Charity Challenge-Need to know the odds

May 2010
I recently submitted a challenge (for a charity) to guess how much money is in a 2.5 gallon water bottle filled with mixed us coins, dollars coins (only a few), quarters, dimes, nickles and pennies. I have no idea of the percentage of silver vs. copper but I'd say 4-1 silver coins over pennies.

This was my challenge to a closed group of contestants (7650) possible people are allowed 1 guess.

If someone guesses to within a dollar, not over I give them XXX bucks

If no one wins that but gets within five dollars without going over I give them xx dollars

If no one wins that but gets within ten dollars without going over, I give them them x dollars.

Finally, if someone gets to within a nickle on either side of the exact amount I give them a third of the total amount of money.

For the sake of argument I have narrowed down the smallest amount of money there is in the bottle @ 300 bucks and the highest possible amount is 1700.00. Given those numbers what are:

The overall odds of winning if 7650 actually play?

The odds of winning each particular category?

The way I set it up, there can will only be one likely winner but two possible winners, if someone guesses correctly (within a nickle above and another guesses correctly within a nickle below).

If they coordinated and ran their all guesses in a middle range within 5 cents of each other could they cover all likely bets and guarentee a win?
Nov 2009
Big Red, NY
Via Monte Carlo:

\(\displaystyle \approx .43167\) chance someone will win.

May 2010
Thank you for the calculation!

Forgive my ignorance but what would that be expressed in a 1 in X chance? 1 in 232?

Also wouldn't the fact that you need to be within x but cannot go over, increase the odds?