Expectation Question
 

Consider two lotteries:

Lottery A pays 1000 oz. of gold to 1 winner.
Lottery B pays 10 oz. of gold to 100 winners.

Assuming this lotter repeats indefinitely, the expectation is the same (right?) but wouldn't you prefer to play lottery B because you have a better chance of winning something?

Re: Expectation Question
 

Assuming you could play the lottery indefinitely, it should not matter to you which you play. The outcome of both will be the same as the number of trials approaches infinity. This is most literally what expected value indicates.

Now, if you were forced to play the lottery in the short term with about 10,000 other people, and the only thing that mattered to you was whoring some money, you'd be better off playing the second one. You'd have a greater chance of winning.

Re: Expectation Question
 

Well, you left out some information.

The expectation is only the same if you assume that the lotteries will each have the same number of contestants... what if the first lottery is very unpopular, because of the higher risk? Then the best play is definitely to buy a ticket for lottery A. (and what about the entry fees? again, they'd have to be the same.)

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wouldn't you prefer to play lottery B because you have a better chance of winning something?

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Simply a personal preference! Assuming equal numbers of lottery entrants and the same cost to enter, I'd play lottery A -- why not "go for the gold"? [img]/images/graemlins/smile.gif[/img]
-DB

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.

OT: Re: Expectation Question
 

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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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good for him. collectible <blank> games are scamtastic.