I got an Overwhelming response in favor of Option C (66%). which is a Rational way of thinking, as every new coin toss is independent of another.

But wait a second, all this rational talk is good to sell the books, win a few awards, write very engaging blogs, But does this rational thinking pass the test of REAL LIFE SITUATIONS.

Nasim Taleb, introduced a character name FAT TONY. Now although, 05 instances is too small a sample size, but at least FAT Tony should have an iota of doubt in his mind that may be, just may be this coin is rigged and has HEADS on both sides.

Going by that hypothesis, now it makes sense to bet on HEADS, WHY? because if the coin is not rigged, you have 50% chance of getting it right. and if the coin is rigged, you have 100% probability of winning.

People who chose tails in a normal coin toss example are playing revert to the mean play which apparently makes NO SENSE. Because as Rational decision maker would tell you, since every toss (instance) is independent of another, there is no mean and so there cannot be any revert to it.

If we take this situation to the stock market however, things change on its head. Let us just say that a stock has HIT 05 lower circuits in a row (of 10% each).

NOW, with your scuttlebutt, research and analyses, you might reach a conclusion that you know something that market doesn’t and you can bet on TAILS in that situation, playing revert to the mean. Revert to the mean would work here because each lower circuit is not independent of the other and is part of a bigger scheme of things that is manifesting.

Similarly 05 lower circuits might also tell you that there is an Information mismatch and may be markets know something that you don’t. And you need to be humble enough to admit that may be you don’t know everything, despite your research and so you select HEADS (sell or short)

As you can see, there is no right answer, the idea is to know where you are in the information distribution curve. Value investors try to call Tails when they know something. Trend followers call heads, cutting the ego and admitting that they don’t know and nobody does.

 

As always comments are welcome.

3 thoughts on “Coin Toss

  1. Applying crude Bayesian theory, we’re trying to estimate if the coin is rigged given 5 heads in a row. In other words, estimating, posterior odds from prior odds and likelihood ratio. Prior odds of heads and tails are 50 and 50. Likelihood of 5 heads in a row if the coin is fair is 1/32, while the likelihood of 5 heads in a row if the coin is rigged is closer to 1. So, here goes.
    Heads Tails
    Prior odds 50 50
    Likelihood 32 01
    Posterior 1600 50
    So, odds are now at 1600/1650, or close to 97% of the coin being rigged! So, the next bet ought to be heads!

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