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You shouldn’t buy them at all but if you want to get the most out of what good they can provide, yes, earlier is better:
We analyze one of the explanations why people participate in lotteries. Our hypothesis stipulates that part of the value that a unit of money buys in lotteries is consumed before the actual resolution in the form of emotions such as hope. In other words, a person holding a lottery ticket may prefer a delayed resolution of risk due to positive anticipatory emotions. This conjecture is tested in an experiment with real lottery tickets. We show that our theoretical considerations may contribute to explaining empirical puzzles associated with lottery participation, timing of resolution and the spreading of drawings. More speci cally, we find that a substantial number of participants prefer delayed resolution, that anticipated thrill is the main variable explaining this choice, that emotions actually experienced during the waiting period are indeed predominantly positive and correlated with predictions. Finally, we find that a great majority prefers to `spread’ chances, that is, to obtain one ticket for each of two drawings rather than two for the same drawing.
Source: “`Let me dream on!’ Anticipatory emotions and preference for timing in lotteries.” from Tinbergen Institute Discussion Papers # 09-098/1.
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