## Can You Bet Better?

Would you take this bet?

Your friend he’s going to pick two different random numbers from a distribution not known to you. He will then write the two numbers of two small pieces of paper and put each one in each of his enclosed hands. You then pick a hand and he will reveal the number in that hand.

You then place your money on which hand you think contains the larger number. He will match your money, betting on the other hand (regardless of whether or not you chose correctly — this is a precondition), the numbers will then be revealed and whoever was right keeps the sum of the money.

You only get one shot at this, and the bet is £1… If you can’t afford to lose it – don’t bet! The question is, is there a strategy to beat 50:50 odds and if so how?

August 20th, 2014 at 2:46 am

See how long he takes to write each number. Go for the hand that took the longest to write.

If negative numbers are allowed, then that won’t help much.

August 21st, 2014 at 10:33 am

I like Chris’ answer…

But this is a tough one since we do not know anything about the distribution. My guess would be to pick the revealed number if its first digit is between 5 and 9, and to pick the other hand otherwise.

This strategy would work if the distribution is uniform between 0 and one million for example.

August 21st, 2014 at 2:54 pm

Hi Zorglub. I agree with your strategy. All you can do is to guess at a pass-mark number. If you see a number less than that, select the other hand. I’m pretty sure that no harm will be done if you’re wrong.

However, my first answer was serious. Why else bother with all that stuff about writing on pieces of paper.

January 20th, 2015 at 9:14 am

Have him write the larger number in Roman Numerals and spell out the smaller number.

I would have my own set of numbers such as 1-10 and choose 1. If the number is 6-10 I bet on the hand selected otherwise if 1-5 I bet on the other.

Monty Hall could answer this one!