(Based on true story) A friend of mine and myself were drinking and we wanted to decide who will pay for the next round of drink. We decided to toss a coin so as to ensure a fair chance (1/2 prob.) for each of us. However since none of us had a coin with us, we decided on the following game that seemed to imitate the same probability numbers.
"We have a box containing a number of matchsticks (n) (not know to either of us beforehand). I ask a third friend to grab a bunch of matchsticks(k) and throw away. So now we are left with some matchsticks in the box (n-k).Now one of us calls whether the number left is even or odd.If I call even and the number is even, I win or else I lose."
- Is my probability of winning 50% ?
- If my opponent knows beforehand whether the number n is even or odd, does it impact my chances in the game?
- If my opponent knows beforehand whether the number k is even or odd, does it impact my chances in the game?
I have a feeling 1 is true. However I think 2 and 3 may not always go in my favour. (In the real game, we borrowed the matchbox from an unknown patron and asked someone else to throw the matchsticks away)