(As a useful oversight, the expected return is equal to the bet, so as an additional question, is there a reason to play at all?) — Michael
So, given that the expected return is the same, is there a reason to prefer one way over the other? — Michael
So, given that the expected return is the same, is there a reason to prefer one way over the other? You're more likely to win if you place two bets on one game but you have the chance to win a bigger prize if you place one bet on each game. — Michael
↪Michael Without calculations I'd go with betting twice in two lotteries because there's a chance of winning 20 GBP if you win in both but only a maximum of winning 10 GBP if you bet in only one lottery. — Benkei
In commercial lotteries the expected return is much less than the bet, so if your utility function is just the expected return, then most lotteries are losers. And yet people buy lottery tickets. Which means that utility for those people is more than just the expected return. — SophistiCat
If you place both bets on one game then your odds of winning are 0.2. If you place one bet on each game then your odds of winning are 0.19. — Michael
I was never any good at math. How does this work out exactly? In my mind, by playing the two games instead of one, someone or something just seems to magically lower the chance by .01 for no rhyme or reason. — Outlander
In situations where losing (ending up with 0$ or a very low amount) is disproportionately bad, I would play both games to reduce the chance of going bust. If given the option, I would place as many single bets on as many games as possible to ensure that I would win at least one of them. — VagabondSpectre
If you want to ensure that you win at least one then you want to place all your bets on a single game as there's a better chance of winning. — Michael
is there a reason to play at all? — Michael
People's utility functions with the lottery can't resemble expected gain, then. Assuming it's a monetary return required, the cost of investing in any single bet is negligible but the possible return is comparatively huge. If you're spending $1 per week on the lottery and can continue that indefinitely, and it really is a negligible cost, then effectively you're paying nothing to be exposed to the small chance of a relatively large payoff. — fdrake
In both cases, there's no purely rational decision. — Michael
Well, how would you define a rational decision? — SophistiCat
I suppose one where you just look at probabilities and payouts to determine expected returns. If the expected returns are the same then there's no rational preference to play one way or the other, and if the expected return is the same as the bet then there's no rational preference to play or to not play. — Michael
Any preference to play, or to play one way over the other, will likely involve something like "hope" for a big win, which isn't a rational reason. — Michael
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