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For all you fans of ATS racing cubes out there...

Posted By: Bob Koca
Date: Wednesday, 4 September 2024, at 1:21 a.m.

In Response To: For all you fans of ATS racing cubes out there... (Timothy Chow)

How much clock time? It is enough near the end to just calculate the win chance. White needs to win slight more than 1/9 of the games for it to be a take.

31/36 x 31/36 of the time blue does not get working doubles and white has a chance by being of in 2. If we call it 5/6 x 5/6 instead we are at 25/36 and will be slightly understating chances for white.

Given that white gets that chance how many games would white win out 1296?

66 and 55 give 2 x 36 = 72 72 so far.

44 gives 1 x 25= 25 97 so far.

33, 65, 64, 63, 62, 54, 53, 22 gives 14 x 5 = 70 and at 167 so far.

61, 52, 43 gives 6 x 4 = 24 and at 191 so far.

51, 42 gives 4 x 3 = 12 and at 203 so far.

41, 32 gives 4 x 2 = 8 and at 211 so far.

31, 11 gives 3 x 1 = 4 and at 214 so far.

21 gives 0

So 214 games out 1296.

Conveniently, extremely close 216 out of 1296 which is 1/6th. That adjustment favors white but I think is less than the adjustment we made earlier in the other direction.

1/6 x 25/36 = 25/216 This is between 12.5% = 1/8 = 25/200 and 11.1% = 1/9 = 25/225 and closer to the latter. Adjustments favored white so my guess is about that 12.5% figure.

So clear take. Volatility is enough so I think recube.

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