Marvel Snap: the win chance where staying equals retreating
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Nothing here is tied to one game. Any match you can walk out of part way through, for less than a full loss, is the same arithmetic.
Results
| Win chance at which the two are equal, in per cent | — |
| What staying is worth at your guess | — |
| What leaving is worth | — |
| Staying minus leaving | — |
The first row is almost always lower than people expect, and the reason is in the third. Saying you will only stay if you think you are winning sets the bar at half, and half would be right if leaving cost nothing. Leaving does not take you back to nothing, it takes you to a loss of its own, so the comparison is between a bad outcome and a worse one rather than between a bad outcome and none.
The bar is set by what leaving costs
| Cost of leaving | Win chance you would need, in per cent |
|---|
That ladder falls in a straight line, which makes it easy to carry around. When leaving is free the bar sits at half, and as leaving gets more expensive the bar drops towards nothing, until leaving costs as much as losing and there is no longer any reason to leave at all. It is the price of the exit, not the size of the pot, that decides how sure you have to be.
Doubling everything changes nothing, which surprises people who think a bigger pot demands more certainty. What does change the bar is asymmetry: winning more than you would lose pulls it down, and standing to lose more than you could win pushes it up. Size is not the question, shape is.
The one number the page cannot supply is your guess at winning, and it is the one carrying the decision. Everything else is read off the screen in front of you, so if the answer flips when you move that guess by a few points, the honest conclusion is that you do not know yet rather than that the page has decided.
Why is the bar so much lower than half?
Because leaving does not take you back to nothing. It takes you to a smaller loss, so you are comparing a bad outcome with a worse one rather than with none at all.
Saying you will stay only if you think you are winning puts the bar at half, and half would be right only if walking away were free. With a stake of four either way and an exit costing two, the real bar is a quarter.
What actually sets the bar?
The price of the exit, and it moves the bar in a straight line. Free to leave puts it at half, and the more leaving costs the lower it drops, until leaving costs as much as losing and there is no reason left to leave.
This is why the ladder is worth carrying around: the numbers in it come from your own stakes, and the shape never changes.
| Cost of leaving | Win chance you would need, in per cent |
|---|---|
| 0,00 | 50,00 |
| 1,00 | 37,50 |
| 2,00 | 25,00 |
| 3,00 | 12,50 |
| 4,00 | 0,00 |
Does a bigger pot mean I need to be more sure?
No, and that is the part people get backwards. Doubling everything leaves the bar exactly where it was, because it divides out: four against four with an exit of two and eight against eight with an exit of four both ask for a quarter.
What does move the bar is asymmetry. Standing to win more than you would lose pulls it down, and standing to lose more than you could win pushes it up. Size is not the question, shape is.
What is the page not deciding for me?
Your chance of winning, which is the only input it cannot read off the screen and the one carrying the whole decision.
If the answer flips when you move that guess by a few points, the honest conclusion is that you do not know yet, not that the arithmetic has settled it.
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