Coin Flip Probability: Non-Random Switching & Skewed Distribution

[lukas_b]

Hi I have a question on probability which I am not sure of.

If you have a coin and flip it 20 times then of course the probability of getting H or T is 0.5. And even in 20 flips you should roughly get a 50% distribution, correct?

Now what if to each side of the coin you affix a number, #1 for H, #2 for T.
And before each flip of the coin, you randomly switch the the numbers affixed to each surface.

After flipping the coin another 20 times, both the H-T distribution and the 1-2 distribution should be ~50% right?

Ok now before each coin flip, let's say the numbers 1 and 2 are switched in some non-random way. For example, the rankings of two players in a sport (although I'm not sure if this is considered truly non-random from the perspective of the coin).

Now you flip the coin another 20 times and you still get a ~50% distribution for H-T, but the distribution for 1-2 is very skewed, let's even say 100% '1'. Looking at the H-T distribution it seems normal and random, but looking at the 1-2 distribution one has reason to suspect something is unusual.

Is there a reason to think that someone could have tinkered with the coin flip process to get this skewed distribution or is it not completely abnormal for this very skewed distribution since 1-2 were apparently not switching randomly?

Hope that made sense.

Thanks.

 

[lurflurf]

Yes there is a reason to think that someone could have tinkered with the coin flip process. The number '1' is effectively a guess of the result, one that is 100% accurate. It is very much like if we flipped two coins each time and they always match. It would be very suspicious. In fact the randomness of '1' and '2' is not important, if we change them in any random or deterministic way we should get about 50% if the coin flip is random.

 

[lukas_b]

But is that true even if the second coin was not random? i.e. the players rank could have been fixed (since it is non-random) at #1 and #2 for all 20 flips in which case the 1-2 distribution would equal the H-T distribution.

 

[martix]

Just replace the tokens #1 and #2 with "this side" and "not this side".
And lurflurf already said that the randomness of #1 and #2 is not important.

 

[CellCoree]

Hello,

Thank you for your question on probability and coin flips. It is correct that in a random coin flip, the probability of getting heads or tails is 0.5, and in a series of 20 flips, you would expect to see a roughly 50% distribution of each. However, when you introduce the concept of affixing numbers to each side of the coin and randomly switching them before each flip, the probability changes.

In this scenario, the probability of getting a certain number (1 or 2) is still 0.5, but the probability of getting heads or tails is now 0.25. This is because there are now four possible outcomes for each flip: heads and 1, heads and 2, tails and 1, tails and 2. Each of these outcomes has a 0.25 probability, resulting in a 50% distribution for both the H-T and 1-2 categories.

However, when you introduce a non-random way of switching the numbers before each flip, the probability changes again. In this case, the probability of getting a certain number is still 0.5, but the probability of getting heads or tails is now 0.75. This is because only two outcomes are possible: heads and 1, or tails and 2. This results in a skewed distribution for the 1-2 category, with a 100% chance of getting 1.

From a scientific perspective, this skewed distribution could be considered unusual or non-random, as it goes against the expected 50% distribution. It is possible that someone could have tinkered with the coin flip process to achieve this result, but without further evidence, it is difficult to say for sure. It may be worth investigating further to determine if there is any external influence on the coin flips. I hope this helps clarify the situation.