Yes, what you are talking about in your 'edge' comment is expectation. Lets not confuse expectation with probability. If you can't see why probabilistically it always makes sense to switch - strictly under the MontyHall scenario, then draw a phreakin' Venn diagram and consider the event space. Yes, in a once off event, it will be about luck, there are not enough events to let the Law of Large numbers do its bit with regards to expectation. But who cares. Even if you had 100 cups with 98 cups being winners and you had to choose only one, you can still choose the cup without the ball. So what? Are the odds in your favour? They sure are. Same with the monty hall problem, if you remain with the original choice your probability of winning is 1/3, if you switch it is 2/3. Now concentrate on the next sentence: Regardless of the eventual outcome. For goodness sakes, its not Girsanov's theorem!
To add, yes it DOES pay off to switch even if you play the game only a single time. The probabilities of winning double from 1/3 to 2/3. Agreed, one single game does not guarantee that you win, you still lose with a probability of 1/3 after switching. But what do you prefer 1/3 or 2/3? ;-)
Would you like to play with me this modification? After the dealer has taken out the empy one I will pay an extra 2.9 if you don't switch and you pay me ONLY 1.5 if the coin is in the other cup. If you switch I will pay you nothing. Want to play?
actually i did not read the question wrong. the question was written incorrectly. "if you had a chance to change your decision..." i outta this thread.
Look I am not trying to piss anyone off but in my humble opinion it seems like you want your cake and to eat it also. Ok I feel the problem lies in your brain knowing too much information and fail to realize how simple the problem is. So I'll try and explain for the no so smart. 3 choices a,b,c all picked 100 times comes out the same. We pick one and then take away one. Ok now we have a 50/50 game. Hmmm what just happened. We have a new game now and you want to be payed 2.9 to 1 for a 50/50 game. Well I like those odds also but you fail to see were the problem lies. You run all the numbers you want. You will win 1/2 of the time whether you chose the same or not. Just because you switch from A to C you think something life changing will happen? If you chooce A and we take B out of the equation can we say that B had no part in the equation in the first place? One last thing before beddy bye time.... If you always choose A and we always remove B do you seriously think you have a advantage on switching to C? If you can answer that question I'll be happy. Now lets take it a step further. Numbers 1-10. You pick a number.... i remove 8 wrong numbers just leaving the one you picked and one other one. You can switch to the other one if you like....... Do you expect to be paid 10-1 odds????? Hmmm don't think so. That would be like playing craps throwing one die and then choose what you want to bet on. First die is a 6.... well load up on the 12 since it pays 31-1..... Kinda of unfair asking someone to pay you 2.9 when its a even money payoff. One last note. Look some people have a lot less experience in math then others. I post on things I like. I come up with a lot of math questions in a casino and it strikes my curiosity. This post striked my brain and I wanted to learn more about it. I did read the online links provided and saw the little cartoon. Just because I don't agree with it doesn't mean I come here and try and pick fights. Can't anyone have a different opinion even when one is wrong? Well nighty night everyone
isn't TRMP still trading? maybe, that's not the best example but the casino biz is booming. check out HET, MGM, LVS, WYNN, etc. the point was its all based on probability.
The explanation I liked best was this: Take a 1000 cups with one coin. Choose one cup and the dealer (who knows where the coin is) removes 998 of the cups leaving us with 2 cups. Would it be logical to switch to the cup the dealer didn't take away or do you think you guessed right the first time and your cup has the coin? Hmmm...
Is the 1.5 a) the new price instead of 1.0 you charge for playing the game? Or b) is this in addition to the 1.0 I pay to play in case I dont switch and subsequently lose? If a) play but still switch If b) play but dont switch