July 23rd, 2018 at 4:54:46 PM
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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.

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.

It’s all about making that GTA

July 23rd, 2018 at 7:25:18 PM
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agree. Yahoo!Quote:Ace2This 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.

I think your error is thisQuote:Ace2C (x1) = 155/216C + 25/216D

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

> 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

6,8 | 7,7 | 68-77 | from | mean rolls |
---|---|---|---|---|

0.526716142 | 0.425127058 | 0.048156801 | 0,0 | 7.410042457 |

0.700080623 | 0.258263908 | 0.041655469 | 1,0 | 5.340499866 |

0.238276782 | 0.714067861 | 0.047655356 | 0,1 | 4.570339306 |

0.409836066 | 0.508196721 | 0.081967213 | 1,1 | 3.540983607 |

I was off on this one too, going by feel

Sally

I Heart Vi Hart

July 23rd, 2018 at 9:47:22 PM
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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 it’s 10 in 36.

But the final result seemed reasonable so I didn’t bother checking my math. That’s why people should check their math

But the final result seemed reasonable so I didn’t bother checking my math. That’s why people should check their math

It’s all about making that GTA