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<p>But buying tickets in future lotteries increases your chances of winning future lotteries. Let’s say that for each lottery and each ticket, there is a probability p that that ticket is the winning ticket. If you buy n different tickets for the same lottery, your probability of winning that lottery is now np. If you buy n tickets in n different lotteries, your probability of winning at least one lottery becomes 1 - (1-p)^n. Since 1-p < 1, it should be clear that as the number of lotteries entered increases, the odds of winning one of them also increase. </p>
<p>And intuitively this should be clear too. If you roll one die, you’re probably going to get something other than a 6 (~83%). If you roll 50 dice, it would be very surprising if none of them turned out to be a 6 (~0.011%). Entering a separate lottery is just like rolling a separate die for a 6, except that the odds are astronomically longer.</p>