[dreams]

Congratulations, HarryT! You are quick with these.

**putting away paper and crayons, as I try to answer.. I don't do well with probability ones. **

Q1 :

Spoiler:

Cups .. L - C - R 1/3 chance when placing bet

L Cup empty so now it's 2/3 that my choice was correct.

For making the decision to stay or change the chance is 1/2.

So 1 coin at 2/3 or 2 coins at 1/2

Some how I'm lost already, but it looks like that if I stay with the 1 coin on my original guess of 2/3, then I will end up with spending less and earning more over time?

Q2:

Spoiler:

Someone knocks a cup over and it may not be the one that the showman was going to show you was empty.

You started with a 1/3 chance, but the unexpected cover lifting changed it for the showman, but I don't think it changed it for you. You still have the 2/3 chance with one cup gone, which is now 1/2.

I would still continue and not double my bet, because of the reasoning I used in Q1.

Q3:

Spoiler:

I would still continue the game as my known odds aren't different.

I still wouldn't double my bet as my odds of coming out with more money over the long run is better by staying with the original bet.

I think this is the same reasoning I used for all the Q's...