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Active Forums => Programs => Topic started by: Qwerkey on November 24, 2021, 12:41:38 pm

Title: Maximum Consecutive Same Heads/Tails in Coin Toss
Post by: Qwerkey on November 24, 2021, 12:41:38 pm
When I created my coin toss graphics program https://www.qb64.org/forum/index.php?topic=4117.msg134684#msg134684 (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
  9.     Heads%% = False
  11. OldHeads%% = Heads%%
  13.  
  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
  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.
Title: Re: Maximum Consecutive Same Heads/Tails in Coin Toss
Post by: bplus on November 24, 2021, 02:44:01 pm
Wasting polls usually made it worse but I got it to do 26 with this (2 wasted polls):

Code: QB64: [Select]
  2. lastH = -1
  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
  31. Print MaxSame
  32.  

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