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High Rollers (Posted on 2004-12-08) Difficulty: 3 of 5
If I rolled n fair six-sided dice rolled simultaneously, what's the expected value (in terms of n) of the highest valued die?

(Note: "expected value" refers to the number you would expect to get if you ran this simulation many times and averaged the results.)

See The Solution Submitted by Gamer    
Rating: 2.5000 (4 votes)

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Simulation results | Comment 3 of 6 |
(In reply to solution by Charlie)

The following program simulates a million trials for each of n = 1 through 20, and the results compare well with the calculated values:

CLS
FOR n = 1 TO 20
 tot = 0: tr = 0
 FOR trial = 1 TO 1000000
  vMax = 0
  FOR i = 1 TO n
    v = INT(6 * RND(1) + 1)
    IF v > vMax THEN vMax = v
    IF v = 6 THEN EXIT FOR
  NEXT i
  tot = tot + vMax
  tr = tr + 1
 NEXT trial
 PRINT n, tot / tr
NEXT n

1             3.500303
2             4.473519
3             4.957712
4             5.245496
5             5.431711
6             5.558989
7             5.65431
8             5.724804
9             5.778415
10            5.819911
11            5.853186
12            5.880825
13            5.900625
14            5.918705
15            5.933204
16            5.944188
17            5.95386
18            5.962127
19            5.968116
20            5.97373


  Posted by Charlie on 2004-12-08 19:00:05
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