Need heads up calculation help

dboy23 · #1 10-31-2006, 01:18 PM

Ok, so I want to come up with some percentages of being ahead after x number of matches heads up with a 60% winrate. Breakeven is 52.5% due to rake.

So basically the output I need is

% after 1 game
ahead: 60%
behind: 40%

% after 5 games

% after 25 games, and so on.

I don't know where to begin on making this equation.

BruceZ · #2 10-31-2006, 05:42 PM

[ QUOTE ]
Ok, so I want to come up with some percentages of being ahead after x number of matches heads up with a 60% winrate. Breakeven is 52.5% due to rake.

So basically the output I need is

% after 1 game
ahead: 60%
behind: 40%

% after 5 games

% after 25 games, and so on.

I don't know where to begin on making this equation.

[/ QUOTE ]

Take 52.5% of the number of matches, and round any fractional part up to the next integer, to get the number of matches that you must win to break even or better. For 5 matches, 0.525*5 = 2.625, so you must win at least 3 matches. The probability of this is given by the Excel function BINOMDIST as

=1-BINOMDIST(2,5,0.6,TRUE) =~ 68.3%.

This is 1 minus the probability of winning 2 or less.

For 25 matches, 0.525*25 = 13.125, so you must win at least 14 matches. The probability of this is

=1-BINOMDIST(13,25,0.6,TRUE) =~ 73.2%.

The following shows the number of matches in the 1st column, the number that you must win to break even or be ahead in the 2nd column, and the probability of being even or ahead in the 3rd column.

<font class="small">Code:</font><hr /><pre>
1 1 60.0%
2 2 36.0%
3 2 64.8%
4 3 47.5%
5 3 68.3%
6 4 54.4%
7 4 71.0%
8 5 59.4%
9 5 73.3%
10 6 63.3%
11 6 75.3%
12 7 66.5%
13 7 77.1%
14 8 69.2%
15 8 78.7%
16 9 71.6%
17 9 80.1%
18 10 73.7%
19 10 81.4%
20 11 75.5%
21 12 69.1%
22 12 77.2%
23 13 71.3%
24 13 78.7%
25 14 73.2%
26 14 80.1%
27 15 75.0%
28 15 81.3%
29 16 76.6%
30 16 82.5%
31 17 78.1%
32 17 83.5%
33 18 79.4%
34 18 84.5%
35 19 80.7%
36 19 85.4%
37 20 81.8%
38 20 86.2%
39 21 82.9%
40 21 87.0%
41 22 83.9%
42 23 80.3%
43 23 84.8%
44 24 81.4%
45 24 85.6%
46 25 82.5%
47 25 86.4%
48 26 83.5%
49 26 87.2%
50 27 84.4%
</pre><hr />

dboy23 · #3 10-31-2006, 08:58 PM

That is very cool. Thanks for that. I'm going to see it I can do this in excel now.

BruceZ · #4 11-01-2006, 12:13 AM

It turns out that you can put the 0.525*N into the BINOMDIST function directly, and it will handle the fractional part correctly. For example, for N = 25, you can just do

=1-BINOMDIST(0.525*25,25,0.6,TRUE)

=~ 73.2%.

dboy23 · #5 11-01-2006, 02:49 PM

So it appears that if I play 300 games at a 60% rate (easily doable) I have a 99.57% chance to make money.

That seems alot better than LOL cashgameaments.