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 High Rollers (Posted on 2004-12-08)
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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