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View Full Version : Dice game. Calculation off odds. [calling out MISC statisticians] (semi-serious)



\G/
09-15-2009, 07:38 AM
So a couple of months ago I was at a party in Surfers Paradise (not my home town) and a dice game broke out. The rules were local to the reigon and I had never heard them before, but being a bit of a gambler I thought I would learn and have a punt. I came out behind about $160 but that doesn't bother me at all. What bothers me is that the game seems fundamentally flawed (not that it is rigged, because all players play by the same rules - but you will see what I mean).

The rules were simple.

You play with three dice.
All three are rolled at once.
If your roll is a scoring roll, you pass to the player to your left.
If your roll is not a scoring roll, you roll again.
The dice are passed round the circle until every player has a scoring roll.
Highest scoring roll wins the buy ins (equal for every player - in this case $20 per game).
If the highest score is equalled, the game resets from the start and all scores are cancelled.

Scoring rolls go like this (from lowest to highest):

1,2,3

A double. (doubles are ranked by the 3rd dice - ie: the dice which is different to the other two. EG: double one with a six, is better than double six with a two)

A triple.

4,5,6


Now I am not a great statistician but appear to me that:

The highest roll and the lowest roll have the exact same probability of occuring.
Worse still the odds of rolling the second highest roll (triple 6) or any other triple are substancially lower than rolling the highest scoring roll (4,5,6).

Here is my logic:


The odds of rolling triple 6 are:

6x6x6 = 216 (6x6x6 because only one number may appear on each die)

216 to 1.


The odds of rolling 4,5,6 are:

2x3x6 = 36 (as the first die can be any one of three numbers, the second can be either one of the remaining numbrs, while the third
can only be one).


This would appear to mean you are 6 times more likely to roll the best score than the second best.


Is my logic correct or flawed, please tell me!


Cliffs:

- Trying to work out is my odds calculations are correct.

andrewholler
09-15-2009, 07:42 AM
http://topbanana.files.wordpress.com/2009/02/confused.jpg

FunkLord
09-15-2009, 07:44 AM
The odds of getting triples is the same as the odds of getting 4,5,6.

There are 6 sets of triples, and 6 ways 4,5, and 6 can be arranged.

NY Money Mike
09-15-2009, 07:45 AM
LOL at never hearing C-low (sp?) before.

games been played for years. However I do agree even though your stats are wrong. I'll give you correct stats in a min if no one else does

edit:

odds of rolling all the same

111
222
333
444
555
666

6/216 = 1/36

odds of 123 or 456

3c1 x 2c1 x 1c1 = 3 x 2 x 1 = 6/216 = 1/36

edit2: looks like you go pwned. trips or 456 are scored the same:

http://en.wikipedia.org/wiki/Cee-lo

nickk
09-15-2009, 07:45 AM
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\G/
09-15-2009, 07:45 AM
http://topbanana.files.wordpress.com/2009/02/confused.jpg

FUUUUUUUUUUUUUUUUuuuuuuuu

Your rep power has increased by like 3000 in a fortnight.

Good job Dave man.

Jburn
09-15-2009, 07:46 AM
http://topbanana.files.wordpress.com/2009/02/confused.jpg

lol

\G/
09-15-2009, 07:51 AM
LOL at never hearing C-low (sp?) before.

games been played for years. However I do agree even though your stats are wrong. I'll give you correct stats in a min if no one else does

edit:

odds of rolling all the same

111
222
333
444
555
666

6/216 = 1/36

odds of 123 or 456

3c1 x 2c1 x 1c1 = 3 x 2 x 1 = 6/216 = 1/36

Different perspective to what I was taking - I was talking about the odds of rolling 666, not "a triple". I suppose though when you look at it that way the odds don't look so bad.

Am I correct about the odds of rolling specifically triple 6 though?

NY Money Mike
09-15-2009, 07:52 AM
Different perspective to what I was taking - I was talking about the odds of rolling 666, not "a triple". I suppose though when you look at it that way the odds don't look so bad.

Am I correct about the odds of rolling specifically triple 6 though?

only one way to roll 666. so yes 1/216

see my second edit above...

\G/
09-15-2009, 05:07 PM
only one way to roll 666. so yes 1/216

see my second edit above...

It doesn't say anything about odds anywhere in that wiki article?

SeizeTheWeight
09-15-2009, 05:14 PM
LOL at never hearing C-low (sp?) before.

games been played for years. However I do agree even though your stats are wrong. I'll give you correct stats in a min if no one else does

edit:

odds of rolling all the same

111
222
333
444
555
666

6/216 = 1/36

odds of 123 or 456

3c1 x 2c1 x 1c1 = 3 x 2 x 1 = 6/216 = 1/36

edit2: looks like you go pwned. trips or 456 are scored the same:

http://en.wikipedia.org/wiki/Cee-lo

Spot on

I thought I was gonna have to type this out as I was scrolling down, so thanks :)

\G/
09-15-2009, 05:47 PM
Spot on

I thought I was gonna have to type this out as I was scrolling down, so thanks :)

But the odds of rolling any particular double (ie: 666 or 555) is 1/216 correct?

NY Money Mike
09-16-2009, 06:31 AM
It doesn't say anything about odds anywhere in that wiki article?

I was pointing this out


The Banker rolls the dice

Each player gets 3 rolls a turn.When all the bets have been established, the Banker then rolls the dice.

If he rolls 4-5-6, or "triples" (all three dice show the same number), then he instantly wins all bets.

If he rolls 1-2-3 he instantly loses all bets and breaks the bank.

If he rolls a pair and a singleton, then the singleton becomes his "point." E.g. a roll of 2-2-4 gives the banker a point of "4."



you said 456 is higher than trips but I believe it is scored the same. (as we just proved it should be)


But the odds of rolling any particular double (ie: 666 or 555) is 1/216 correct?

I answered this yes already.

1 way to roll 666, 216 total combinations. 1/216