# Interesting Math Problem

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• Feb 4th 2009, 03:56 AM
LovePokerHateMath
Interesting Math Problem
Okay the game is texas holdem, you have 1 card to come. The math below allows us to calculate the percentage of your card turning pretty accurately, max varince of 1.5%.

Very little brain usage required, essential in my case!

12+ Outs: (Outs X 2) + 2 = % of hitting
3-11 Outs: (Outs x 2) + 1 = % of hitting
1-3 Outs: Outs x 2 = % of hitting

Outs / Actual Percentage / Our easy to calculate %

20 43.50% 42%
19 41.30% 40%
18 39.10% 38%
17 37.00% 36%
16 34.80% 34%
15 32.60% 32%
14 30.40% 30%
13 28.30% 28%
12 26.10% 26%
11 23.90% 23%
10 21.70% 21%
9 19.60% 19%
8 17.40% 17%
7 15.20% 15%
6 13.00% 13%
5 10.90% 11%
4 8.70% 9%
3 6.50% 6%
2 4.30% 4%
1 2.20% 2%

Example we have 5 outs, so we times 5 by 2 to get 10 and +1 for an 11% chance of hitting 1 of our cards. actual 10.90%.

Alot of poker players will just work to a rule of x2 but doing it like this gives us a little edge and edges are good in poker! The problem I am having is finding a similar soultion for the following percentages (2 cards to come)..... So just wondering if any great math brains can help me find something similar to the above but practical to use.

20 67.5%
19 65.0%
18 62.4%
17 59.8%
16 57.0%
15 54.1%
14 51.2%
13 48.1%
12 45.0%
11 41.7%
10 38.4%
9 35.0%
8 31.5%
7 27.8%
6 24.1%
5 20.3%
4 16.5%
3 12.5%
2 8.4%
1 4.3%

again x4 seems to be the best for outs 1 - 8, 36% is acceptable for 9 outs but its from 10 onwards that i cant find any "simple" consistency that i could use in a simlar manner.

Thanks
• Feb 4th 2009, 07:08 PM
metamorphaze
20 67.5% 69%
19 65.0% 66%
18 62.4% 63%
17 59.8% 60%
16 57.0% 57%
15 54.1% 54%
14 51.2% 51%
13 48.1% 48%
12 45.0% 45%
11 41.7% 42%
10 38.4% 39%
9 35.0% 36%
8 31.5% 32%
7 27.8% 28%
6 24.1% 24%
5 20.3% 20%
4 16.5% 16%
3 12.5% 12%
2 8.4% 8%
1 4.3% 4%

x4 works up to 8, but then it looks like you need to subtract on a sliding scale: \$\displaystyle 3x+9\$. I started with a more complicated formula, but this is how it worked out. It's pretty close for 9 on.

would give you % in green. You could change again at 19, but if you have 19 outs, what are you complaining about???
• Feb 6th 2009, 01:40 PM
LovePokerHateMath
Exceptional response!

Love this forum already just wish the poker traffic was slightly higher.

After doing some more reading found out about "Solomans Law", harrington on cash, advocates ((outs x 4)-(outs-8)). Again only worth doing for when we have 9+ outs.

Think I find your way easier, both seem very accurate for quick live table calculations.

Thanks very much, hope to discuss more holdem math poker topics with you in the future
• Feb 7th 2009, 07:07 AM
metamorphaze
Quote:

Originally Posted by LovePokerHateMath
After doing some more reading found out about "Solomans Law", harrington on cash, advocates ((outs x 4)-(outs-8)). Again only worth doing for when we have 9+ outs.

I actually started with something close to that when I did it the first time:

\$\displaystyle 4x-(x-9)\$

I had a nine instead of an eight. But then we can simplify by distributing the negative:

\$\displaystyle 4x-x+9\$

And finally:

\$\displaystyle 3x+9\$

Where x is the number of outs. It's the same formula as Solomon's, only written in a different way.