Maximum Consecutive Same Heads/Tails in Coin Toss

[Qwerkey]

When I created my coin toss graphics program https://www.qb64.org/forum/index.php?topic=4117.msg134684#msg134684 as a check that it was working correctly, there must not have been many consecutive same heads or tails (the program did seem OK in this respect).

But I wondered if you let QB64 run continuously with a 50/50 random, what would the maximum same consecutive be.  [Theoretically (?) if you do 50/50 for an infinite time you'd get a sequence sometime of infinite consecutive same].

So this simple program examines this.

Code: QB64: [Select]

1. CONST False = 0, True = NOT False
2. Count& = 0
3. Cycle& = 0
4. SameCount% = 0
5. MaxSame% = 0
6. IF RND < 0.5 THEN
7.     Heads%% = True
8. ELSE
9.     Heads%% = False
10. END IF
11. OldHeads%% = Heads%%
12. RANDOMIZE (TIMER)
13.  
14. WHILE INKEY$ = ""
15.     IF RND < 0.5 THEN
16.         Heads%% = True
17.     ELSE
18.         Heads%% = False
19.     END IF
20.     IF Heads%% = OldHeads%% THEN
21.         SameCount% = SameCount% + 1
22.         IF SameCount% > MaxSame% THEN MaxSame% = SameCount%
23.     ELSE
24.         SameCount% = 0
25.         'IF Heads%% THEN
26.         '    OldHeads%% = False
27.         'ELSE
28.         '    OldHeads%% = True
29.         'END IF
30.         OldHeads%% = NOT OldHeads%%
31.         'IF RND < 0.5 THEN
32.         '    Heads%% = True
33.         '    OldHeads%% = True
34.         'ELSE
35.         '    Heads%% = False
36.         '    OldHeads%% = False
37.         'END IF
38.     END IF
39.     Count& = Count& + 1
40.     IF Count& / 10000000 = Count& \ 10000000 THEN
41.         Count& = 0
42.         PRINT MaxSame%
43.         RANDOMIZE (TIMER)
44.     END IF
45.     Cycle& = Cycle& + 1
46.     IF Cycle& > 2147483646 THEN END
47. WEND
48. PRINT Cycle&
49.  

The program runs freely and occasionally prints the maximum number of same consecutive "heads or tails".  On my laptop this number is 24, seemingly never exceeded.  The likelihood of getting 24 same consecutive heads or tails is low (~ 1 in 16 million, but the program is doing billions of cycles).  Occasionally, one might expect the maximum of 24 to be exceeded.

I think that I must be doing something stupid with the code.

[bplus]

Wasting polls usually made it worse but I got it to do 26 with this (2 wasted polls):

Code: QB64: [Select]

1. Randomize (Timer)
2. lastH = -1
3. While InKey$ = ""
4.  
5.  
6.  
7.     ' get 24 max run unless I uncomment next
8.     x = Rnd 'waste a poll
9.     x = Rnd ' again
10.     'x = Rnd ' again
11.     'x = Rnd ' again
12.  
13.     If Rnd < 0.5 Then
14.         H = -1
15.     Else
16.         H = 0
17.     End If
18.     If H = lastH Then
19.         same = same + 1
20.         If same > MaxSame Then MaxSame = same
21.     Else
22.         same = 0
23.         lastH = H
24.     End If
25.     C = C + 1
26.     If C Mod 10000 = 0 Then
27.         Print MaxSame
28.         Randomize (Timer + Rnd * 10000)
29.     End If
30. Wend
31. Print MaxSame
32.  

Not every time but often and don't have to wait long: