Originally Posted by Poker_play
^^thanks, good analysis.
I find that 3betting preflop with hands like these often throws opponents off (as they put me on the wrong range now), allowing me to get paid if I hit a turn or river here. Especially if the river is a 5 or a 10..even a small spade I could probably get a good bet off. I think you're giving him too much credit if you give me no implied odds (he won't c/f any 5, 10 or spade lol). That's really all speculation though..I see why you say raise flop.
In this case, river (Ah) was clearly in what he thought was my range...I forget the river bet, but it was good enough to force a laydown.
Ya, you are right to say that he never gives us value on the river isn't correct because nothing in poker is absolute. But, we are trying to guesstimate whether we can get more value by raising the flop compared to value-raising the river, right?
Consider this.. Let's say villain will call a 1/2 PSB on the river 50% and fold 50%. He will call this bet regardless of the card on the river.
Pot is: $845. (round it to 844 so I can divide by 2. lol)
Also assume max equity from the flop, which is ~60%.
60% of the time, you get $422, 40% of the time, you lose $422. I use these numbers because 60% from the flop we will be there by the river. And 40% of the time, we aren't.
Our EV is $85. So our physical bet on the river makes us $85.
For the entire pot: EV is $253.2 (759-506)
Now on the flop, assume that he will shove 50% of the time:
After you call his shove, the pot will be $3,270. You win 60% and lose 40%
Getting it in yields and EV of $654. But, you only get $654 50% of the time. The other 50% of the time you win instantly when he folds. So, $327 + times he folds > $253.
My calculations might be off.. as I'm doing this on the fly. My point is though, you asked about the most EV line. I'm trying to illustrate that the most EV is gained from the line you were trying to avoid. Because of that, it was a mistake, even if we can get value on the river. In order to really get value, you have to assume villain will stack off on the river. Which seems unlikely, given the range you give him. Thus, the reason why I made my assumption of villain NOT giving us value on the river.
If I messed something up, let me know, I haven't done the maths in my head in a long time! lol