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I'm not sure I follow, but you're probably talking about a scenario where the risk/reward ratio is not 1:1. Sure, it's more complicated then. If you take a 10% chance bet 10 times and it has a risk of -1 and reward of +10, on average you'll get (-1 * 9) + (+10 * 1) = 1.

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> bet 10 times

The point in option 1 and 3 is to illustrate that betting 10 times isn’t an option in many systems. You can’t say you should always do something because the risk reward is favorable. That’s still gambling, and sometimes a stupid decision.

The average outcome of a gamble is not the likely outcome of taking it. And even ignoring that, it’s still a gamble unless you can confidently run it at sufficient scale to hit the theoretical distribution.

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