You’re in a Las Vegas Casino, the newly opened Straight Dope Hotel & Casino. You walk past a handsome man in a tuxedo and he suddenly flips you a single melon-colored chip worth $25,000 and says you can use it to place any “even money” bet on any roulette table in the joint. You keep the winnings, or you’re out nothing if you lose.
What do you bet?
I’m not sure exactly what you’re asking. Are you restricting the choices to the official even money bets? Red/black, odd/even, high/low? Casinos vary somewhat, but so far as I’m aware the house edge on all these bets comes from deeming them a loss on a zero, so the expected return is exactly the same.
Am I missing some more subtle aspect on what you’re allowing us to do with the chip?
No. It’s entirely a pointless exercise in selecting between equal choices.
Woot, I thought I was killing it in the poll, but I was the first one to vote. Did I win?
My first instinct was Red. But then I wondered if that makes me a racist.
Then I thought even. But is that ableist?
Then I thought low. But is that ageist?
I think it’s a trap.
Last time I did that I got into a long argument over what I considered to be an odd number.
I’d put the chip on red and then put $25,000 of my own money on black. Then I can’t lose! Mwah ha ha ha!
Whaddya mean “zero”?
38 would be an odd number to bet on in roulette.
One common definition of “even money bet” is that the expected value is equal to the amount bet (e.g. betting $1 to win $1 on the flip of a fair coin).
By this definition, none of the options offered in the poll qualifies.
Lame, but I laughed … 
Well, it clearly doesn’t matter, and I clearly am going to make the bet since I lose nothing in doing so.
So I picked 1-18, because that’s one of the three options that includes 13, and it’s the option that does so that references numeric values specifically. I’ve shown a historical tendency to win things on the number 13, so who knows, maybe that’ll work out.
Wouldn’t that be a guaranteed way to walk away with the stranger’s 25k?
Put down the chip and your 25k (one on red, one on black). There’s now 50k on the table. The croupier (is that the right word?) spins the wheel and then takes either your 25k or the chip, but then matches the other one. There’s still 50k on the table that you get to pick up and leave with.
You missed the punchline. There is a 1/37 chance on European tables and a 1/19 chance on US tables that both red and black will lose.
So maybe roulette was not a good example for the OP to choose, since there are no true even money bets in roulette. If there were really a pair of even money bets, one of which must win, then my strategy would indeed be a way of walking away with $25K.
It was fine for the OP to use, since it allowed him to make a poll where all the options he provided (except walking away) provided no advantage over the others at all and there is no rational way for anybody to choose one over the other, causing observers’ brains to experience a syntax error, a blue screen of death, and then a scanners-style explosion. In other words it’s a murder plot. (I narrowly escaped it only by making an irrational choice.)
Sure it wasn’t a good setup for your ploy to work perfectly, but that wasn’t really the point.
Well, you can include a small bet on zero to lock in a ~3% smaller return.
Hey, if I can’t game the system, I’m not interested in playing.
Heh, I game-theoried the system, and realized that I was coming out ahead just by playing at all. Arguably ahead of you, because if I do win I come out $25000 ahead of you which balances out your win when I lose, and I’m at no risk of being sucker-punched by green.
Not to mention I don’t have a loose $25000 to throw down anyway…
Which bet I made would depend on where I was standing. All of the odds are equal, so I’d plunk it down on whichever “even money” square was closest. No need to bother thinking about it.
I also bet on 1-18, and for the exact same reason, except that my lucky number is 11.