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I joined a Lotto pool of 3 people four months ago. Since then, we've pooled \$200 once a month for the last four consecutive months, to buy 100 games in the \$2 Cash4Life game. Odds on the jackpot are 21 million:1, but 210,000:1 with 100 tickets. It's a six number game: 60 numbers in the top panel, and 4 "supplemental numbers" (1-4).

We play the same numbers each month. So far, the results demonstrate what I believe is called "regression toward the mean", i.e., we pulled in between \$24-\$48, the average winnings one can expect in this particular game with these odds and 100 tickets.

Oddly, though, in each successive month, we have won \$10 more than in the previous month.

My question is, is this \$10 increase just dumb luck, or does playing the same numbers repeatedly, rather than getting new ones each month through Quick-Pick, confer a slight advantage? Or does the old truth hold about flipping the coin: no matter how many times one side comes up, its odds of coming up again on the next toss are still 50-50, and thus with every number in every Lotto game?

Thank you! Tom Cullem

Darsen
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Tom Cullem
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  • You do know that your expected return on every Lotto and similar game is negative—right? I'd love to know how anyone who understands basic arithmetic—let alone pools and such—willingly gives away money in this way. – David G. Stork Oct 18 '20 at 22:49
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    @DavidG.Stork Perhaps their amusements are different from yours. – saulspatz Oct 18 '20 at 23:21
  • @DavidG. Stork - Actually, we 3 do know that. But, as it happens, periodically, this jackpot, like most others is won by someone. You do know that the only zero probability is not playing at all-right? The monthly contribution is well within our means; no food is being taken out of our children's mouths :). Lotto pools minimise expected losses (we're not fools) and raise chances (not odds, we know that, but chances) and, it's fun. I'd add to my question that as the Supplemental Numbers (1-4 in this case) give some numbers two chances to come up, how this skews the coin-flip issue. Cheers, TC – Tom Cullem Oct 23 '20 at 22:14
  • Well I'm glad you, at least, view this as "fun." "You do know that the only zero probability is not playing at all-right?" Duh. But you do know that *not playing* is the Bayes optimal, "best" strategy among all others (including pooling)... for expected return... right? Even (again, duh) given that someone will win. Oh "Lotto pools minimise expected losses (we're not fools)." Oh??? Explain how pools minimize expected losses. I'd love to hear it. Use equations, not imprecise words. (Of course, expected loss per dollar paid.) – David G. Stork Oct 23 '20 at 22:26

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