Ace2
Ace2
Joined: Oct 2, 2017
  • Threads: 22
  • Posts: 817
July 23rd, 2018 at 4:54:46 PM permalink
Though I haven't verified this, my initial calculation is:

A wins...........80,875 / 160,003
Tie.....................7,025 / 160,003
B Wins..........72,103 / 160,003

This is actually a bit easier than the last calc since you don't have to distinguish which player is rolling, so there are only 4 states instead of 8.

A (xx) = 65/108A + 25/108B + 13/108C + 5/108D
B (1x) = 5/36 + 155/216B + 31/216D
C (x1) = 155/216C + 25/216D
D (11) = 25/216 + 155/216D + 5/216E

E is a tie.
Itís all about making that GTA
mustangsally
mustangsally
Joined: Mar 29, 2011
  • Threads: 25
  • Posts: 2463
July 23rd, 2018 at 7:25:18 PM permalink
Quote: Ace2

This is actually a bit easier than the last calc since you don't have to distinguish which player is rolling, so there are only 4 states instead of 8.

agree. Yahoo!

Quote: Ace2

C (x1) = 155/216C + 25/216D

I think your error is this
i got
C (x1) = 65/108C + 25/108D
(and it shows. my simulations were very close at 1st so I figured something you had was incorrect)
> p = count68/sims
> error = 3.29*sqrt(p*(1-p)/sims)
> error
[1] 0.0009997312
> p
[1] 0.5262815
> p-error
[1] 0.5252818
> p+error
[1] 0.5272812
> #1-p
> ##########################
> sims
[1] 2700000
> count68
[1] 1420960
> count7
[1] 1149491
> count7/sims
[1] 0.4257374
> tie
[1] 129549
> tie/sims
[1] 0.04798111

my transition matrix (rows sum to 1)



so,
6,8 wins: 0.526716142
7,7 wins: 0.425127058
tie: 0.048156801

more
6,87,768-77frommean rolls
0.5267161420.4251270580.0481568010,07.410042457
0.7000806230.2582639080.0416554691,05.340499866
0.2382767820.7140678610.0476553560,14.570339306
0.4098360660.5081967210.0819672131,13.540983607


I was off on this one too, going by feel

Sally
I Heart Vi Hart
Ace2
Ace2
Joined: Oct 2, 2017
  • Threads: 22
  • Posts: 817
July 23rd, 2018 at 9:47:22 PM permalink
Good catch. Apparently when I wrote the equation for C, I was thinking 5 in 36 ways for player A to advance, when of course itís 10 in 36.

But the final result seemed reasonable so I didnít bother checking my math. Thatís why people should check their math
Itís all about making that GTA

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