Dice rolls and probabilities...

Anybody know what the odds are of HAL rolling the exact same outcome 3 times in a row? It seems to happen far too often in these games. Having played the board game with dice I remember the frequency of rolling the same outcome twice, it did happen fairly often, but three times was a rare event as I recall.

What was the roll? The chances of rolling 2-12 three times in a row would be greater than the chance of rolling 2-7 - not 100% sure of the math but it appears rolling three straight 3-7's would be equal to rolling two straight 3-12's

2.78?

How is rolling a 2 - 12 a greater probability than rolling a 2 - 7?!? The ONLY way to roll a 2 - 12 is with a "2" and two "6's"...and with a 2 - 7...you, of course, need the "2"...but...can roll a 1 & 6, 2 & 5, 3 & 4, 4 & 3, 5 & 2 & 6 & 1. So...doesn't that lead one to believe that it's much "easier" to roll a 2 - 7 than a 2 - 12?!?

HUH

Let's say you roll a 2-7 as above.
The chances of that happening 2 more times in a row would be...

there is a 1/36 chance of rolling the 2 again 2 in a row.

there is also 36/1296 chance of rolling 7 2 more times in a row.

So the overall chance of getting 2-7 twice more in a row after it comes up the first time is 1/36 * 36/1296 = 36/46656
(that's 1/1296)


the odds of getting a 2-12 are smaller

still 1/36 of getting that 2 again 2 times in a row, but

there is only a 1/36 chance of getting that 12 to come up again once...or 1/1296 of it coming up twice after the initial roll.

Therefore the chance of rolling 2-12 twice more after it comes up once is only 1/46656.

if you take all rolls that start with 2, I calculate you have a 146/46656 chance of getting 3 in a row, or roughly
1/320 chance.

you also have similar odds of 3 in a row for each of the other 5 first numbers that can come up.
So, my take on it is regardless of the first number rolled, overall your chances of getting 3 in a row being the same is roughly 1/320.

My math may be faulty, but with a minimum of 55 rolls a game and 162 games played there should be 3 in a row of some kind occurring in a game you play at least 27 times a season.

WOW! Good analysis!

When I said greater I meant like 36 to one is greater than 12 to 1 - poorly worded on my part! Of course 7 is the most likely roll.