What has better odds: betting $13 to win $12 on a coin flip, or betting $13 on a roulette table?

Question

What has better odds: betting $13 to win $12 on a coin flip, or betting $13 on black on a roulette table?

Answer 1

Calculating expected values, the coin flip is a better bet.

Assuming you bet $13, the expected value of the coin flip is,
0.5*12 - 0.5*13 = -0.5

A $13 bet on red on a roulette wheel with 0 & 00 gives,
0.4736*13 - .5263*13 = -0.685

so putting your money on the coin flip is less bad.

Answer 2

On the coin flip you can expect to win $12 half the time and lose $13 the other half of the time, so over the long run, on each play your bankroll will change by ( $12 ) / 2 - ( $13 ) / 2 = $6 - $6.50 = - $.50, that is, you can expect to lose 50 cents for each flip you bet on.

A roulette wheel in the U. S. has 18 black numbers, 18 red numbers, and two zeroes. If you bet $13 on black, you can expect to win $13, 18/38 of the time, and you can expect to lose $13, 20/38 of the time. Over the long run, your money changes by ($13)(18/38) - ($13) (20/38) = $13 ((18-20)/38) = $13 (-2/38) = -$13(1/19) = - $.68 each time you bet.
Either way you will go broke in the long run. However, you will lose your money more slowly by betting on the coin flips.

But in Europe the roulette wheels have only one zero. If you bet $13 on black there, you can expect a change of ($13) (18 /37) - ($13) (19 / 37) = $13 ((18 - 19) / 37) = ( $13 ) (-1/37) = - $.35 per bet. When you are in Europe, you lose more slowly when you play roulette.

Answer 3

Your odds are slightly better on the 12/13 coin flip. There are 38 numbers on the roulette wheel of which 18 are black. On the average, if you bet $13, 38 times you will win
(18)(13)=$234. and lose 260 for a net loss of $26 per 38 bets.
38 coin flips at 12 for 13 would give you 19(12)=$228 on the average when you win minus 19(13) when you lose or a loss of $247 for a net of -$19 for 38 bets. So the coin flip is definitely better.


Either way your taking the worst of it and the casino wins.
Stick to Texas holdem.

Answer 4

The odds of betting on the coin flip are better than a roulette wheel, as the coin has only two possible options, yet the roulette wheel has those annoying Green slots (unless you choose to entertain the possibility of the coin landing on its rim).
However, they key to your trick question was betting $13, to win $12 on the coin flip, a profit of 91 1/6%, which divided by 2 (50%) chance, is a random profit potential of only 45 7/12ths %, yet as the Roulette wheel has 38 positions, and the odds of hitting green are 1 in 19 on an American Wheel, or 1 in 37 on an English wheel (The English wheel does not have a double zero), your odds of winning on the roulette wheel are actual 3.07% better than a coin flip versus the American Wheel, and 0.05% on the English Wheel

Answer 5

Betting $13 on black, on a single zero wheel (which I think are mostly found only in Europe), your odds against are 19:18 to win even money, which would be a slightly better bet than laying 13:12 on a "fair" coin flip.

On the more typical American double zero wheel, your odds against winning a bet on black jump to 20:18 or 10:9, making the 13:12 coin flip now a better proposition, based purely on mathematical considerations.

Of course, ALL of the above are sucker's bets, as they are all losing propositions in the long run. That is, unless you get to flip the coin and you know what you're doing. A good sleight-of-hand artist can improve his/her odds of winning a coin flip to well better than 50%, as long as they get to flip the coin. :)

Answer 6

On your coin flip example, the probability that you win is 0.5. For the roulette example, the probability that you win is 18/38 = 0.474, so you are more likely to win with the coin flip.

It would probably be more interesting to talk about expected values. That means that, if we were to actually play these games, it is the amount you would expect to win in one game.

For the coin flip, you have a 0.5 chance of winning 12 dollars and a 0.5 chance of losing 13 dollars. So you would expect to win...

0.5*12 + 0.5*-13 = -0.5, or you would expect to lose $0.50 every time you play the game.

For the roulette bet on black, you have a 18/38 chance of winning 13 dollars and a 20/38 chance of losing 13 dollars (this is because a bet on black is 2 to 1). So you would expect to win...

(18/38)(13) + (20/38)(-13) = -0.68, or you would expect to lose $0.68 every time you play the game.

Again, I would go with the coin flip.

Answer 7

If you mean odds of winning, then the coin flip is better than any bet on the roulette table.

On the other hand, if you are looking for a better payout, roulette is the way to go.

Answer 8

The probability of winning a coin flip is .5.
According to wizardofodds.com/roulette, the probability of winning by betting black on roulette using U.S. rules is .4737.

It's not a lot different, but the zero and double zero change things.

Answer 9

betting on black or red is the better bet, much better if it is a single zero wheel