September 13th, 2014 at 9:07:59 PM
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Quote:ThatDonGuyIf it's Coverall, I did a Monte Carlo with 50 million runs, and won 1/763 of the time.

Spread sheet transitional matrix (or whatever they are called): 1 in 766.867413 google doc here

“Man Babes” #AxelFabulous

September 14th, 2014 at 7:22:33 AM
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Are there payouts for patterns other than coverall?

Those might make it a playable game.

Those might make it a playable game.

May the cards fall in your favor.

September 14th, 2014 at 7:35:50 AM
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Quote:mipletSpread sheet transitional matrix (or whatever they are called): 1 in 766.867413 google doc here

I can not imagine how long it took people to do that before excel existed.

Expect the worst and you will never be disappointed.
I AM NOT PART OF GWAE RADIO SHOW

September 14th, 2014 at 8:33:31 AM
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Quote:mipletSpread sheet transitional matrix (or whatever they are called): 1 in 766.867413

I started out trying one of those, but didn't have the "House light bulb moment" to figure it out. It never dawned on me that it's really five identical independent problems ("what is the probability that, if you draw a number from {1, 2, ..., 15} 22 times with replacement, each of the numbers from 1 to 5 will be drawn at least once?").

For those of you playing at home:

Assume the card is B1-5, I16-20, N31-35, G46-50, and O61-65

Concentrate on just the Bs:

Let S(n,k) be the probability of k different numbers from 1-5 being drawn after n Bs have been drawn.

S(0,0) = 1

S(n,0) = S(n-1,0) x 10/15

S(n,k) = (S(n-1,k-1) x (6-k)/15) + (S(n-1,k) x (1 - (6-k)/15)), for 0 < k < 5

S(n,5) = (S(n-1,4) x 1/15) + S(n-1,5)

S(22,5) is the probability that you have drawn all of the numbers from 1 to 5 in 22 draws

The probabilities of drawing 16-20, 31-35, 46-50, and 61-65 are the same, so the overall probability of winning is S(22,5)

^{5}.

September 14th, 2014 at 5:16:53 PM
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busted.

Some people need to reimagine their thinking.

September 16th, 2014 at 9:11:51 AM
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Quote:mipletSpread sheet transitional matrix (or whatever they are called): 1 in 766.867413 google doc here

I tried to copy your Google doc to analyze the 4x4 variant described in my OP and got 1 in approximately 828. Is this right?

September 16th, 2014 at 9:13:27 AM
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Quote:DieterAre there payouts for patterns other than coverall?

Those might make it a playable game.

Some machines had payouts for patterns other than coverall, but then the payout for coverall was reduced.

September 16th, 2014 at 10:02:53 AM
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Quote:DaveG44131Quote:mipletSpread sheet transitional matrix (or whatever they are called): 1 in 766.867413 google doc here

I tried to copy your Google doc to analyze the 4x4 variant described in my OP and got 1 in approximately 828. Is this right?

I'm getting 361.0339019 . I added another sheet.

“Man Babes” #AxelFabulous

September 16th, 2014 at 11:06:30 AM
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Quote:mipletQuote:DaveG44131Quote:mipletSpread sheet transitional matrix (or whatever they are called): 1 in 766.867413 google doc here

I tried to copy your Google doc to analyze the 4x4 variant described in my OP and got 1 in approximately 828. Is this right?

I'm getting 361.0339019 . I added another sheet.

Thanks for checking. I had a feeling I miscopied something.

September 16th, 2014 at 11:56:24 AM
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Quote:DaveG44131Some machines had payouts for patterns other than coverall, but then the payout for coverall was reduced.

Yeah, but an all or nothing payout eats into your playing money quickly.

Some little wins along the way mean you have a better chance of not going broke before the big one hits.

May the cards fall in your favor.