rumba434
• Posts: 34
Joined: May 13, 2020
March 14th, 2023 at 9:37:19 AM permalink
3 random numbers, all different, are picked between 0-36.

Scarlett wins if at least one is red
Jet wins if at least one is black
Oddette wins if at least one is odd
Evan wins if at least one is even
Magnus wins if at least one is 19-36
Minos wins if at least one is 1-18

If one of the numbers is 0 it helps nobody.

What are the odds all 6 players win?
DJTeddyBear
• Posts: 11011
Joined: Nov 2, 2009
March 14th, 2023 at 11:18:00 AM permalink
EDIT: I completely missed the different numbers part.
My math below allows duplicates.

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I assume you mean for the purposes of this calculation, the ball always lands in 1-36.

Let's think about a single condition, and work backwards.

What's the odds that all three spins will be red?

18/36 * 18/36 * 18/36, or 1/2 * 1/2 * 1/2 = 1/8.

Since we don't care if it's all black or all red, the odds of all black OR all red is 1/8 * 2 or 1/4.

Therefore, it's 3/4 that there's at least one red and one black.

In other words, there's a 3/4 chance that both of your black/red people will win.

Similarly, there's a 3/4 chance that both of your even/odd people will win, and 3/4 that both high and low will win.

Therefore, it's ( 3/4 ) ^ 3 that all all six people will win.

( 3/4 ) ^ 3 = 42.1875%

Mind you, I'm no math expert, but I think that's right. Anybody got a different answer?
Last edited by: DJTeddyBear on Mar 14, 2023
I invented a few casino games. Info: http://www.DaveMillerGaming.com/  Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
DJTeddyBear
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Joined: Nov 2, 2009
March 14th, 2023 at 11:35:22 AM permalink
Assuming my logic is right, here's how to calculated it for a double zero wheel:

Start with failure: Any color, then red or green, then red or green:

38/38 * 20/38 * 20/38 = 0.277008

So one success is 1 - 0.277008 = 0.722992

So all three successes is 0.722992 ^ 3 = 0.377920 = 37.792%

FYI: Single zero: 39.9182%
Triple zero: 35.8000%
I invented a few casino games. Info: http://www.DaveMillerGaming.com/  Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
rumba434
• Posts: 34
Joined: May 13, 2020
March 14th, 2023 at 11:51:33 AM permalink
Quote:

I assume you mean for the purposes of this calculation, the ball always lands in 1-36

Nope, single zero table, 3 random unique numbers. One of them can be 0, in that case there are only 2 "useful" numbers for the players.
rumba434
• Posts: 34
Joined: May 13, 2020
March 14th, 2023 at 12:06:12 PM permalink
For example the chance of Scarlett winning as an isolated case is 1-((19/37)*(18/36)*(17/35)) or 87.529%
rumba434
• Posts: 34
Joined: May 13, 2020
March 14th, 2023 at 12:33:47 PM permalink
I've just realised that the odds of getting a green and 2 alike colours is 0.03828 (3/37)*(17/36)
The probability of getting 3 alike non greens is (34/37)*(17/36)*(16/35)=0.19836.

(1-0.23664)^3 (not quite as colour, size and parity are not completely independent, but good enough) 0.44482 for a single zero table I think.
rumba434
• Posts: 34
Joined: May 13, 2020
March 14th, 2023 at 12:47:54 PM permalink
Actually 3 alike non greens is (34/37)*(17/35)*(16/34) or 0.21003

1-(0.24831)^3=0.42473

I think I've solved my own question and got it right now, but I'd be happy if any mathemagicians were to check.
rumba434
• Posts: 34
Joined: May 13, 2020
March 14th, 2023 at 1:00:23 PM permalink
OK here we go again

a green and 2 alike colours is actually 0.03938 (3/37)*(17/35)

total 0.24941

(1-0.24941)^3= 0.42287 final chance
ThatDonGuy
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March 14th, 2023 at 4:40:04 PM permalink
I did a brute-force search on all 7770 sets of 3 different numbers drawn from the 37 possible (I assume it's a single-zero wheel), and found 3294 that won, which is about 42.394% of the time.
rumba434
• Posts: 34
Joined: May 13, 2020
March 14th, 2023 at 5:41:53 PM permalink
Quote: ThatDonGuy

I did a brute-force search on all 7770 sets of 3 different numbers drawn from the 37 possible (I assume it's a single-zero wheel), and found 3294 that won, which is about 42.394% of the time.

Nice one, thanks.
DJTeddyBear
• Posts: 11011
Joined: Nov 2, 2009
March 14th, 2023 at 8:20:39 PM permalink
Quote: ThatDonGuy

I did a brute-force search on all 7770 sets of 3 different numbers

First of all, 3 different numbers?
Oh. I missed that part. That changes my math a bit.

Secondly, howd you get 7770?
37 * 36 * 35 = 46,620
I invented a few casino games. Info: http://www.DaveMillerGaming.com/  Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
rumba434
• Posts: 34
Joined: May 13, 2020
March 15th, 2023 at 3:43:44 AM permalink
Quote: DJTeddyBear

Secondly, howd you get 7770?
37 * 36 * 35 = 46,620

6 combinations
DJTeddyBear
• Posts: 11011
Joined: Nov 2, 2009
March 15th, 2023 at 5:27:05 AM permalink
Quote: rumba434

Quote: DJTeddyBear

Secondly, howd you get 7770?
37 * 36 * 35 = 46,620

6 combinations

6 combinations of WHAT?
Show the math.

I tried to figure out what you meant, but 6 ^ 5 = 7,776
So I have no clue.
I invented a few casino games. Info: http://www.DaveMillerGaming.com/  Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
rumba434