theory post: ISF theorem and overbetting
I came up with this post by thinking about a recent 2-4 NL hand that I misplayed. I raised Q8s to $12 on the button, and a regular called from the big blind. The flop came A22 rainbow, I cbet $16 and he called. The turn was 7 giving me a flush draw, I bet $40 into the $55 pot and he called again. The river was an offsuit 6, I gave up and his AJ took the pot down. The reason I misplayed the hand is, first of all, my turn semibluff is -EV if I'm not also planning on bluffing the river when I miss. Occasionally he folds something like TT on the turn but usually I'm getting snapcalled by a hand I have 9 outs against, and that won't fold blank rivers either but might fold if I make a flush. So I should have just taken the free card on the turn...
...unless I was planning on overbet shoving a blank river! We can easily have hands like AA, 77, AK, and 22 here, and he rarely has those hands. Actually he probably never has any of them except quads once in a blue moon. So from the ISF Theorem this is a good spot for us to fire three barrels because we have the nuts way more often than he does. This might be -EV if I just bet 3/4 pot three times, but it becomes +EV if I overshove the river, allowing me to three-barrel more often and just making it tougher in general for him to play marginal hands out of position vs. me, which is what I want when I'm on the button.
Before I get into the math of why overbetting lets us bluff more often, first of all let's list the hands could I be betting the turn and the river for value with given his range. I think his calling range of a 3-barrel is overwhelmingly AT-AQ, so we should three-barrel every hand that's ahead of that range, which includes AA, AK, AQ, A7s, A2s, 77, K2s. That's 25 combos once we take into account the ace blocker that he almost definitely has. Assuming that I want him to be indifferent between calling and folding to a river bet, if I bet $100 into the $135 pot on the river I should only be bluffing 30% of the time. This means I can 3-barrel 10 combos of missed flush draws. But if I overbet shove the river for 2.4 times the pot with the above hands, he's indifferent between calling and folding when I bluff 41% of the time. This means I can also 3-barrel 17 combos of missed flush draws instead of just 10. These 3-barrel bluffs are +EV because they're neutral EV if we brick the river and they're obviously +EV if we happen to hit our flush.
If you know your opponent has a bluff-catcher, overbetting the river allows you to profitably 3-barrel him more often than you could do with a normal sized bet. Obviously the best play game-theory wise isn't necessarily the best play in practice but in this case I think it very well may be. If I had overshoved the river here I think my opponent would probably have just shrugged his shoulders and folded since he'd never seen me do anything like that before.
