Er, then the previous guy was wrong. And for that matter, if the bet is 3, then the payout is surely a multiple of it. Hmm. Well, it can't be 500, it seems, I'm pretty sure of that.

This line of replies is starting to feel very clandestine.

A system of equations can only be uniquely solved if you have at least as many equations as you have variables. There are infinite answers here. However, most will not fit the criteria of natural number solutions.

Definitely still the nuts.. Play the 9 3 of spades.. what flush can beat you?

999xx and 22223 are the other two.. Meraxes ftw!

It seems that your friend is jerking your chain. I've tried every way I can think of and the closest I can get is 499. I can only get 500 with 19 chips or on an american (double zero) wheel.

This was an awesome thread until the math nerds started nitting it up.

Dealer-Guy FTW

If that was top set, then a straight is possible, and you don't have the nuts.

Meraxes got the Omaha question correct; pfap the hold'em question.

Sorry, you are correct. Failed to see beyond the board while ironically stating you can't play the board.

Typo. He meant "inside" bets. The problem is impossible without inside bets since 20 wagers ain't gonna get you back 500 at 2:1.

It ain't rocket science. It's computer science. It's only 3.2 million possibilities.

% cat roulette.c
#include <stdio.h>
main() {
int a,b,c,d,e,sum,tot;
for (a = 0; a < 21; a++ )
for (b = 0; b < 21; b++ )
for (c = 0; c < 21; c++ )
for (d = 0; d < 21; d++ )
for (e = 0; e < 21; e++ ) {
sum = a + b + c + d + e;
tot = 35*a+17*b+8*c+11*d+5*e;
if ( sum == 20 && tot > 495 && tot < 504 )
printf("%d %d %d %d %d %d\n",tot,a,b,c,d,e);
}
}

% gcc -O3 roulette.c
% ./a.out |& sort
496 10 6 0 4 0
496 10 7 0 2 1
496 10 7 2 1 0
496 10 8 0 0 2
496 11 2 0 7 0
496 11 3 0 5 1
496 11 3 2 4 0
496 11 4 0 3 2
496 11 4 2 2 1
496 11 4 4 1 0
496 11 5 0 1 3
496 11 5 2 0 2
496 12 0 0 6 2
496 12 0 2 5 1
496 12 0 4 4 0
496 12 1 0 4 3
496 12 1 2 3 2
496 12 1 4 2 1
496 12 1 6 1 0
496 12 2 0 2 4
496 12 2 2 1 3
496 12 2 4 0 2
496 12 3 0 0 5
496 13 0 0 1 6
496 13 0 2 0 5
496 9 10 0 1 0
499 10 7 1 2 0
499 10 8 1 0 1
499 11 3 1 5 0
499 11 4 1 3 1
499 11 4 3 2 0
499 11 5 1 1 2
499 11 5 3 0 1
499 12 0 1 6 1
499 12 0 3 5 0
499 12 1 1 4 2
499 12 1 3 3 1
499 12 1 5 2 0
499 12 2 1 2 3
499 12 2 3 1 2
499 12 2 5 0 1
499 12 3 1 0 4
499 13 0 1 1 5
499 13 0 3 0 4
502 10 7 0 3 0
502 10 8 0 1 1
502 10 8 2 0 0
502 11 3 0 6 0
502 11 4 0 4 1
502 11 4 2 3 0
502 11 5 0 2 2
502 11 5 2 1 1
502 11 5 4 0 0
502 11 6 0 0 3
502 12 0 0 7 1
502 12 0 2 6 0
502 12 1 0 5 2
502 12 1 2 4 1
502 12 1 4 3 0
502 12 2 0 3 3
502 12 2 2 2 2
502 12 2 4 1 1
502 12 2 6 0 0
502 12 3 0 1 4
502 12 3 2 0 3
502 13 0 0 2 5
502 13 0 2 1 4
502 13 0 4 0 3
502 13 1 0 0 6
502 9 11 0 0 0

Took 0.008 seconds to determine it's not possible.

Too much math, but I got the Omaha and Hold'em questions right, even though I initially forgot about the 999xx where x<9.

Are you claiming to have entered that code in .008 seconds?

I was going to try something like that in C++ but I wasn't sure how to approach the nested FOR loops. FWIW, what you did is kind of what I was thinking, but I shyed away from it thinking there had to be a better, more efficient way. I guess I didn't take in to account that even a few million iterations isn't much on a newer processor.

If the xx are 78 and they're suited and someone holds the JTxx of the same suit wouldn't a straight flush beat 4 of a kind?

Overhead costs are amortized.

I actually did the code a couple days ago before my first post saying it was impossible--didn't really figure I needed to post it. But somehow the debate continued, so fine... there wasn't much effort to rerun it and cut/paste.

If you add "f" and "g" bets at 2:1 and 1:1, it'll spit out lots of ways to hit 500 while taking a whopping 1.8 seconds to run--takes a bit longer to enumerate 1.28 billion possibilities (kinda mind blowing for someone who's been doing this computer stuff for over 30 years that this 3-year-old Intel CPU can compute 1.28E9 roulette payouts of 7 bets in less than 2 seconds using one of four CPU's--there was a time that 10 billion calculations might take a fair while).

Also note you can optimize the loops trivially and make it run a gazillion times faster since I'm not using the sum having to be 20 to stop extra loops--if a = 20, then b,c,d,e must be 0 and there's no point iterating over all of them. But when it takes <2 seconds to run unoptimized, worrying about making it run 1000x faster ain't real important.

This stuff is SOOO off topic.

You mean most casino dealers don't daylight as computer programmers?

Oh, FFS!

EVERYONE FORGET THAT YOU EVER READ THE TEXT "999xx"!

The answer is:

--quad 9's (the easiest answer)

--flush, if board is AKQJTs (the answer that takes a little thought)

--top boat with board of 32222 (the answer that takes more thought)

That is pretty typical of me. I screwed up the easy one, but got the hard one right!

Yeah, well... shut up.

I enjoyed my paper and pencil approach, so nyeah.

Tho' it did take me a while to notice that it was impossible for the result to be integers, but I was too focused on trying to isolate variables in a situation where they couldn't be isolated.