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What constitutes a good bet in theory and in practice? How do psychological and emotional states affect what constitutes a good bet? In this post, I explore the tension between subjective psychological states and objective mathematical expectation. It’s important to lay out the assumptions behind expectation that are usually taken as axiomatic and viewed as the correct way to make decisions versus how they actually affect real-life decision-making.
Classical economic, financial, and gambling theory states that making a bet should only be dictated by the expectation of outcomes of the bet. Let us consider the following:
- X = Expected Payoff
- p(win) = probability of winning bet
- X(win) = payoff of winning bet
- p(lose) = probability of losing bet
- X(lose) = payoff of losing bet
X(total) = p(win) * X(win) + p(lose) * X(lose)
The assumption is that any bet (ignoring transaction costs) with
- X(total) > 0 is a good bet and should be taken
- X(total) < 0 is a bad bet and should be avoided
- X(total) = 0 is a neutral bet and should be viewed with indifference
