Choosing a zero probability of an infinite good over a certainty of a finite good

Sometimes it is rational to choose a zero probability of an infinite good over a certainty of a finite good.

Suppose there are uncountably many benevolent people, each of whom is assigned a number in (0,1), the interval from zero to one non-inclusive.  A random number Y is chosen in (0,1) with a continuous distribution (say, a uniform one, or a cut-off Gaussian).  The people aren't informed of its value, but they know the setup of the story.

Person number x is now given this choice:  

• wager: if Y=x, then everyone gets $1; else, nothing happens.  
• don't wager: the person with number x/2 gets $1.

Then:

• If everybody wagers, then everybody gets $1.
• If nobody wagers, then all and only the people with numbers in (0,1/2) get $1.

So surely at least some, and probably all, should wager.  But if you wager, you're choosing a zero probability of an infinite good (since the probability that your number matches Y is zero) over the certainty of a finite good.  (The goods are to others, but since you're benevolent, that doesn't matter.)