GielenDJ wrote: ↑20 September 2023, 23:21
Just played another "low" posibility game of the 7 doubles on 23 for one of both parties.
GielenDJ, I assume that you expect something from random numbers that random numbers will not fulfill. If I read your posts correctly you are interested in your rate of doubles, in your opponent rate of doubles, and in the total rate of doubles of each game. You feel that there are too many outliers, i.e. you don't claim that doubles occur to often or too seldom but that there are too many extremes. Please correct me, if I am wrong.
I want to explain my point in more detail...
The game you mentioned above had 23 rolls by you, 23 rolls by your opponent. You got 2 doubles, he got 7.
It is easy to calculate how many doubles to expect out of 23 rolls. 23/6 = 3.83, so the expected value is approx. 4.
Many people do not consider the fact that is quite unlikely (!) to reach exactly 4 doubles out of 23 rolls - even if this is the expected and most likey outcome. The probability is 21.4%.
If you expect yourself to get the expected number (4) AND your opponent to get the expected number (4) then the probability to get this in a match is only 4.5%. I.e., in 95.5% of your games you will detect an outlier either in your statistic, the statistic of your opponent, or both.
Of course your expectations will probably be not that strict. You will probably also accept 3/23 as "normal", although it has only 13% doubles instead of the expected 16.67%. From your posts I rather doubt that you will accept 5/23 doubles since this would be a 21.7% double-rate instead of the expected 16.67%. But even if you accept both outliers as "normal results", i.e. 3,4, or 5 out of 23 is "normal" you still have a probability of 65% that you will detect an outlier in your statistic or your opponents statistic. If you also look at the joined statistic of both players (as you did) then the probability of getting an outlier surpasses the 70% mark.
Summary1: It is expected to find small outliers in almost every game (95%) and it is expected to find large outliers in the majority of games (70%) if you look at small sample sizes of approx. 25 rolls.
GielenDJ wrote: ↑20 September 2023, 23:21
But, in real life games, i never had this feeling.
I assume that you have never(!) made a statistic of doubles in your real life games. Not even a single game! Let alone 50+ like on BGA...
My assumption is quite safe since I - as a tournament player - have not done such a statistic on my real life games - ever. And I do not know of any Backgammon player that does for real life games.
If you don't record your game with video you would need to track every roll of the game while playing - which would be hugely distracting. You need 4 columns (double/no double/double opponent/no double opponent) and you are not allowed to forget a single roll of the whole game log - otherwise your statistic is skewed. Don't tell me you do this regularly, I don't know any player that does.
And if you record your life games with video - as I often do - one does not count the number of doubles while/after watching the video because the only interesting thing is if one made mistakes. Analysis tools like XG provide you with a luck rating and a statistic of rolled doubles - but nobody looks at them. There is no point of analyzing if I could have kept the precision dice a little longer in my hand to change their temperature, shaked the dice cup a little bit shorter, or thrown the dice a little bit higher in the air... Things that I cannot influence I don't need to analyze.
Summary2: Since you never got an exact feedback of rolled doubles in your real life games your "gut feeling" that in real life anything is different to BGA is just wrong. In real life the dice also behave as mathematicians predict (on the long run!). The "dice" on BGA also behave as expected since they rely on a well documented and well tested PHP-function that is used world-wide for far more important things like throwing dice on BGA...