Monty Hall Probabilities
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1
Simulation results:
Calculated expectation:
2
Player stays & wins:33.49%33.33%
3
Player switches & wins:66.51%66.67%
4
5
Car hidden behind door #
Player's first choice:
Host shows door #
Player stays & wins?
Player switches & wins?
6
33110
7
31201
8
31201
9
23101
10
33210
11
22310
12
11210
13
13201
14
22310
15
33210
16
11310
17
33110
18
11310
19
13201
20
33110
21
12301
22
31201
23
11310
24
32101
25
11310
26
11210
27
13201
28
33210
29
32101
30
22110
31
32101
32
33210
33
13201
34
12301
35
12301
36
21301
37
12301
38
31201
39
22310
40
13201
41
12301
42
32101
43
33210
44
13201
45
23101
46
13201
47
21301
48
22310
49
12301
50
11210
51
12301
52
11310
53
32101
54
32101
55
23101
56
23101
57
12301
58
32101
59
31201
60
11210
61
31201
62
12301
63
23101
64
33110
65
21301
66
22310
67
13201
68
23101
69
22310
70
13201
71
31201
72
11310
73
23101
74
23101
75
32101
76
31201
77
11310
78
21301
79
31201
80
33210
81
12301
82
11210
83
21301
84
21301
85
33110
86
11310
87
21301
88
11210
89
23101
90
31201
91
11210
92
12301
93
32101
94
32101
95
31201
96
12301
97
32101
98
23101
99
33110
100
21301
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