On January 14, 2023 at 4:38:29 PM UTC-7, Philippe Michel wrote:
> On 2023-01-13, MK <
mu...@compuplus.net> wrote:
>> What about dancing against a closed board?
>> All rolls and the average equity are -0.969 so
>> you break even on luck rate and not lose any
>> equity while falling further behind but the player
>> bearing off is gaining equity with each roll??
> The rolls of the closed-out player being all
> equally lucky should be obvious.
Yes, I'm not basing any argument on that.
> The other player doesn't necessarily gain equity
> though.
Okay, but I won't dwell on rarities, (i.e. your second
example), since X's gains/losses are accounted for.
I'm questioning what happens to O's equity.
Based on your example, lets go back a little to:
Gnubg ID: dncHAEDbtgHgAA:QQkAAAAAAAAA
X's average: +0.862 O's average: -0.809
Gnubg ID: dncHAEDbth0AAA:QQkAAAAAAAAA
X's average: +0.893
-0.880
This is your example:
Gnubg ID: dncHAEDbtg8AAA:QQkAAAAAAAAA
X's average: +0.917 O's average: -0.919
After X rolls 65:
Gnubg ID: dncHAEC3bQcAAA:QQkAAAAAAAAA
X's average: +0.759 O's average: -0843
After X rolls 61:
Gnubg ID: dncHAEDbtgEAAA:QQkAAAAAAAAA
X's average: +0983 O's average: -0.924
Playing from first position above, X rolled/moved
4 times 66, 33, 65, 61 and O danced 5 times. Game
analysis shows X gained +0.265 but O lost +0.000
If I want to compensate O for the 5 times that it
danced by giving it proportionately lucky dice when
it can enter after X opens its board, can I somehow
figure it out from the averages of the positions?
While X gained +0.121 in four rolls on the average,
O lost -0.115 in five rolls.
From these numbers, can we derive the real equity
loss for O that is not accounted for?
Any other ideas?
MK