[Guest]

Bob offers Jim and Jack a gamble. Jim and Jack are allowed to discuss a strategy before hand, but won't be able to communicate in any way afterwards.

Jim and Jack will be put in separate rooms, with 1 fair coin each. Bob will go into one room, and ask Jim to flip his coin. He will then ask Jim to predict the result of the upcoming flip by Jack. Bob will then go into Jack's room. He will ask Jack to flip his coin. He will then ask Jack to guess what Jim flipped. If BOTH of them guessed right, Bob will give them 2 dollars each. If EITHER of them are wrong, they each have to give Bob 1 dollar. Should they accept the gamble?

[superprismatic]

By no means!

[bushindo]

By no means!

Interesting puzzle. Your puzzles are superb, howardl1963, and I hope you'll regularly post more.

The key here is that Jim and Jack are asked to predict the other's flip AFTER they flip their own coin. So, Jim should always predict head if his own coin turns up head, and tail if otherwise. Jack should do the same. Under this strategy, their chance of winning is now 50%, as opposed to 25% when randomly guessing.

Edited June 4, 2010 by bushindo

[Guest]

Interesting puzzle. Your puzzles are superb, howardl1963, and I hope you'll regularly post more.

The key here is that Jim and Jack are asked to predict the other's flip AFTER they flip their own coin. So, Jim should always predict head if his own coin turns up head, and tail if otherwise. Jack should do the same. Under this strategy, their chance of winning is now 50%, as opposed to 25% when randomly guessing.

Thanks bushindo. I'll make one other observation in a spoiler:

I love where the strategy is all or nothing. Even with the tiniest bit of information they are able to create an all or nothing strategy.

By pure guessing their results would be:

right right

right wrong

wrong right

wrong wrong

with only a 25% chance of success.

But with this simple strategy they are either:

right right

or

wrong wrong

[Guest]

i wouldnt

[Guest]

Jim and Jack decide beforehand that they will assume that the coins land oppositely (that is, if Jim gets a head, he will assume that Jack will flip a tail, and so on). This also works if they assume that the coins will land in the same way, but I will continue as if they went with the first case.

Jim flips his coin, and he will guess that Jack will flip the opposite of him. So if he flips heads, then he will guess that Jack will get tails, and vice versa. Jack will flip, and he will guess the opposite of what he flipped as well, so if he gets tails, he will guess that Jim got heads. No matter what, if Jim ends up being correct, then Jack will always be correct, and if Jim is wrong, then they will both get it wrong. Jim has a 50% chance of guessing Jack's flip correctly, so the chance of winning with this strategy is 50%. However, since you get $4 for winning and you lose $2 for losing, it's a favorable bet to make.

[Guest]

if it is decided upon the base of the coin for the flip,say head or tail,both common for the two, it likely that the opposite side is viewed as the head,when flipped .so,it is obvious of the others chance of the coin!!

[Guest]

I wouldn't do any bet if there's even 0.1% chance I won't win...

[Guest]

Thanks bushindo. I'll make one other observation in a spoiler:

I love where the strategy is all or nothing. Even with the tiniest bit of information they are able to create an all or nothing strategy.

By pure guessing their results would be:

right right

right wrong

wrong right

wrong wrong

with only a 25% chance of success.

But with this simple strategy they are either:

right right

or

wrong wrong

i got the same solution as bushindo

but in ur spoiler do u mean..

right right

or

wrong right

???

coz

Jack will get it right no matter what happens...

[Guest]

i got the same solution as bushindo

but in ur spoiler do u mean..

right right

or

wrong right

???

coz

Jack will get it right no matter what happens...

Using the strategy, they will be either

right right or

wrong wrong

Jack will not always be right. How could he? He has no idea what Jim flipped. He only knows Jim's strategy. Let's say they agree to guess the same as they flip (if they both guess opposite, it yields the same odds). If Jim flips heads, he will guess that Jack will flip heads. Now, when Jack flips, he might flip heads and guess heads, and they will both be right. But, if he flips tails, he will guess tails, and be wrong. But so will Jim, which is why their strategy is optimal. There is no way for them to guess right wrong or wrong right using this strategy.

[Guest]

Using the strategy, they will be either

right right or

wrong wrong

Jack will not always be right. How could he? He has no idea what Jim flipped. He only knows Jim's strategy. Let's say they agree to guess the same as they flip (if they both guess opposite, it yields the same odds). If Jim flips heads, he will guess that Jack will flip heads. Now, when Jack flips, he might flip heads and guess heads, and they will both be right. But, if he flips tails, he will guess tails, and be wrong. But so will Jim, which is why their strategy is optimal. There is no way for them to guess right wrong or wrong right using this strategy.

oh i'm so sry...i read the solution incorrectly...so i thought it was similar to what i had in my mind...

i actually very stupidly assumed that jack could hear Jim's guess .. and hence my answer..

shud have read it more closely....

[Guest]

I wouldn't accept the bet unless Bob offers $2.01 (or more) each.

Here's why:

With random guessing, their chances of winning are obviously 1/4 making 2:1 unfavorable bet odds.

If they both guess the opposite of what they flipped, then they will win if they flip different sides of the coin.

There are 4 combinations:

1. Heads - Heads

2. Tails - tails

3. Heads - Tails

4. Tails - Heads

Using the above strategy, they will win in scenario 3. and 4. giving them 1/2 bet odds.

But, Bob is giving them only twice the money they might pay if they lose. Unless Jack and Jim find the idea of flipping coins very thrilling, they should ask Bob for atleast $2.01 each.

I personally won't take the bet for less than 4 (hoping to convince Bob that the bet odds are infact 4:1), but that's me :-)