shell game

[Darrell]

See yourself out on the city streets where you encounter a fellow entertaining a small crowd with a shell game. This is the game where the player has three half shells with a pea hidden inside one of them. Feeling lucky you decide to play after watching to see that he has been honest in his dealings.

Upon mixing the three shells and pea on the table in front of you, he becons you to make your selection. You do so by placing your finger upon the shell where you believe the pea to be located.

Once done, he surprises you by uncovering one of the other shells to show that the pea isn't there. After that he gives you a choice: either stay with your original selection or change your selection to the other shell. Which do you do; and why?

[Jurgen]

I would say switch to the other shell. That way 2 out of 3 times you will win.

[Miss Deetective]

I would stay with my orginal choice because I would have done my best to follow the shell that I saw him put the pea under.

[Jurgen]

Look at it 3 times... in all instances you choose the most left shell and all 3 times the pea is under a different shell.

__________________________________________________
1st time: pea under left shell, got shown right shell, you switch to middle shell and loose.

2nd time: pea under middle shell, got shown right shell, you switch to middle shell and win.

3rd time: pea under right shell, got shown middle shell, you switch to right shell and win.

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

This means when you switch you win 2 out of 3 times thus giving you a 66.6% chanse when switching

[Antrikshaadmi]

Given that Jurgen has it figured out I'd like to point out what I'd do the next day. Depending on whether I see him in the company of the people who were playing the game earlier and they were his accomplices in a scam, I'd do what Jesus of Nazareth would do and destroy some of his private property.

[Darrell]

Originally Posted by Antrikshaadmi

Given that Jurgen has it figured out I'd like to point out what I'd do the next day. Depending on whether I see him in the company of the people who were playing the game earlier and they were his accomplices in a scam, I'd do what Jesus of Nazareth would do and destroy some of his private property.

Not me! I'd go play the guy as many times as I could for as much as I could. Me winning 2/3 times is way better than most casinos do longterm.

(btw, antri, you seem to have lots of issues. seeing the opportunity to win the majority of the time as a scam should be a clue to you.)

[Antrikshaadmi]

Originally Posted by Darrell

(btw, antri, you seem to have lots of issues. seeing the opportunity to win the majority of the time as a scam should be a clue to you.)

Shell games can be rigged, more complex things can be done by a magician.

[Jurgen]

Originally Posted by Antrikshaadmi

Shell games can be rigged, more complex things can be done by a magician.

Questions like that always become problamatic when you change the parameters...
for every one knows shell games were made to scam people.

If the guy is smart, he will put the pea under the most left shell every time so you'll never win, but that isn't an issue in this case.

For your sake... change the shells into 3 closed doors and put up a game show host to ask you which door you will pick to win the brand new car.

You pick a door and the host opens another one to show you there's nothing behind it...

Now... should you change doors or not? Same result though... you still have a 66.6% chanse to win the car when you switch doors.

[Antrikshaadmi]

Originally Posted by Jurgen

Questions like that always become problamatic when you change the parameters...
for every one knows shell games were made to scam people.

If the guy is smart, he will put the pea under the most left shell every time so you'll never win, but that isn't an issue in this case.

For your sake... change the shells into 3 closed doors and put up a game show host to ask you which door you will pick to win the brand new car.

You pick a door and the host opens another one to show you there's nothing behind it...

Now... should you change doors or not? Same result though... you still have a 66.6% chanse to win the car when you switch doors.

If he's a skilled magician and his props are good, in a rigged shell game the pea will never be in the shell you picked. In which case, not winning 66% of the time would be a tip off.

[Darrell]

Originally Posted by Antrikshaadmi

Shell games can be rigged, more complex things can be done by a magician.

so what? I wrote the problem with an honest host (which was directly implied in the problem statement).