[ QUOTE ]
[ QUOTE ]
Our House: let's say you needed him to lose 10% that hand
Our House: and it's really 6%
Our House: you're a 4% dog on one bet
Our House: you're losing 4% of $20
Our House: 80 cents bro
Our House: not $20
Victor: makes sense
[/ QUOTE ]
Math weenie jumps in to say: this is wrong.
If you're getting 9-1 (so you need to win 10%) and will actually win 6% (which I am going to approximate as one time in 16), it stacks up like this:
15 times in 16 you lose $20: -$300
One time you win $180: +$180
for a net loss of $120 over 16 trials, i.e. $7.50 a hand.
This is a pretty significant mistake.
Guy.
[/ QUOTE ]
Based on this I whipped up a real quick spreadsheet and found the results to be quite interesting so I thought I would share them.
<font class="small">Code:</font><hr /><pre> Pot Size
Win % 9 10 11 12 13 14 15 16 17 18 19 20
1/1 100.0% 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00 19.00 20.00
1/2 50.0% 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 8.50 9.00 9.50
1/3 33.3% 2.33 2.67 3.00 3.33 3.67 4.00 4.33 4.67 5.00 5.33 5.67 6.00
1/4 25.0% 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25
1/5 20.0% 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00 3.20
1/6 16.7% 0.67 0.83 1.00 1.17 1.33 1.50 1.67 1.83 2.00 2.17 2.33 2.50
1/7 14.3% 0.43 0.57 0.71 0.86 1.00 1.14 1.29 1.43 1.57 1.71 1.86 2.00
1/8 12.5% 0.25 0.38 0.50 0.63 0.75 0.88 1.00 1.13 1.25 1.38 1.50 1.63
1/9 11.1% 0.11 0.22 0.33 0.44 0.56 0.67 0.78 0.89 1.00 1.11 1.22 1.33
1/10 10.0% 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10
1/11 9.1% -0.09 0.00 0.09 0.18 0.27 0.36 0.45 0.55 0.64 0.73 0.82 0.91
1/12 8.3% -0.17 -0.08 0.00 0.08 0.17 0.25 0.33 0.42 0.50 0.58 0.67 0.75
1/13 7.7% -0.23 -0.15 -0.08 0.00 0.08 0.15 0.23 0.31 0.38 0.46 0.54 0.62
1/14 7.1% -0.29 -0.21 -0.14 -0.07 0.00 0.07 0.14 0.21 0.29 0.36 0.43 0.50
1/15 6.7% -0.33 -0.27 -0.20 -0.13 -0.07 0.00 0.07 0.13 0.20 0.27 0.33 0.40
1/16 6.3% -0.38 -0.31 -0.25 -0.19 -0.13 -0.06 0.00 0.06 0.13 0.19 0.25 0.31
1/17 5.9% -0.41 -0.35 -0.29 -0.24 -0.18 -0.12 -0.06 0.00 0.06 0.12 0.18 0.24
1/18 5.6% -0.44 -0.39 -0.33 -0.28 -0.22 -0.17 -0.11 -0.06 0.00 0.06 0.11 0.17
1/19 5.3% -0.47 -0.42 -0.37 -0.32 -0.26 -0.21 -0.16 -0.11 -0.05 0.00 0.05 0.11
1/20 5.0% -0.50 -0.45 -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05
1/21 4.8% -0.52 -0.48 -0.43 -0.38 -0.33 -0.29 -0.24 -0.19 -0.14 -0.10 -0.05 0.00
1/22 4.5% -0.55 -0.50 -0.45 -0.41 -0.36 -0.32 -0.27 -0.23 -0.18 -0.14 -0.09 -0.05
1/23 4.3% -0.57 -0.52 -0.48 -0.43 -0.39 -0.35 -0.30 -0.26 -0.22 -0.17 -0.13 -0.09
1/24 4.2% -0.58 -0.54 -0.50 -0.46 -0.42 -0.38 -0.33 -0.29 -0.25 -0.21 -0.17 -0.13
1/25 4.0% -0.60 -0.56 -0.52 -0.48 -0.44 -0.40 -0.36 -0.32 -0.28 -0.24 -0.20 -0.16
1/26 3.8% -0.62 -0.58 -0.54 -0.50 -0.46 -0.42 -0.38 -0.35 -0.31 -0.27 -0.23 -0.19
1/27 3.7% -0.63 -0.59 -0.56 -0.52 -0.48 -0.44 -0.41 -0.37 -0.33 -0.30 -0.26 -0.22
1/28 3.6% -0.64 -0.61 -0.57 -0.54 -0.50 -0.46 -0.43 -0.39 -0.36 -0.32 -0.29 -0.25
1/29 3.4% -0.66 -0.62 -0.59 -0.55 -0.52 -0.48 -0.45 -0.41 -0.38 -0.34 -0.31 -0.28
1/30 3.3% -0.67 -0.63 -0.60 -0.57 -0.53 -0.50 -0.47 -0.43 -0.40 -0.37 -0.33 -0.30
</pre><hr />
Conclusion:
It sure looks like folding on the river in a big pot isn't nearly as bad as we make it out to be. Was Ed Miller wrong?
Example from chart:
Pot is 20BB and our opponent bets into us. We need to be good 5% of the time for the call to be correct. This is obvious.
Now if our winning chances are actually 6.7% (1/15) then we net a profit of 0.25BB's. But if our winning chances are only 3.3% (1/30 then we lose 0.33 BB's on the hand. Both of these scenarios represent a 1.7% change from our break even point. But, we can also look at the case where we are 1/25 (4%), which would be the a change of 5 hands in the denominator (6.7% is 1/15 and 4% is 1/25 and the breakeven point is 1/20...) and find that we lose 0.2 BB's per hand which is a similar amount to what we win when we look at it in the opposite direction.
Help me understand the results of this table which is basically looking at our EV of calling 1 big bet on the river in a pot of various size vs. our chance of winning that pot. It appears that incorrectly calling for one bet on the river is worth almost the same as incorrectly folding. (If calling is worth +0.25 then folding is -0.25.)