Re: Expectation Question
The expectation is the same, but the variance is a lot different. The variance in the first lottery is about 1000 times that in the second. That's why the second lottery seems more tempting, because in some sense it's a "safer" bet due to the lower variance. As stated, this assumes equal number of players.
There was actually a collectible dice game where this came into play. You could use a certain number of dice, with rare dice counting as three dice with tripple the results. Thus the expectation was the same with one rare vs. three commons, but the variance was lower with the commons. This actually made the commons more useful in play, and the first championship was won by a guy playing with all common dice. This of course seriously undermined the collectability of the game.
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