Quote:
Originally Posted by ChocolateMoo
Question(s): Is it correct to say I need 20% equity to call-down profitably from turn? (pay 2 BB to win a final pot of 8BB)
It's sort of correct. As you noted, there's another player that's all-in for about 2 SB = 1 BB. This means that 3 BB of the 8 BB pot you're looking at is 3-way and you're only HU for 5 BB. Here's your share of the pot:
[Equity] = 5 * [HU % equity] + 3 * [3-way % equity]
There's a nice little mathematical shortcut here, which is that your 3-way equity only goes down from the times you beat villain but lose to all-in. So [3-way % equity] is [HU % equity] - [% beat villain and lose to AI]. A little bit of algebra and you get
[Equity] = 8 * [HU % equity] - 3 * [% beat villain and lose to AI]
Now, who knows what that value is. But whatever it is, it's smaller than your % beat villain, which is already a small number because you're bluff-catching. We'll look at this again later.
It's already been noted that the 85% range is pretty optimistic in terms of what villain might be doing. It helps sometimes to do a high and low estimate to see how elastic or inelastic the numbers are. Here's a 50% range, with the tables put side-by-side for easy comparison.
Hand | Pot equity | Wins | Ties |
---|
AsJc | 31.17% | 11,484 | 316 |
85% | 68.83% | 25,556 | 316 |
Hand | Pot equity | Wins | Ties |
---|
AsJc | 33.59% | 7,085 | 316 |
50% | 66.41% | 14,159 | 316 |
Notice how stable things are on the turn. That's because there are a lot of junk hands floating around in that bottom 35% of his range. You're adding in a lot of Qx/Jx/Tx hands that you're beating at the same time you're adding in 7x/6x/5x hands that are beating you.
However, on the river...
Hand | Pot equity | Wins | Ties |
---|
AsJc | 17.97% | 143 | 8 |
85% | 82.03% | 667 | 8 |
Hand | Pot equity | Wins | Ties |
---|
AsJc | 24.58% | 114 | 8 |
50% | 75.42% | 358 | 8 |
There's a pretty significant difference now. You do better against the smaller range because now all those random Qx/Jx/Tx hands have made a bunch of pairs and straights and you're now glad to see them not in the range. (Any 3, 4, 5, 6, 7, 8, or K beats you. Notice how many more bad cards there are and how many of those formerly junky hands got there.)
Back to your equity: On the turn, we might estimate your HU equity to be somewhere close to 33%*. Ignoring the all-in, you're looking pretty good. We can try to factor in the all-in. Let's estimate that he's taking 50% of your wins away from you and see what happens. 50% of 33% = 16.5%. This decreases your equity from 2.64 (33% of 8 BB) to 2.15 (33% of 8 - 16.5% of 3). That changes your % equity from 33% to 27%. But in both cases, it's above the 20% for a blind calldown.
(* Note: Munga's calculation has your equity down in the 20% range. I may be reading the range wrong, but it looks like his range is suggesting that villain would be giving up on hands with no pair/no draw. That's entirely plausible and worth considering. In two of the three hands you posted, villain had a piece of the flop. In the third case, it was a paired ragged flop. Also, none of those were 3-bet hands.)
But given that the pessimistic Munga range is borderline and the optimistic range says it's fine, it's probably fine to call down.
And (perhaps counter-intuitively) you would actually prefer his range to be slightly narrower for this particular river if he's betting everything he's got. You would much prefer his range be biased more mid-range connected stuff (like J9) than high-low combos (like Q4).