Domester Joined: Oct 31, 2011
• Posts: 2
November 1st, 2011 at 1:09:01 PM permalink
I just received a promotion from one of the Reno casinos about a dice-based giveaway. You throw five dice and your prize is based on the poker hand generated. A large straight (1-5 or 2-6) pays \$5,000. Is this the correct formula for the probability of hitting such a payout --

2*5!*(4/6)*(3/6)*(2/6)*(1/6)/(6^5) = 0.000572 ??

7outlineaway Joined: Nov 13, 2009
• Posts: 282
November 1st, 2011 at 2:02:46 PM permalink
There are 5!= ways to roll 12345, and  ways to roll 23456.

There are 6^5 = 7776 ways to roll five dice.

 / 7776 = [.03086]
boymimbo Joined: Nov 12, 2009
• Posts: 5994
November 1st, 2011 at 2:20:12 PM permalink
There are indeed 6^5 ways = 7776 ways to throw the dice. You are looking for combinations of 2, 3, 4, 5, 6.

Assume that the 1st die is any number (be it a 1 - 6). The 2nd die must be different from the 1st die. That has a 5/6 shot. The third die must be different from the 1st two that has a 4/6 shot. Then you have 3/6 and 2/6.

So, that leaves 5/6*4/6*3/6*2/6, giving you a .092593. But of these, only a fraction are straights. You have 12346 12356 12456 13456 and 12345 and 23456. So, multiply by 1/3 to get .030864.

However, if this is the Harrah's promotion, the prize structure is as folllows:

Prizes:
Five of A Kind = \$5,000
Four of A Kind = \$1,000
Large Straight = \$750
Full House = \$500
Small Straight = \$250
3 of a kind = \$150
Two Pairs = \$100
One Pair = \$50
Less than one pair wins another roll until prize is earned
----- You want the truth! You can't handle the truth!
boymimbo Joined: Nov 12, 2009
• Posts: 5994
November 1st, 2011 at 2:23:48 PM permalink
Quote: 7outlineaway

There are 5!=125 ways to roll 12345, and 125 ways to roll 23456.

There are 6^5 = 7776 ways to roll five dice.

250 / 7776 = .03215

5! is 120.
----- You want the truth! You can't handle the truth!
7outlineaway Joined: Nov 13, 2009
• Posts: 282
November 1st, 2011 at 2:26:46 PM permalink
Quote: boymimbo

5! is 120.

Back to sixth grade for me. 240 / 7776 = .03086, as you calculated above.
dm Joined: Apr 29, 2010
• Posts: 699
November 1st, 2011 at 3:06:11 PM permalink
Quote: boymimbo

There are indeed 6^5 ways = 7776 ways to throw the dice. You are looking for combinations of 2, 3, 4, 5, 6.

Assume that the 1st die is any number (be it a 1 - 6). The 2nd die must be different from the 1st die. That has a 5/6 shot. The third die must be different from the 1st two that has a 4/6 shot. Then you have 3/6 and 2/6.

So, that leaves 5/6*4/6*3/6*2/6, giving you a .092593. But of these, only a fraction are straights. You have 12346 12356 12456 13456 and 12345 and 23456. So, multiply by 1/3 to get .030864.

However, if this is the Harrah's promotion, the prize structure is as folllows:

Prizes:
Five of A Kind = \$5,000
Four of A Kind = \$1,000
Large Straight = \$750
Full House = \$500
Small Straight = \$250
3 of a kind = \$150
Two Pairs = \$100
One Pair = \$50
Less than one pair wins another roll until prize is earned

By golly, that's an advantage play if I ever saw one! Can they run out of dice?