What are the odds

[Rchawks]

So for you Mathematicians out there, what are the odds of two players with a backgammon game rolling 5 sets of the same number at the opening of the game to determine who will be first? My wife and I did did just that yesterday. ??

 

[msinger]

ChatGPT says the odds of rolling the same number on both dice for five consecutive turns are 1 in 7776

 

[Rchawks]

We've been watching marathon episodes of Bewitched from the library, lol, then that...Thanks.

 

[MS Coast]

ChatGPT says the odds of rolling the same number on both dice for five consecutive turns are 1 in 7776

1:7776 looks like the odds of rolling the same number on one die for five turns. 1 / 6^5 = 1/7776

Doesn't he mean rolling the same total of two dice by two people on five consecutive turns? Much more unlikely and more complex to calculate.

 

[msinger]

Doesn't he mean rolling the same total of two dice by two people on five consecutive turns? Much more unlikely and more complex to calculate.

Yep! I asked for clarification and the response was:

1. The probability of one pair of players rolling the same number five times in a row is 1/77761.
   
   
2. The probability of two independent pairs of players doing this at the same time is:
   
   

Thus, the odds of two different pairs of players rolling five sets of matching numbers simultaneously are 1 in 60,466,176.

 

[Rchawks]

It was 1 dye each to see who had the higher number for first choice. We rolled 3's, 5's, 2's,4's, 6's, then she got the higher number and got to go first.

 

[msinger]

There's only one thing to do now...

Go for 6 matching sets!

 

[Rchawks]

It was crazy, very fun game we haven't played in years. Maybe I should film future games, lol.