Selling lotteries is a very profitable business and has been income sources of some governments’ welfare benefits. The potential gain of buying a lottery ticket is enormous that people can potentially earn millions of pounds from buying a single lottery ticket; however, meanwhile the chance of earning such enormous money is so tiny that it could almost be seen as zero. The expected return of buying a lottery ticket is negative, and more tickets one buys, more negative the expected return becomes; therefore, buying lotteries does not make sense if a person is rational (a rational person should be risk averse as well). However, many people still buy lottery tickets and why?
The main reason is people overestimate their winning probabilities. When they overestimate their winning probabilities, then their behaviour of buying lotteries is completely understandable, sensible and rational (if we ignore the irrationality in overestimating the probability). Because under such circumstance, even with risk averse risk preference, it is still possible to see that the utility of buying a lottery ticket is greater than the utility of not buying one.
Also people sometimes actually love risk and enjoy risk for fun, as long as the risk is minor, that is why people love Bungee and parachuting. Buying a lottery probability has the smallest cost among the risk that people are willing to take, so buying a lottery can give people fun of taking risk. Therefore, the fun gained from buying a lottery ticket and the potential money award makes buying lottery tickets very appealing even without overestimating the winning probability.
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