[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums

Backgammon SD (was Stanley's table)

Posted By: Daniel Murphy
Date: Sunday, 21 October 2007, at 6:07 a.m.

In Response To: Stanley's table (Stick)

I had Gnubg expert with world class cube play against Gnubg supremo with world class cube 800 money games, Jacoby = NO.

Gnubg supremo with world class cube won a net of 97 points, which is .12125 point per game. This is somewhat more than I'd have expected relative to the result Michael Depreli reported of a much longer session of 0.06/ppg cubeless, much longer being about 100,000 games. However, 800 games really are not very many.

More interestingly, I think, because for these purposes 800 games is a lot:

(A) the average game value (points won by either side per game) = 2.3, a value consistent with previously reported data.

(B) I supposed that two reasonably adept and expert human players could play 10 games per hour, so I divided the 800 games into 80 groups of 10, reflecting 80 hours of play.

1. No. of Entries = 80 (hours, i.e, groups of 10 games)

2. Sum of Entries = 97 (Gnubg 2-/2-ply's net win)

3. Mean Average = 1.2125 (Gnubg 2-/2-ply's win/hour

4. Std. Dev. = 9.5547027033812

If I've understood Stanley's figures correctly, this SD value is not too different from the figure(s) he used. I think it's a reasonably good estimate of SD between two fairly equal and expert players.

Of the 80 groups of ten games:

71.25% of "hourly" results were within +-1 SD. Expected (with normal distribution) = 68.2%

95% of "hourly" results were within +-2 SDs. Expected (with normal distribution) = 95.45%

98.75% of "hourly" results were within +-3 SDs. Expected (with normal distribution) = 99.73%

Distribution of the 80 "hourly" results:

Standard Deviations:-3 or more-3 to -2-2 to -1-1 to 00 to 11 to 22 to 33 or more
Results 1 1 8 31 26 11 2 0

(C) another day!

Links:

An online standard deviation calculator (Excel would work, too)

http://invsee.asu.edu/srinivas/stdev.html

An online risk of ruin calculator

http://www.poker-tools-online.com/riskofruin.html

Raw "per hour" results of the Gnubg/Gnubg session (turned sidewise, sorry):

Points
-28
Mean Average - 3*9.5547 = -27.4516 = 3 Standard Deviations from the Mean Average
-23
Mean Average - 2*9.5547 = -17.8969 = 2 Standard Deviations from the Mean Average
-17
-16
-14
-13
-11
-10
-9
-9
Mean Average - 1*9.5547 = -8.3442 = 1 Standard Deviation from the Mean Average
-8
-8
-8
-7
-7
-6
-6
-6
-5
-5
-4
-3
-3
-3
-3
-3
-3
-2
-2
-2
-1
-1
-1
-1
-1
+0
+0
+0
+0
+1
+1
Mean Average = 1.2125/pph
+2
+2
+2
+2
+3
+3
+3
+3
+3
+4
+4
+5
+5
+6
+7
+7
+7
+7
+7
+8
+8
+8
+8
+9
+10
+10
----- 1.2125 + 1*9.5547 = 10.7672 = 1 Standard Deviation from the Mean Average
+11
+12
+12
+12
+13
+13
+14
+14
+16
+19
+20
----- 1.2125 + 2*9.5547 = 20.3219 = 2 Standard Deviations from the Mean Average
+21
+24
----- 1.2125 + 3*9.5547 = 29.8766 = 3 Standard Deviations from the Mean Average

Messages In This Thread

 

Post Response
Your Name:
Your E-Mail Address:
Subject:
Message:

If necessary, enter your password below:

Password:
 

 

[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums is maintained by Stick with WebBBS 5.12.