Re: A dice game I play at the bar, help me.
From: Top Spin (ToppSpin_at_hotmail.com)
Date: 12/18/04
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Date: Fri, 17 Dec 2004 17:27:44 -0800
On Sat, 18 Dec 2004 00:08:26 GMT, "dg" <dan_gus@hotmail.com> wrote:
>Math wizards,
>I stop at the bar on Fridays for a beer with the guys. They have a jar of
>money on the counter and a cup with 5 dice. On the jar is 5 numbers. If
>you roll the numbers, you win the money from the jar. (it costs $1 for 2
>rolls) Then you roll another time and THOSE numbers get written on the jar
>for the next guy. 10% stays in the jar to keep the game alive.
>
>So, to get to the point of this post. Right now the numbers are: 1, 1, 1,
>1, 5
>
>Nobody has hit these numbers for weeks. There must be $500 in the jar right
>now. The guys at the bar seem to think that they are less likely to hit 1,
>1, 1, 1, 5 because there is so many 1s. I disagree, but I can't exactly
>explain why.
>
>Can anybody give me any insight?
I will assume that you don't care about the order of the numbers on
the dice. That is, you shake the dice cup and turn it over on the bar.
When you look at the numbers on the dice, you don't care wjich nuber
is on which die.
If that is true, the guys are right.
To see it more easily, change the game so that instead of rolling 5
dice, you are flipping 2 coins. There are 2 possibilities for the each
coin (H/T). To get the math right, it is necessary to keep track of
the order of the flips. That is, we need to number the coins (or the
dice) so that we know what the value of each coin (or die) is.
For two coins, there are 4 possibilities:
Coin 1 2
H H
H T
T H
T T
So each outcome has a 1 in 4 (25%) chance of coming up.
If you DO care about the order, then "HT" would be different from "TH"
and each possible combination on the jar (HH, HT, TH, or TT) would be
equally liklely.
If you do NOT care about the order, then HT would be the same as TH so
that there are only 3 possible outcomes:
TT (25%)
HH (25%)
TH or HT (50%)
As you can see, the combinations with "lots of heads" or "lots of
tails" are less likely than the ones with both heads and tails.
In the case of the dice, there are a total of 7,776 combinations
(6x6x6x6x6). There are only 5 ways to get a roll that has 4 1s and 1
5:
Die 1 2 3 4 5
1 1 1 1 5
1 1 1 5 1
1 1 5 1 1
1 5 1 1 1
5 1 1 1 1
so the odds are 5/7,776 or 1 chance in 1,555.2 tries.
There are 120 ways to get 1-2-3-4-5 or 120/7776 which would be 1
change in 64.8 tries.
I won't list them all, but they start out like this:
Die 1 2 3 4 5
1 2 3 4 5
1 2 3 5 4
1 2 4 3 5
1 2 4 5 3
1 2 5 3 4
1 2 5 4 3
So, the odds right now (at $500) are very bad. I am surprised that
anyone would play. It's actually worse since you will be leaving $50
behind for the next guy.
Since you have one chance in 1,555 of winning the pot, the pot would
need to contain $1,555 after the 10% discount to make it even money.
If you have enough money and you are allowed to play al many times in
a row as you like, you could just keep playing until you win. ;-)
-- Email: Usenet-20031220 at spamex.com (11/09/04)
- Previous message: Ray Koopman: "Re: Help with Tricky Designed Experiment"
- In reply to: dg: "A dice game I play at the bar, help me."
- Next in thread: Horst Kraemer: "Re: A dice game I play at the bar, help me."
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