At least a few of you got the correct answer, which is approximately 15.9%. There was no need to over complicate the answer since we only specified win/lose as the criteria. The percentage of people that will fall within + or - 1 standard deviation of mean is 68.2% of the remainder, half will do worse and half will do better. Therefore 100% - 68.2% / 2 = 15.9%. As I said it was easy math. Now what does it mean and what are the in-obvious implications.
That is to say:
Group A: Out of the 100 people Playing 1 million hands of 99% return machines, about 16 of them would be ahead at the end of a full year of play...even though they were playing with a negative expectancy.
Group B: Out of the 100 people Playing 1 million hands of 101% return machines, about 16 of them would be stuck at the end of a full year of play...even though they were playing with a positive expectancy.
Obviously, Group A would have 84 losers and Group B would have 84 winners.
Now imagine this:
Before running the experiment you told each group what their expectancy was, and whether or not they were supposed to win or lose. You even told them how much they were supposed to win or lose, which was $50,000. During the one year experiment none of the subjects was allowed to discuss their results or talk about the experiment publicly (for instance on-line forums).
Your job is to reason out which folks in each group would be the most vocal at the end of the experiment and what they might have to say about things.
Group A The 84% losers: They were told they should lose playing these games and they lost.
1. What do you think would be on their mind, and what if anything would they be saying if they posted on on-line forums.
2. And how likely do you think it would be that they would be talking on on-line forums.
Group A The 16% Winners: They were told they should lose, but they won. Same questions as above.
Group B The 84% Winners: They were told they should win and they won. Same questions as above with careful attention to whether you'd think they would even bother posting on forums. Keep in mind everything went exactly as planned for these folk and they likely don't feel they have anything to learn or share on a forum.
Group B The 16% Losers: They were told they should win, but they lost instead. Same questions as above, with extra attention to what they would likely now think and be saying about positive expectation gambling.
When answering these questions consider this seemingly unrelated question: When was the last time you got up in the morning, brushed your teeth, drove to work, had an uneventful day, drove home, had dinner, watched a TV show, and went to sleep...and then felt the need to talk to everyone about your completely unremarkable and normal day???.???
