Test your Psychic powers! + Understand the Odds of guessing 20 coin tosses correctly in a row

Are you psychic? Do you understand probability? What are the odds of guessing 20 coin tosses correctly?

The odds of guessing one fair coin toss correctly are 50/50. You’d be right 1/2 of the time. (50%)

The odds of guessing the second coin are still 50/50, but for the odds of being correct both times in a row, you’d multiply the two probabilities. So, you’d get 0.5 * 0.5 = 0.25. You would guess both correctly 1/4 of the time (25%)

For three coin tosses, the odds of guessing all three correctly are 0.5 * 0.5 * 0.5 = 1/8 or 12.5%. Looked at another way, there is an 87.7% chance that you could not guess three in a row.

For 10 coin tosses, you would guess all 10 correctly only 0.1% of the time. In other words, the 99.9% of the time you would not do this.

For 20 coin tosses, the odds of guessing all 20 correctly are 0.0001%, or 1 in 1 million 48 thousand five hundred seventy six. You are more likely to be struck by lightning this year than to guess 20 coins in a row. It could happen, but the odds are over 1 million to one against that happening.

For comparison: According to NOAA, the odds of being struck by lighting are 1 in a million (1,000,000) in any given year. If you live to be 80 years old, the odds increase to 1 in 10,000 that you will be struck by lightning. In other words, guessing 20 coin tosses correctly is about as likely as getting struck by lightning some time in your life. Very un-likely! 1 in a million!

Try this psychic coin guessing demo:

http://www.stat.tamu.edu/~west/applets/psychictest.html

Psychic Test Demonstration.

For my guesses, I got 8, 12, 10 correct when I did 20 in a row. I never could get 13 or 14 correct out of 20 guesses. Let me know how you do!

Here’s my chart you can use with the above test to see if you are amazing at either guessing correctly, or missing:

Odds of guessing:			%	Probability	Odds (1 in … )
20		OMG!!!	0.0001%	9.53674E-07	1,048,576
19		REALLY??	0.0019%	1.90735E-05	52,429
18		AMAZING	0.0181%	0.000181198	5,519
17		WOW	0.1087%	0.001087189	920
16		WOW	0.4621%	0.004620552	216
15		STRANGE	1.4786%	0.014785767	68
14		STRANGE	3.6964%	0.036964417	27
13		STRANGE	7.3929%	0.073928833	14
12		RANDOM	12.0134%	0.120134354	8
11		RANDOM	16.0179%	0.160179138	6
10		RANDOM	17.6197%	0.176197052	6
9		RANDOM	16.0179%	0.160179138	6
8		RANDOM	12.0134%	0.120134354	8
7		STRANGE	7.3929%	0.073928833	14
6		STRANGE	3.6964%	0.036964417	27
5		STRANGE	1.4786%	0.014785767	68
4		WOW	0.4621%	0.004620552	216
3		WOW	0.1087%	0.001087189	920
2		AMAZING	0.0181%	0.000181198	5,519
1		REALLY??	0.0019%	1.90735E-05	52,429
0		OMG!!!	0.0001%	9.53674E-07	1,048,576

My purpose is to be able to apply this to other things, such as testing other paranormal claims.

To prove something works and is not just by chance then, I’d want to test it 20 times. If there is a yes/no option, I’d expect about 8 to 12 hits correct by pure chance. Notice that the odds of getting 16 correct are 216 to 1, but the odds of 19 correct are 52,429. Quite a difference!

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