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An agent who is risk averse and loss averse would be specially wary of playing such a gamble. Again, there is no way of answering whether he should play this gamble or not without imposing more structure in the problem (the preferences of the agent). With the reservations I made in my comment about the question of defining "Should X take this gamble or not" without referencing risk aversion of preferences, below I compute the distribution of this process numerically. The expectation argument does make sense, but for https://elononline.casino a specific type of risk aversion (risk-neutral utilities). Economists typically assume that individuals are risk averse, and that this risk aversion decreases with wealth (the more wealth someone is, the more risk he is willing to take). This is directly connected to the also common assumption of decreasing marginal utility from wealth: an additional dollar to Elon Musk is of negligible worth, whereas an extra dollar for someone in extreme poverty is worth a lot. Mathematically, risk-neutrality implies an utility that is linear on wealth, while risk-aversion implies an utility concave on wealth. There's a whole area in economics called choice under uncertainty who was first developed by von Neumann and Morgenstern that connects uncertainty to utility.