| Scenario | Figures | Stay | Switch |
|
| #1 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 1 |
| Can switch to door # | 2 |
|
| #2 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 3 |
| Can switch to door # | 2 |
|
| #3 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 2 |
| Can switch to door # | 3 |
|
| #4 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #5 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 1 |
| Can switch to door # | 3 |
|
| #6 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 2 |
| Can switch to door # | 3 |
|
| #7 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 1 |
| Can switch to door # | 3 |
|
| #8 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #9 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 3 |
| Can switch to door # | 2 |
|
| #10 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 3 |
| Can switch to door # | 2 |
|
| #11 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 2 |
| Can switch to door # | 1 |
|
| #12 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 3 |
| Can switch to door # | 2 |
|
| #13 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 1 |
| Can switch to door # | 2 |
|
| #14 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #15 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 2 |
| Can switch to door # | 1 |
|
| #16 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #17 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 2 |
| Can switch to door # | 3 |
|
| #18 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 2 |
| Can switch to door # | 3 |
|
| #19 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #20 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 2 |
| Can switch to door # | 1 |
|
| #21 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 2 |
| Can switch to door # | 3 |
|
| #22 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 3 |
| Can switch to door # | 2 |
|
| #23 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 3 |
| Can switch to door # | 2 |
|
| #24 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 1 |
| Can switch to door # | 3 |
|
| #25 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 2 |
| Can switch to door # | 1 |
|
| #26 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 2 |
| Can switch to door # | 3 |
|
| #27 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #28 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 2 |
| Can switch to door # | 3 |
|
| #29 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 2 |
| Can switch to door # | 3 |
|
| #30 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 2 |
| Can switch to door # | 1 |
|
| #31 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 1 |
| Can switch to door # | 3 |
|
| #32 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 1 |
| Can switch to door # | 2 |
|
| #33 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #34 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 1 |
| Can switch to door # | 3 |
|
| #35 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #36 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 3 |
| Can switch to door # | 2 |
|
| #37 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #38 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 1 |
| Can switch to door # | 2 |
|
| #39 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 1 |
| Can switch to door # | 3 |
|
| #40 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 1 |
| Can switch to door # | 3 |
|
| #41 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 1 |
| Can switch to door # | 2 |
|
| #42 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 1 |
| Can switch to door # | 2 |
|
| #43 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 2 |
| Can switch to door # | 1 |
|
| #44 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 1 |
| Can switch to door # | 2 |
|
| #45 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 1 |
| Can switch to door # | 3 |
|
| #46 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #47 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #48 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 2 |
| Can switch to door # | 1 |
|
| #49 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #50 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 3 |
| Can switch to door # | 2 |
|
| #51 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 2 |
| Can switch to door # | 3 |
|
| #52 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 1 |
| Can switch to door # | 3 |
|
| #53 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 2 |
| Can switch to door # | 1 |
|
| #54 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 1 |
| Can switch to door # | 2 |
|
| #55 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #56 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #57 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #58 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 1 |
| Can switch to door # | 3 |
|
| #59 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 1 |
| Can switch to door # | 2 |
|
| #60 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 2 |
| Can switch to door # | 1 |
|
| #61 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 1 |
| Can switch to door # | 3 |
|
| #62 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 2 |
| Can switch to door # | 1 |
|
| #63 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 1 |
| Can switch to door # | 2 |
|
| #64 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 1 |
| Can switch to door # | 2 |
|
| #65 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 1 |
| Can switch to door # | 3 |
|
| #66 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 2 |
| Can switch to door # | 1 |
|
| #67 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 1 |
| Can switch to door # | 2 |
|
| #68 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 3 |
| Can switch to door # | 2 |
|
| #69 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 2 |
| Can switch to door # | 1 |
|
| #70 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #71 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 1 |
| Can switch to door # | 3 |
|
| #72 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 1 |
| Can switch to door # | 3 |
|
| #73 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #74 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 1 |
| Can switch to door # | 2 |
|
| #75 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 2 |
| Can switch to door # | 3 |
|
| #76 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 1 |
| Can switch to door # | 3 |
|
| #77 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #78 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 2 |
| Can switch to door # | 3 |
|
| #79 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #80 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 1 |
| Can switch to door # | 3 |
|
| #81 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 2 |
| Can switch to door # | 3 |
|
| #82 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 1 |
| Can switch to door # | 3 |
|
| #83 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 1 |
| Can switch to door # | 2 |
|
| #84 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 2 |
| Can switch to door # | 1 |
|
| #85 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 2 |
| Can switch to door # | 1 |
|
| #86 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 2 |
| Can switch to door # | 1 |
|
| #87 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 1 |
| Can switch to door # | 2 |
|
| #88 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 3 |
| Can switch to door # | 2 |
|
| #89 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 1 |
| Can switch to door # | 2 |
|
| #90 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 1 |
| Can switch to door # | 3 |
|
| #91 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 2 |
| Can switch to door # | 1 |
|
| #92 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 3 |
| Can switch to door # | 2 |
|
| #93 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 3 |
| Can switch to door # | 2 |
|
| #94 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 3 |
| Can switch to door # | 2 |
|
| #95 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 2 |
| Can switch to door # | 3 |
|
| #96 | Correct door # | 3 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 2 |
| Can switch to door # | 3 |
|
| #97 | Correct door # | 2 | Stay | Switch |
| Player chooses # | 3 |
| Host reveals # | 1 |
| Can switch to door # | 2 |
|
| #98 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| #99 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 1 |
| Host reveals # | 2 |
| Can switch to door # | 3 |
|
| #100 | Correct door # | 1 | Stay | Switch |
| Player chooses # | 2 |
| Host reveals # | 3 |
| Can switch to door # | 1 |
|
| Final Results | # Correct | 38 | 62 |
| % Correct | 38% | 62% |
My explanation:
The fact that the host reveals one of the wrong answers AFTER you choose your initial answer does something really cool!
I think the easiest way to think of it is this:
1.) In order to win by switching your answer, all you have to do is choose a WRONG answer initially.
2.) You have a 2/3 chance of choosing a wrong answer initially!
3.) You have a 2/3 chance of choosing the right door by switching!
Another way of looking at it is this:
1.) The door you initially choose has a 1/3 chance of being correct. Each of the other two doors still have a 1/3 chance of being correct at this point.
2.) However, the host REVEALS one of these two other doors as wrong, meaning that door now has a 0/3 chance of being correct!
3.) So now there is 2/3 of a chance needing to be assigned to a door still… The last remaining door that you would switch to is the door that now has that 2/3 chance of being correct!