poker table bag

Brilliant Statisticians please?

There are three (3) poker chips: 1) red top / red at the bottom, 2) at the top red / black on the bottom, 3) at the top black / black on the bottom. (The game is played with replacement.) Launched the three chips in a bag. It reaches 1 chip from the bag at random and place it on the table. You can guess the color of the bottom of the tab picked up. If you guess the color correctly, you get $ 1.00; if it is incorrect, you pay me $ 1.05. The game is played for a long time (100 times). Question: In the end, why will end up with all my money?

Well, if you win or not depends on what I suppose. Let's say you draw a chip and get the black side up. Well, that means you have one of the two chips. But we must keep the two sides different in mind. R / PB B1/B2 (Black background | black on top) = P (B1 or B2 on the bottom is at heart | black is on top) = 2 / 3 And same goes for red, and if you take a tab and the top is red, the probability that the bottom is red is 2 / 3. So the best guess would guess the same color as shown on the top. So, if you will then use a ratio of 2 / 3 the time and wrong 1 / 3 the time. (2 / 3) ( 1.00) + (1 / 3) (-1.05) = 0.31 (6) (six repeats) This means that if you play 100 times, then you can expect to earn 100 ( 0.31 (6)) = $ 31.67. The reason why I'll have you all, because money is the probability that I'm right is 2 / 3, 1 / 2, which is the typical response, and I am sure that many people respond to that. This problem of the same paradox that is at the link below. The probability is 2 / 3 for the same reason, as I said above.

IPSC 3 Gun Poker Table Shoot