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I regret this already.

Now, which game would you choose? See?

Your analogy is flawed. If you don't care how much money you lose, as in this case, your expected outcome changes dramatically. It situation one, you have a 51% chance of living and a 49% chance of dying. In situation 2, you have around an ~86%-88% chance of living, depending on the game. Easy choice (and a good example of applying expected outcomes to small samples).

Unfortunately, gambling doesn't offer payoff without gradation (i.e. you would much rather lose less money than more money, but you don't care how much you lose by when it's live or die). In real life, you also have approximately 86%-88% chance of winning your game, assuming your strategy is similar to the death game (martingale if you lose, walk away if you win). But you also have a 12%-14% chance of losing 7X your initial bet, something you don't care about in your game. That impacts your expected outcome (when you do care), and not surprisingly reduces your expected outcome to exactly what it was initially. So, assuming your craps expecation is 49% win / 51% lose (or, -0.02), you can calculate your expected outcome under the strategy like this: ((0.13 * -7)+(0.87 * +1)/2) = -0.02).

In your game, the pain of losing 7X your money was equivalent to the pain of losing 1X you money, so the expected outcome shifted to 0.87 versus 0.51 for the jar. If only it were that easy.

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