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Originally Posted by spadebidder
With all due respect, it looks to me like it is you who has reversed those two concepts in the red/black example. A color bet pays even money, which could be referred to as 50:50. If you bet 50, you either lose 50 or win 50, every time. But the "odds" of winning are 19:18 on single zero, or 20:18 on double zero. The odds of winning are not 50:50. So you win $50 fewer times than you lose $50.
The probability of an outcome is generally expressed as either favorable outcomes vs. all outcomes or as the decimal representation of that ratio. Sometimes it's expressed as favorable outcomes vs. unfavorable outcomes -- but there's some subtlety in the language. A coin flip is often referred to as 50/50, 1 out of 2, or 1:1. In any case, none of them refer to the payoff, only the probability of the outcome.
Odds, on the other hand, represent the payoff. So at a racetrack when you see 3:1 it represents the payoff vs. the wager -- wager 1, get 3 back = win 2. In this case the ":" symbol represents "for". On a craps table 3:1 generally represents the win vs. the wager -- wager 1, win 3 (keep the wager) = win 3. In this case the ":" symbol represents "to". The casino sometimes mixes "for" and "to" wagers on the layout, and they are very different.
Sometimes you have to simply take representations in context. If a person uses the expression 50/50 or writes 50:50, that has to be interpreted as a representation of outcomes and not payoff. Why would someone choose 50 to represent a wager? They might as well say 1832:1832. Why not say 1:1? It's clear in context that they're talking about the probability of an outcome. If the two possible outcomes being considered are clearly defined, the representation can not be assumed to include all possible outcomes. In roulette, the probability of red vs. black (as an outcome) is 50/50.
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Some bets on roulette do not pay even money, as in your 19 numbers example. If you bet 19 numbers (00 wheel), you will win 50% of the time and lose 50% of the time, but the payoffs are not even here. The payoff for hitting is not 19*2 or 38:1, it is only 36:1. So if you bet $50 total ($2.63 on 19 numbers), you will lose all 19 of them half the time, and you will lose 18 of them and win 1 half the time. But the one win only pays 36:1. So you will lose $50 the same number of times that you win $47.34.
Again, I didn't check your math because it's not pertinent to the discussion.
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So let's compare the two types of bets:
Bet $50 on a color:
You win $50 fewer times than you lose $50.
- 19:18 ratio on outcomes and 50:50 ratio on money.
Bet $50 on 19 numbers, evenly spread:
You win $47.34 the same number of times that you lose $50.
- 19:18 ratio on money and 50:50 ratio on outcomes.
So which one of those is a 50/50 proposition?
So which one of those is a 50/50 proposition? In the first case, you did not mention a specific color, just "a color". If you're thinking red/black, then it's 50/50.
In the second example it's definitely 50/50.
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Most people would say neither, since what matters is the product of outcomes and money, not one or the other.
That would be expected value -- not probability or odds.
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The pitchman in the OP misleadingly talks about only half the equation.
Of course he does.