Game at local bar

[alThor]

[ QUOTE ]
I calculated the chance to qualify to be 77.2426 %

[/ QUOTE ]

I ran a sim with n=10k, so very roughly, margin of error is +/- 1%. Here is what I got:

P(qualify in round 1) ~= 0.154...
P(qualify by round 2) ~= 0.421...
P(qualify by round 3) ~= 0.639...
P(qualify by round 4) ~= 0.791...

Did you mean you ran a sim, or an exact combinatorial calculation? If you simmed it, I can live with our difference. I could run a larger sim if really necessary.

alThor

[gaming_mouse]

[quoteI ran a sim with n=10k

If you simmed it, I can live with our difference.

[/ QUOTE ]

Unless his sim was on a much smaller sample, the difference is very unlikely due to chance. 10k should be more than sufficient here to get your answers closer than that.

The SE for your sime is about:

(.79 * (1 - .79)) / 100 = 0.001659, 1.6%

So you should be within 3% of the true answer, probably closer.

gm

[MickeyHoldem]

Here's some raw data:

Rolling 5 dice... 7776 outcomes
No 6's......3125/7776 - 40.19%
6 no 5's....2101/7776 - 27.02%
65 no 4's...1320/7776 - 16.98%
654 qual....1230/7776 - 15.82%

654 qual with score 11,12......50/7776 - 0.64%

Roling 4 dice... 1296 outcomes
No 5's......625/1296 - 48.23%
5 no 4's....369/1296 - 28.47%
54 qual.....302/1296 - 23.30%

54 qual w/ score 11,12.........24/1296 - 1.85%

Rolling 3 dice... 216 outcomes
no 4........125/216 - 57.87%
4 qual.......91/216 - 42.13%
4 qual w/ score 11,12..........12/216 - 5.56%


Here's the calculation:

= 50/7776
+ 1320/7776 * (9/216+(125/216*(9/216+(125/216*9/216))))
+ 2101/7776 * (24/1296+625/1296*(24/1296+(625/1296*24/1296)+(369/1296*9/216))+369/1296*(9/216+(125/216*9/216)))
+ 3125/7776*(50/7776+(1320/7776*(9/216+(125/216*9/216)))+2101/7776*(24/1296+(625/1296*24/1296)+369/1296*9/216))+3125/7776*(50/7776+(1320/7776*9/216)+(2101/7776*24/1296)+(3125/7776*50/7776))

Here's the calculation to just roll a qualifier:

=1230/7776
+ 1320/7776*(91/216+(125/216*(91/216+(125/216*91/216))))
+ 2101/7776*(302/1296+625/1296*(302/1296+(625/1296*302/1296)+(369/1296*91/216))+369/1296*(91/216+(125/216*91/216)))
+ 3125/7776*(1230/7776+(1320/7776*(91/216+(125/216*91/216)))+2101/7776*(302/1296+(625/1296*302/1296)+369/1296*91/216))+3125/7776*(1230/7776+(1320/7776*91/216)+(2101/7776*302/1296)+(3125/7776*1230/7776))

[alThor]

[ QUOTE ]
[ QUOTE ]
I ran a sim with n=10k

If you simmed it, I can live with our difference.

[/ QUOTE ]

Unless his sim was on a much smaller sample, the difference is very unlikely due to chance. 10k should be more than sufficient here to get your answers closer than that.

The SE for your sime is about:

(.79 * (1 - .79)) / 100 = 0.001659, 1.6%

So you should be within 3% of the true answer, probably closer.

gm

[/ QUOTE ]

??
You're missing a square root, so I stand by my (rough) margin of error Also, I was within 2%, which is borderline close if Micky were simming also, with similar margin of error. However, he was doing exact, so I guess there was an error in my sim. Unfortunately I don't have my sim with me, so I won't get around to debugging it.

I will withdraw my estimates, and go with Mickey's numbers.

alThor

[gaming_mouse]

[ QUOTE ]
You're missing a square root,

[/ QUOTE ]

100 = sqrt(10000)

Am I missing something?

[alThor]

[ QUOTE ]
[ QUOTE ]
You're missing a square root,

[/ QUOTE ]

100 = sqrt(10000)

Am I missing something?

[/ QUOTE ]

You have to square-root the numerator too.

alThor

[Phat Mack]

One question... Suppose you roll a 6,5,4 on the first roll and the other two dice are a 5 and 3

Can you keep the 5 and roll a single die 3 times to try and beat your score of 10?

This game is called "Ship, Captain & Crew." I've always played with three rolls instead of four. Once you've gathered your ship (6), captain (5) and crew (4), you can keep rolling (assuming you have rolls left) for your point, but you must roll both dice.

[gaming_mouse]

[ QUOTE ]
You have to square-root the numerator too.

[/ QUOTE ]

Well, when you are mentally retarded, taking the square root of decimals is not so easy....

[Aytumious]

Thanks guys. I wrote this when I was quite drunk....I'm very impressed with myself [img]/images/graemlins/grin.gif[/img] I knew I was a very big favorite so it seemed like an easy bet. I also lost 100 to him on the superbowl when I took the Pats with 7 point spread. At least the money is going to a cool guy.