Another example, I think, of how altering the frequency of doublets affects a vast number of positions in ways that are far from obvious to players in the SHG "red room." Here are two positions in which, with normal dice, Blue hits exactly 18/36 = 50% of the time immediately:
Unlimited match. Blue on roll.
| White | 75 | ||
|---|---|---|---|
                       | |||
| Blue | 118 | ||
| Position ID: 7g1fAAC2bQOAIQ Match ID: UQkAAAAAAAAE | |||
| White | 61 | ||
|---|---|---|---|
     | |||
| Blue | 112 | ||
| Position ID: d+4GBAC4ewdACA Match ID: UQkAAAAAAAAE | |||
I think it would difficult for you to guess how often Blue hits with either "8.33% doublets" dice or "9.22% doublets" dice in these two positions, so I'll just tell you. In the first position:
| Normal dice | "8.33% doublets" dice | "9.22% doublets" dice | ||||
| 2 doublets | * 2.7777 = | 05.5555 | * 1.3888 = | 02.77777 | * 1.5366 = | 03.0732 |
| 16/2 = 8 nondoublets | * 5.5555 = | 44.4444 | * 6.1111 = | 48.88888 | * 6.0518 = | 48.4144 |
| total | 50.0 | 51.6666 | 51.4876 | |||
In the second position:
| Normal dice | "8.33% doublets" dice | "9.22% doublets" dice | ||||
| 4 doublets | * 2.7777 = | 11.1111 | * 1.3888 = | 05.555555 | * 1.5366 = | 06.1464 |
| 14/2 = 7 nondoublets | * 5.5555 = | 38.8888 | * 6.1111 = | 42.7777 | * 6.0518 = | 42.3626 |
| total | 50.0 | 48.3333 | 48.5090 | |||
That ... just ain't right, whether it's called "backgammon" or not.