TRIAL Door 1 Door 2 Door 3 KEY:  X  is where the MC puts the money. 
1 GX N O G is the first guess
2 G NX O N is the door chosen when contestant decides to change her mind
3 G O NX NX is when the contestant wins the money by changing her mind 
4 G X N O GX is when the contestant wins the money by not changing her mind
5 G NX O O is the vacant door that is opened when contestant says she wants to change her mind
6 G O NX
7 GX N O So, for example in trial #1 the contestant did not change her mind, the MC opened vacant door # 3 
8 G NX O and the contestant won the money (GX) by not changing her mind.
9 G O NX
10 GX N O On trial 2, the contestant wins the money by changing her mind (NX).
11 G NX O
12 G O NX The number of times that the contestant wins by not changing her mind (GX) is 11 or 1 out of 3.
13 GX N O The number of times the contestant wins by changing her mind (NX) is 22 or 2 out of 3.
14 G NX O
15 G O NX This an example of solving the puzzle empirically.  We actually ran the experiment in our minds!
16 GX N O
17 G NX O
18 G O NX
19 GX N O
20 G NX O
21 G O NX
22 GX N O
23 G NX O
24 G O NX
25 GX N O
26 G NX O
27 G O NX
28 GX N O
29 G NX O
30 G O NX
31 GX N O
32 G NX O
33 G O NX
22 CORRECT GUESSES (NX) CHANGING YOUR MIND
11 CORRECT GUESSES (GX) NOT CHANGING YOUR MIND