Post
Topic
Board Service Discussion
Re: Satoshi Dice -- Statistical Analysis
by
dooglus
on 14/11/2012, 02:35:25 UTC
Im not great with odds but can anyone tell me the odds of getting 3 seperate transaction rolls over 64 000 in a row? I know that its about 2.5% to get 1 roll over 64000.

Yes, I can.  You probably mean 64000 or over, since 64000 is a losing roll when you're playing "lessthan 64000" too.

The probability of losing a single "lessthan 64000" is:

Code:
>>> 1 - 64000/65536.0
0.0234375

Or about a 1-in-42.666 shot.

To find the probability of it happening 3 times in a row, you just cube that number:

Code:
>>> (1 - 64000/65536.0)**3
1.2874603271484375e-05

That's scientific notation for 0.00001287, and represents a 1-in-77672 shot.

In other words, it's pretty unlikely and probably has never happened since "lessthan 64000" has been played less than 9000 times.

It may have happened of course - it wouldn't be incredibly unlikely.  Not like losing 60 "lessthan 32000" bets in a row, which is so unlikely it will almost certainly never happen.

Edit: note that you'll need to multiply probabilities by 100 to get percentages.  And note also that 42.666 cubed is 77672.

Edit 2: I notice you didn't specify that you were playing "lessthan 64000" at the time.  It's much more likely that someone has got three rolls over 64000 in a row when they were playing other bets.  It's just that "lessthan 64000" is a relatively unpopular bet, and wasn't even available for probably half of SatoshiDice's lifetime so far.