rumba434
rumba434
Joined: May 13, 2020
  • Threads: 10
  • Posts: 34
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
DJTeddyBear
Joined: Nov 2, 2009
  • Threads: 207
  • Posts: 10987
March 14th, 2023 at 11:18:00 AM permalink
EDIT: I completely missed the ‘different numbers’ part.
My math below allows duplicates.

——

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
DJTeddyBear
Joined: Nov 2, 2009
  • Threads: 207
  • Posts: 10987
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
rumba434
Joined: May 13, 2020
  • Threads: 10
  • Posts: 34
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
rumba434
Joined: May 13, 2020
  • Threads: 10
  • Posts: 34
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
rumba434
Joined: May 13, 2020
  • Threads: 10
  • Posts: 34
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.


Adding them comes to 0.23664

(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
rumba434
Joined: May 13, 2020
  • Threads: 10
  • Posts: 34
March 14th, 2023 at 12:47:54 PM permalink
Actually 3 alike non greens is (34/37)*(17/35)*(16/34) or 0.21003

Adding is 0.24831

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
rumba434
Joined: May 13, 2020
  • Threads: 10
  • Posts: 34
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
ThatDonGuy
Joined: Jun 22, 2011
  • Threads: 117
  • Posts: 6170
Thanks for this post from:
rumba434
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
rumba434
Joined: May 13, 2020
  • Threads: 10
  • Posts: 34
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.
link to original post



Nice one, thanks.
DJTeddyBear
DJTeddyBear
Joined: Nov 2, 2009
  • Threads: 207
  • Posts: 10987
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…
link to original post

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
rumba434
Joined: May 13, 2020
  • Threads: 10
  • Posts: 34
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
DJTeddyBear
Joined: Nov 2, 2009
  • Threads: 207
  • Posts: 10987
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
link to original post

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
rumba434
Joined: May 13, 2020
  • Threads: 10
  • Posts: 34
March 15th, 2023 at 5:55:36 AM permalink
123, 132, 213, 231, 312 and 321 are all the same. There are 6 ways to get the same 3 numbers, so 7770 unique sets of 3 numbers out of 46620 ways

  • Jump to: