
12.10.2010, 12:42

0

This post has been edited 2 time(s), it was last edited by Tim64: 12.10.2010 14:10.
I agree with the principle of what you're saying: when he over bet shoves, his hand is either: nuts or air. That's clear.
So, let's think about what his range is. We don't have any information on villain, so his value range is any flush. First, against these possible flushes {JcTc, Jc9c, Jc8c, Jc6c, Jc4c, Jc3c, Jc2c, Tc9c, Tc8c, Tc6c, Tc4c, Tc3c, Tc2c, 9c8c, 9c6c, 9c4c, 9c3c, 9c2c, 8c6c, 8c4c, 8c3c, 8c2c, 6c4c, 6c3c, 6c2c, 4c3c, 4c2c, 3c2c} we only have 21.4% equity on the River.
we risk $19.98 to win $23.72, so we need 45.72% equity here. If we only have 21.4% equity, we must fold. So therefore villain must be bluffing some proportion of the time to justify a call, to make up for the times when we call and villain has a better flush.
Obviously, if villain is bluffing >50% of the time, we can call.
However, if villain is bluffing only 30% of the time, we get:
0.3* 23.72 = $7.116 plus
0.7* 0.214* $43.70 = $6.54 less
0.7* $19.98 = $13.99 (cost of call*% of time villain is not bluffing)
= $0.33
Well, I'm not sure if I did the calculation correct  maybe someone can confirm? However I think you can see that we need to be pretty sure that villain is bluffing a reasonable amount here to justify a call. We can't just say he either has nuts or air.
(ofc, if he never shoves low flushes, he needs to be bluffing 45% of the time  in my opinion that's unlikely given the size of his bet. Maybe you are right that $5 is not enough to get us to fold our flushes but I don't think he needs to bet $20, so I would say, generally, his overbet 10x pot is more heavily weighted to nutz).
Edit: I just checked this with a very intelligent friend, he gave me the following equation:
EV = F(vb) x (0.214xP  0.786xC) + F(bl) x P
where:
F(vb) is frequency of value bet,
F(bl) is frequency of bluff,
F(vb) = 1F(bl),
P is pot that we can win (excluding amount of our call),
C is amount of our call, and
and 0.214 is our equity.
so, for breakeven:
EV = F(vb) x (0.214xP  0.786xC) + F(bl) x P
0 = F(vb) x ($5.080  $15.70) + F(bl) x P
0 = F(vb) x ($10.62) + F(bl) x P
0 = F(vb) x ($10.62) + (1F(vb)) x P
0 = $10.62 F(vb) + 23.72  23.72 F(vb)
F(vb) = $23.72/$34.34
F(vb) = 0.69
F (bl) = 0.31
So, villain must be bluffing at least 31% of the time given the above assumptions.