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@miraculixx
Last active April 2, 2021 18:37
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coin toss sequence, probability experiment in response to @nntaleb https://twitter.com/nntaleb/status/1377576808590282761
Question by @nntaleb
Throw a coin, H=head, T= Tail. Which sequence one is more likely?
A={H,T,H,T,H,T,H,T,H,T,T,H,T,H,H,T,T,T,H,H}
B={H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H}
C={H,H,H,H,H,H,H,H,H,H,T,T,T,T,T,T,T,T,T,T}
The above is a Python implementation to evaluate this empirically.
Use as follows:
$ python cointoss.py [<N>] [<T>]
Of 10000 trials with 100 samples:
- overall counts Counter({'A': 1, 'C': 1, 'B': 0})
- winner counts Counter({'A': 9999, 'C': 1})
N = number of samples for each trial, defaults to 1000
T = number of trials, defaults to 1000
Overall counts are the number of times each sequence was found, over all trials
Winner counts are the number of times each sequence was found as the most frequent, in any one trial
Reading example for above results: In 1000 trials with each 10000 samples, the sequences A and C
where found exactly once each. Sequence B was never found (out of a total of 10'000'000 samples).
Interesting results:
$ python cointoss.py 1000 1000
Of 1000 trials with 1000 samples:
- overall counts Counter({'B': 1, 'A': 0, 'C': 0})
- winner counts Counter({'*': 999, 'B': 1})
$ python cointoss.py 10000 1000
Of 1000 trials with 10000 samples:
- overall counts Counter({'C': 13, 'B': 12, 'A': 11})
- winner counts Counter({'*': 964, 'C': 13, 'B': 12, 'A': 11})
$ python cointoss.py 100000 1000
Of 1000 trials with 100000 samples:
- overall counts Counter({'A': 114, 'C': 104, 'B': 90})
- winner counts Counter({'*': 734, 'A': 107, 'C': 85, 'B': 74})
$ python cointoss.py 1000000 1000
Of 1000 trials with 1000000 samples:
- overall counts Counter({'B': 1009, 'C': 988, 'A': 986})
- winner counts Counter({'A': 441, 'B': 294, 'C': 209, '*': 56})
Beware of increasing runtime O(N * T)
import sys
from collections import Counter
import numpy as np
def more_likely(N=1000):
H, T = 0, 1
A = np.array([H,T,H,T,H,T,H,T,H,T,T,H,T,H,H,T,T,T,H,H])
B = np.array([H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H,H])
C = np.array([H,H,H,H,H,H,H,H,H,H,T,T,T,T,T,T,T,T,T,T])
sample = np.random.randint(H, T+1, (N, 20))
count = lambda v: len(np.where((sample == v).all(axis=1))[0])
counts = {
'A': count(A),
'B': count(B),
'C': count(C),
}
return counts
def trials(N=1000, T=1000):
# run T trials with N samples each
counts = Counter()
winners = Counter()
for i in range(T):
ex = more_likely(N)
if max(ex.values()) > 0:
# at least 1 sequence found
win = max(ex.items(), key=lambda v: v[1])[0]
else:
win = '*'
counts.update(ex)
winners.update({win: 1})
print(f"Of {T} trials with {N} samples:")
print("- overall counts", counts)
print("- winner counts", winners)
kwargs = {
'N': int(sys.argv[1]) if len(sys.argv) > 1 else 1000,
'T': int(sys.argv[2]) if len(sys.argv) > 2 else 1000,
}
trials(**kwargs)
@miraculixx
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Mine, perhaps easier on the eye :)

nice!

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