It's not always easy to make the right decisions. Are you a gambler? If you're offered 1 btc without playing or 5 btc by playing (with a chance of 2 to 1). What do you do?
In making a decision between a guaranteed 1 BTC and gambling for a chance at 5 BTC with odds of 2 to 1 against winning, it’s wise to consider the expected value but also your personal circumstances and attitude toward risk.
The expected value of the gamble for 5 BTC at 2 to 1 odds is calculated by considering the probability of winning (1/3) multiplied by the reward (5 BTC), plus the probability of losing (2/3) multiplied by zero (since you win nothing if you lose). This gives an expected value of about 1.67 BTC, which is higher than the guaranteed 1 BTC.
However, the rational choice from an expected value standpoint doesn’t necessarily mean it’s the best choice for everyone.