Quote:
Originally Posted by R Gibert
From (2*b + 1)3 = 2*s + 1 where s = Stack/Pot and solving for the betting fraction b you get:b = ((2*s + 1)1/3 - 1)/2
This generalizes to any number (=n) of streets:
b = ((2*s + 1)1/n - 1)/2
Unfortunately, computing roots at the table is not so easy, but we should not let this stop us from trying. The following 2 approximations are within a few percent of being accurate at computing the betting fraction b. For 3 streets:
b = (s + 7)/20
with a useful range of about 3.2 ≤ s ≤ 15.4
Code:
s ≈ = Δ
3.1 50.5% 46.5% +4.0%
3.2 51.0% 47.4% +3.6%
3.3 51.5% 48.3% +3.2%
3.4 52.0% 49.2% +2.8%
3.5 52.5% 50.0% +2.5%
3.6 53.0% 50.8% +2.2%
3.7 53.5% 51.6% +1.9%
3.8 54.0% 52.4% +1.6%
3.9 54.5% 53.2% +1.3%
4.0 55.0% 54.0% +1.0%
4.1 55.5% 54.8% +0.7%
4.2 56.0% 55.5% +0.5%
4.3 56.5% 56.3% +0.2%
4.4 57.0% 57.0% +0.0%
4.5 57.5% 57.7% -0.2%
4.6 58.0% 58.4% -0.4%
4.7 58.5% 59.1% -0.6%
4.8 59.0% 59.8% -0.8%
4.9 59.5% 60.5% -1.0%
5.0 60.0% 61.2% -1.2%
5.1 60.5% 61.9% -1.4%
5.2 61.0% 62.5% -1.5%
5.3 61.5% 63.2% -1.7%
5.4 62.0% 63.8% -1.8%
5.5 62.5% 64.5% -2.0%
5.6 63.0% 65.1% -2.1%
5.7 63.5% 65.7% -2.2%
5.8 64.0% 66.3% -2.3%
5.9 64.5% 67.0% -2.5%
6.0 65.0% 67.6% -2.6%
6.1 65.5% 68.2% -2.7%
6.2 66.0% 68.8% -2.8%
6.3 66.5% 69.3% -2.8%
6.4 67.0% 69.9% -2.9%
6.5 67.5% 70.5% -3.0%
6.6 68.0% 71.1% -3.1%
6.7 68.5% 71.6% -3.1%
6.8 69.0% 72.2% -3.2%
6.9 69.5% 72.8% -3.3%
7.0 70.0% 73.3% -3.3%
7.1 70.5% 73.9% -3.4%
7.2 71.0% 74.4% -3.4%
7.3 71.5% 74.9% -3.4%
7.4 72.0% 75.5% -3.5%
7.5 72.5% 76.0% -3.5%
7.6 73.0% 76.5% -3.5%
7.7 73.5% 77.0% -3.5%
7.8 74.0% 77.5% -3.5%
7.9 74.5% 78.1% -3.6%
8.0 75.0% 78.6% -3.6%
8.1 75.5% 79.1% -3.6%
8.2 76.0% 79.6% -3.6%
8.3 76.5% 80.1% -3.6%
8.4 77.0% 80.5% -3.5%
8.5 77.5% 81.0% -3.5%
8.6 78.0% 81.5% -3.5%
8.7 78.5% 82.0% -3.5%
8.8 79.0% 82.5% -3.5%
8.9 79.5% 83.0% -3.5%
9.0 80.0% 83.4% -3.4%
9.1 80.5% 83.9% -3.4%
9.2 81.0% 84.3% -3.3%
9.3 81.5% 84.8% -3.3%
9.4 82.0% 85.3% -3.3%
9.5 82.5% 85.7% -3.2%
9.6 83.0% 86.2% -3.2%
9.7 83.5% 86.6% -3.1%
9.8 84.0% 87.1% -3.1%
9.9 84.5% 87.5% -3.0%
10.0 85.0% 87.9% -2.9%
10.1 85.5% 88.4% -2.9%
10.2 86.0% 88.8% -2.8%
10.3 86.5% 89.2% -2.7%
10.4 87.0% 89.7% -2.7%
10.5 87.5% 90.1% -2.6%
10.6 88.0% 90.5% -2.5%
10.7 88.5% 90.9% -2.4%
10.8 89.0% 91.4% -2.4%
10.9 89.5% 91.8% -2.3%
11.0 90.0% 92.2% -2.2%
