Coin Flip Probability: Non-Random Switching & Skewed Distribution

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Discussion Overview

The discussion revolves around the probability outcomes of a coin flip experiment, particularly focusing on the implications of non-random switching of labels affixed to the coin's sides. Participants explore the relationship between the expected distribution of heads/tails (H-T) and a skewed distribution of numbered outcomes when the switching mechanism is not random.

Discussion Character

  • Exploratory, Debate/contested, Conceptual clarification

Main Points Raised

  • One participant questions whether a non-random switching of labels (1 and 2) on a coin affects the distribution of outcomes, suggesting that while H-T may appear random, the 1-2 distribution could be skewed.
  • Another participant argues that if the coin flip is random, the distribution of outcomes should remain approximately 50% for both H-T and the numbered outcomes, regardless of how the labels are switched.
  • A further reply raises the possibility that if the switching of labels is fixed (non-random), the 1-2 distribution could mirror the H-T distribution, challenging the assumption that randomness is necessary for equal distribution.
  • One participant suggests simplifying the labels to "this side" and "not this side," reiterating that the randomness of the labels does not affect the outcome of the coin flip.

Areas of Agreement / Disagreement

Participants express differing views on the impact of non-random switching on the distribution of outcomes. There is no consensus on whether the skewed distribution of the numbered outcomes indicates tampering or if it is a natural consequence of the non-random switching.

Contextual Notes

The discussion highlights the assumptions regarding randomness and the definitions of "random" versus "non-random" in the context of the coin flip experiment, which remain unresolved.

lukas_b
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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.
 
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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.
 
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.
 
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.
 

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