Alex's numbers game - [Odds alert]

[bonanova]

I've got a sweet little dice game for ya, boys, and I'll even help

you figure your chances. I know how you hate doing that.

When Alex offers to help, people generally walk the other way.

But this is Morty's, and none of the blokes there wants to be

thought of as timid. So they sauntered over to Alex's table,

where he had laid a sheet of paper, with the numbers 1-6

written, each in its little box:

+---+---+---+

| 1 | 2 | 3 |

+---+---+---+

| 4 | 5 | 6 |

+---+---+---+

Now here's the game, my laddies...

You lay your bet on one of those numbers. Then you roll these three

dice here. If your number shows up, you get double your bet returned.

What do you say?

Davey and Ian weren't sure. Jamie, after thinking a bit, asked

what if my number comes up twice? Shouldn't I get something

extra for that?

You're astute beyond your years, said Alex. Here, and I promised

to help figure the game out. So, let's go through it, OK? Suppose

you bet all six numbers. If no number comes up twice, then you'd

double your money on three of your bets, and you'd lose your

money on the other three. So that way, it's an even game.

So what you're asking for is a little something extra if the dice

aren't all different. Well you caught me in a good mood tonight,

and here's what I'll do. You bet your number, and roll the dice.

If your number comes up once, you win double, just like before.

But now, if it comes up twice, I'll make it triple, and if it shows up

on all three dice, I'll give ya four times your bet. How's that?

Jamie thought a moment, and he was about to reply, when Ian

walked to the table and said, Outta my way, Jamie, I'll play!

Would you have played?

[Guest]

Allright Bonanova,

I think you may have named this one appropriately, correct me if I'm wrong.

I would get $0 if I rolled three different numbers with a buck on all marks but if I rolled three of the same numbers with a buck on all marks I would lose $2? so the house wins more when I roll dubbs or trips. Did I figure that right? I'm workin on the giant mugs one right now so I may be a lil groggy.

Peace

[bonanova]

Alex's momma didn't raise no fools.

[Guest]

so basically your betting that you'll get double your money back on 3*5*5/6^3 = 75/216 probability, triple on 3*5/6^3 = 15/216, and quadruple on 1/6^3 = 1/216. adding all that up you get expected value 2*75/216 +3*15/216 +4*1/216 = 199/216 = .92 so if you bet 1 dollar you could expect to get back 92 cents. i'll leave the potential "win" for betting on two numbers for someone else.

Edited July 18, 2009 by phillip1882

[Guest]

if you bet on all 6 numbers you end up with the following.

if you get 3 different numbers you break even, however if you get 2 of a kind you get 5/6 or 3 of a kind you only get back 2/3.

this leads to the following return...

1*(6*5*4/6^3) +5/6 *6*5*3/6^3 +2/3 *6/6^3 = (120 +75 +4)/216 = 199/216.

if alex wanted to make it a fair game, he simply needs to make it such that if you get 2 of a kind, its 4x value, and 3 of a kind is 6x value.

going back to betting on one for example would give 2*75/216 +4*15/216 +6*1/216 = 1

[bonanova]

if you bet on all 6 numbers you end up with the following.

if you get 3 different numbers you break even, however if you get 2 of a kind you get 5/6 or 3 of a kind you only get back 2/3.

this leads to the following return...

1*(6*5*4/6^3) +5/6 *6*5*3/6^3 +2/3 *6/6^3 = (120 +75 +4)/216 = 199/216.

if alex wanted to make it a fair game, he simply needs to make it such that if you get 2 of a kind, its 4x value, and 3 of a kind is 6x value.

going back to betting on one for example would give 2*75/216 +4*15/216 +6*1/216 = 1

Exactly. But, you know Alex....

[Guest]

The game is known as "Crown & Anchor" and is or was popular in village fêtes and such like. There are special dice, which one can still purchase, the faces showing the four suits from a pack of cards, with the last two faces displaying a crown and an anchor respectively. Bets are made on a special board displaying those particular symbols.