Board Game Arena

Silene is right, and looking at 1 sample piece of data means nothing.
Calculate the odds of rolling the exact die rolls in a game and it's 1 in an astronomical large number.

Here is your data for all your backgammon games. You've rolled the correct amount of doubles:
https://boardgamearena.com/playerstat?i ... 98&game=53

veggivet average All players' average Winners' average
Dice rolls 25.6 25.74 26
Double rolls 4.19 4.18 4.44

I can confirm Jellby's calculation of once within 320 (67-moves-lasting)games on average for you being the player with the single double. (With a simplification of the person with the 8 doubles being the first player and having 1 more roll as the other).

Thanks, that makes perfect sense. Appreciate you guys taking the time to 'set me straight'. Our brains are wired to remember the unusual and not the everyday pattern.

This thread took a different direction than I hoped for. I edited my first post to make my main point more clear.
My main point was: The number of doubles in a Backgammon game can NOT be modeled accurately with a binomial distibution.

Romain672 wrote: ↑25 April 2022, 07:35 If anyone want to calculate the probability himself, read this:
https://docs.google.com/spreadsheets/d/ ... =967036289

This is exactly against my main point of the first post.

To be clear: If you take a number of random dice rolls from all your lifetime Backgammon dice rolls and you want to know the probabilities of how many doubles occur in these rolls, then you can take the above spreadsheet. However if you ask for probabilities of double frequencies in a specific game with that number of dice rolls, it's a different story. As the dice rolls are now structurally grouped together, they are not simply a pre-fixed number of independent rolls anymore.

This gets most clear if you think of very short Backgammon games. Imagine a game that finished after just 20 rolls overall (10 for each player). This game inevitably must contain a large proportion of doubles, otherwise it's impossible to have finished after just 20 rolls. So if you ask about probabilities for double frequencies among all valid games that finish after 20 rolls, it is different from asking what is the probability of certain double frequencies in 20 random dice rolls.

To be more clear: It is still very valuable to use probabilities from binomial distribution as an approximation for the actual probabilities of double frequencies. However, we should all be aware that these probabilites are not precisely correct. This is the most true for the extremely small probabilities of extremely rare events where the binomial model will be far off the correct answer. In the end, the true probabilities will depend on playstyle and there is no general way to calculate them easily.

(To be very clear: All of my points are about properly finished Backgammon games. Don't let me even get started about aborted games...)

Yes, I agree.

1. One thing is: What's the chance of getting 8 doubles in 34 rolls?
2. A different thing is: What is the chance of finishing a game with 8 doubles in 34 rolls?
3. A different thing is: What is the chance of getting 8 doubles in a game, provided we know it finished in 34 rolls?
4. A different thing is: What is the chance of finishing a game in 34 rolls, provided we know we got 8 doubles?

Only #1 is easy to answer, the other 3 depend on play choices, which are not random.

But, on the other hand, when a player comes complaining that their opponent rolled 8 doubles, telling them "that of course they had to roll 8 doubles in order for the game to end so early" doesn't help them much