively neutral as far as blockers are concerned, BTN simply has better candidates. They are already choosing not to bluff with all their 6-x, which has good blocking effects, so there is no reason to bluff with a hand that has no blockers at all.

Barreling Rivers

The only really tricky case is when the board runs out a four-liner to a straight. In this case, BTN still value bets their best two pairs (AJ and above), but 6-x is no longer a good bluff, because A6 and K6 are important parts of BB’s folding range. Blocking AJ and AT is more important, so BTN is more inclined to turn those higher pairs into bluffs.

Once again, this isn’t about checking hands with showdown value. BTN never wins by checking either pairs of Jacks or Sixes, so the only factor determining which to bluff is its blockers.

After overbetting T95r, the dynamic on a blank turn is not fundamentally different from the AK6r turn scenarios we investigated above, though it is less dramatic. This is partly owing to the nature of the board but also partly to the size of BTN’s flop overbet. Betting 125% pot does not polarize BTN’s range or condense BB’s as dramatically as betting 253% pot does. As a result, BTN retains ~42% on a 2♣ turn. Not great, but not nearly as bad as the 34% they had on AK62r.

BTN’s turn sizing remains geometric even on this more dynamic board, but because the flop bet was only 125% pot, the geometric size on the turn is also an overbet for 111% pot.

Despite the overbet, BTN’s range is not terribly polar. They pure check their worst hands, and most of their high-frequency bluffs are semi-bluffs from strong draws like KQ and QJ:

BB is condensed enough that they rarely raise despite the prevalence of draws in BTN’s range, so BTN prefers to bluff hands that retain equity when called, even for an overbet.

Because their turn barreling range contains so many draws, BTN holds a lot of air on blank rivers and must choose bluffs judiciously.

Much of their bluffing strategy revolves around the busted draws in BB’s range, specifically QJ. While the BB folds many of their weaker draws to the turn overbet, they often call with two overcards and an open-ender, making QJ an important part of their river folding range.

For this reason, BTN does not bluff their own QJ and rarely bluffs KQ or KJ. These hands block BB’s folding range and have a shred of showdown value, as they can chop with or beat QJ.

We know these checks are not entirely about showdown value, however, because BTN bluffs with many Ace-high hands, including AJ. While blocking QJ is unfortunate, blocking AT is great, better even than blocking KT, with which BB does not pure call the river shove.

Straight-Completing Rivers

When the draw does come in, BTN’s bluffing strategy is similarly built around blockers: almost all their bluffs on an 8♠ river contain either a Queen or a Jack (or an Ace). These are the very best blockers, other than a Ten which, of course, is too strong to bluff.

The more interesting thing about this river is how wide BTN jams for value. Despite the obvious draw coming in, they purely jam all overpairs and mix jams and checks with AT.

The obvious draw plays a larger role in determining bluffs because most bluffing decisions are close to begin with. Bluffing is rarely very profitable, so blocking a few key combos is enough to nudge a hand to either a pure check or pure bluff.

Value-shoves, on the other hand, are profitable enough that, although they lose value when the draws come in, many remain profitable. BB is very capped after check-calling twice from out of position, so even though the river slightly uncaps them, they still must defend with many marginal hands to keep BTN indifferent to bluffing. This is what incentivizes BTN to jam as wide as AT for value.

Straight-Completing Turns

When the draw completes on the turn, things play out a bit differently than when it comes in on the river. BTN loses their nuts advantage and wants to get in some thin value/protection bets, so they bet 67% pot rather than the geometric 111% pot size. They still draw almost all their bluffs from the Queen-x and Jack-x holdings, but they are more conservative with their value bets. QQ and JJ mostly bet because they benefit from protection, block turned straights, and can river straights, but KK mostly checks, and AA is a pure check. Despite the smaller bet size, BTN overall bets less frequently when the draw completes on the turn than when it completes on the river.

Conclusion

Dynamic boards are often less good for overbetting, but in the event that you do overbet them, pay careful attention to the draws in your opponent’s range. When those draws miss, you want to bluff when you unblock them and consider checking when you can beat them, even if your hand seems quite weak.

When they come in, your best bluffs will usually block those draws. But don’t get skittish about value! These draws usually represent just a few combos, and you should still jam for value with many hands that beat the rest of your opponent’s range despite the risk of running into a monster.