JBeachy wrote: ↑08 December 2022, 03:12
I just lost a game where my opponent rolled 8 doubles in a row. 11 of their final 13 turns were doubles, and 13 of their 26 total dice rolls were doubles.
Let me check since that claim would be really weird if it was true, here is all his rolls of his game (
https://boardgamearena.com/gamereview?table=324587603 ):
ndnnndnnnnnnnddddddddnnddd
13doubles/26, so this was true. it has a probability of (
https://docs.google.com/spreadsheets/d/ ... 1846324187 ): 0.009%.
1/11 012.
You find 8 doubles in a row, it has a probability of (8^6)
1/1 679 616.
But a single probability said nothing, so let's go deeper.
Usually when people find some weird events about double happening, they will look for their double, the opponent double, or both number of doubles.
So, let's take back that
1/11 012, I will 'multiply properly' (i will explain at the very bottom what i mean by that) by 3, and find
1/3 671 which I assume would be the probability I would keep for your game.
But not for your profile, since you did 138 games of backgammon, i could go further and 'multiply properly' by 138. And I find
1/27.
So congrats, if 27 people like you played backgammon for 138 games and shared in the forum their game with the most amount of double between yourself, the opponent, or both player, you would be the one which would get the most unlikely outcome.
And let's take back the second which was
1/1 679 616.
On your game, there was 26 rolls, so there was 19 (26-8+1) starting of 8 streaks of 8 doubles possible. So let's start by 'multiply properly' by 19: 0.001131%, so
1/88 401. Then multiply properly by 3 because you could take your number of double, opponent number, or both player doubles: 0.00339%, so
1/29 467 which is for me the probability i would keep for that game.
Then for your profile, i can multiply properly by 138: 0.467%, which give
1/214.
So if 214 people like you played backgammon for 138 games and shared in the forum the highest number of doubles in a row they got in a single game, you would be the highest.
(and finally about 11 doubles / 13 at the end, it's cherry picking, so I will not analyse that)
My two cents is that it's not likely, so thanks for sharing, but we would need way more testimony like yours to see something weird is happening. Many people just share some thoughs with their game, when in reality, their perception of randomness is wrong and just got slightly unlucky, or just got their one game out of one hundred the most weird.
And thanks for not lieing on your post, it's pretty rare
Finally, since people like saying my maths are wrong (mainly because of langage barrier), I'm open to discussion. But let's said you rolled 5 dices, and got 2 doubles in a row at maximum. It has a probability of 1/36. Then You can have ddnnn or nddnn or nnddn or nnndd for your two doubles in a row, which leave 4 possibilities (5-2+1). So I will multiply properly by 4: "1-(1-1/36)^4" which leave 10.7% chance. You can see that multiply by any number will never make it reach 100% since it multiply the 1-x probability with itself.
Thanks for reading