Quote:
Lets say we know that the villan is a bot and is programmed to push with either range A 50% and range B 50%.
Range A = KK+
Range B = QQ+,AK
If we knew that was his "range distribution" then we should fold because our EV is
+27.24 bb - 42.42 bb = -15.18bb
Again, shout out if Im wrong here but that means that we can still be cautious even if his range is QQ+,AK half the time??
I think we need to clarify what "range" means.
I think you're trying to say that when he pushes, 50% of the time he has KK+ and the other 50% of the time he has QQ+/AK.
That doesn't really make any sense because when he has a range of QQ+/AK that
includes KK+. So we're actually counting the KK+ portion of his range twice. You're trying to take a range of ranges, that doesn't really work very well when those ranges overlap.
What you're really trying to do is assign villain a
dynamic range. We want to model the assumption that he doesn't always play his hands the same way. Most of the time when he has AA he pushes, sometimes he just calls and traps. OTOH, when he has QQ he's more likely to call and see if he likes the flop, he only pushes QQ sometimes.
Normal ranges assume an even distribution and consistent play. As modelled up thread, he always plays AA the same and he always plays QQ the same.
We want to say he's more likely to push AA than he is to push QQ.
So I'm going to pull some numbers out of my ass to represent just how often he pushes a particular hand.
Lets say he pushes the following hands the following percentage of times when he holds them:
AA 80%
KK 70%
AKs 60%
AK 50%
QQ 50%
When he's not pushing he's just calling our 3bet or folding (obv he's never folding AA but he may fold QQ or AK/AKs sometimes).
So then we need the distribution of hands to figure out how often he will hold each of them. Since we have KK we know there are the following ways he can have these hands:
AA 6 ways x 80% = 4.8
KK 1 way x 70% = .7
AKs 2 ways x 60% = 1.2
AK 6 ways x 50% = 3
QQ 6 ways x 50% = 3
So when he pushes, he has
AA 37.7% of the time (4.8/12.7)
KK 5.5% of the time (.7/12.7)
AKs 9.45% of the time (1.2/12.7)
AK 23.62% of the time (3/12.7)
QQ 23.62% of the time (3/12.7)
Our equity against these hands are:
AA 18.054%
KK 50%
AKs 65.894%
AK 69.881%
QQ 81.935%
To find our equity:
(We're figuring a weighted average of equity given the likelyhood of him holding any particular hand)
(37.7%)(18.054%)+(5.5%)(50%)+(9.45%)(65.894%)+(23. 62%)(69.881%)+(23.62%)(81.935%)
51.64%
So, given the dynamic range outlined above, where he pushes AA 80% of the time, KK 70% of the time, etc, we have 51.64% equity against that range.
With 113.5bb in the pot and needing to call 88 bb, the break even point is 43.67% equity.
Now you can use this relatively simple formula and adjust his range - If you think he ALWAYS pushes AA and KK but is less likely to push QQ then you can easily recalculate our equity. However, also keep in mind that we've assume a pretty limited range. We aren't allowing him to EVER have JJ or 89s here. Adding those kinds of hands, even as a small possibility, will improve our equity dramatically because we're so far ahead.
And keep in mind how dead money affects EV. The more dead money in the pot, the less equity we need to be profitable.
The bottom line is that folding KK preflop is difficult because while we are crushed if villain has exactly AA, if his range is anything more than just AA we are crushing the rest of his range. So unless we can put him on AA with a high degree of certainty felting is going to be a +EV proposition.
(Somebody please tell me all that made sense!
)
Last edited by Cry Me A River; 04-01-2008 at 04:57 PM.