11.1 90.5% 92.6% -2.1%
11.2 91.0% 93.0% -2.0%
11.3 91.5% 93.4% -1.9%
11.4 92.0% 93.8% -1.8%
11.5 92.5% 94.2% -1.7%
11.6 93.0% 94.6% -1.6%
11.7 93.5% 95.0% -1.5%
11.8 94.0% 95.4% -1.4%
11.9 94.5% 95.8% -1.3%
12.0 95.0% 96.2% -1.2%
12.1 95.5% 96.6% -1.1%
12.2 96.0% 97.0% -1.0%
12.3 96.5% 97.4% -0.9%
12.4 97.0% 97.7% -0.7%
12.5 97.5% 98.1% -0.6%
12.6 98.0% 98.5% -0.5%
12.7 98.5% 98.9% -0.4%
12.8 99.0% 99.3% -0.3%
12.9 99.5% 99.6% -0.1%
13.0 100.0% 100.0% +0.0%
13.1 100.5% 100.4% +0.1%
13.2 101.0% 100.7% +0.3%
13.3 101.5% 101.1% +0.4%
13.4 102.0% 101.5% +0.5%
13.5 102.5% 101.8% +0.7%
13.6 103.0% 102.2% +0.8%
13.7 103.5% 102.5% +1.0%
13.8 104.0% 102.9% +1.1%
13.9 104.5% 103.3% +1.2%
14.0 105.0% 103.6% +1.4%
14.1 105.5% 104.0% +1.5%
14.2 106.0% 104.3% +1.7%
14.3 106.5% 104.7% +1.8%
14.4 107.0% 105.0% +2.0%
14.5 107.5% 105.4% +2.1%
14.6 108.0% 105.7% +2.3%
14.7 108.5% 106.0% +2.5%
14.8 109.0% 106.4% +2.6%
14.9 109.5% 106.7% +2.8%
15.0 110.0% 107.1% +2.9%
15.1 110.5% 107.4% +3.1%
15.2 111.0% 107.7% +3.3%
15.3 111.5% 108.1% +3.4%
15.4 112.0% 108.4% +3.6%
15.5 112.5% 108.7% +3.8%
For 2 streets:
b = (s + 1)/5
with a useful range of about 1.1 ≤ s ≤ 4.5
Code:
s ≈ = Δ
1.0 40.0% 36.6% +3.4%
1.1 42.0% 39.4% +2.6%
1.2 44.0% 42.2% +1.8%
1.3 46.0% 44.9% +1.1%
1.4 48.0% 47.5% +0.5%
1.5 50.0% 50.0% +0.0%
1.6 52.0% 52.5% -0.5%
1.7 54.0% 54.9% -0.9%
1.8 56.0% 57.2% -1.2%
1.9 58.0% 59.5% -1.5%
2.0 60.0% 61.8% -1.8%
2.1 62.0% 64.0% -2.0%
2.2 64.0% 66.2% -2.2%
2.3 66.0% 68.3% -2.3%
2.4 68.0% 70.4% -2.4%
2.5 70.0% 72.5% -2.5%
2.6 72.0% 74.5% -2.5%
2.7 74.0% 76.5% -2.5%
2.8 76.0% 78.5% -2.5%
2.9 78.0% 80.4% -2.4%
3.0 80.0% 82.3% -2.3%
3.1 82.0% 84.2% -2.2%
3.2 84.0% 86.0% -2.0%
3.3 86.0% 87.8% -1.8%
3.4 88.0% 89.6% -1.6%
3.5 90.0% 91.4% -1.4%
3.6 92.0% 93.2% -1.2%
3.7 94.0% 94.9% -0.9%
3.8 96.0% 96.6% -0.6%
3.9 98.0% 98.3% -0.3%
4.0 100.0% 100.0% +0.0%
4.1 102.0% 101.7% +0.3%
4.2 104.0% 103.3% +0.7%
4.3 106.0% 104.9% +1.1%
4.4 108.0% 106.5% +1.5%
4.5 110.0% 108.1% +1.9%
4.6 112.0% 109.7% +2.3%
Beware that the above betting scheme may be fine for a bluff catcher vs polarized range toy game, but in real world poker, there are many more variables to consider. As long you keep this in mind when using this, some of you might sometimes find it useful at the table.
Last edited by R Gibert; 08-25-2016 at 07:31 PM.
