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Comment by swid | Hacker News Reader

Lets says I have a coin. I have no data on it. I do not know if it will come up heads or tails or if it is a fair coin.

I throw the coin N number of times and determine the coin is fair. I still do not know which side the coin will come up.

But this isn't the same as having no data on the coin. I've determined the coin is fair by gathering data, which otherwise I would not know. Often this added piece of information is crucial to making good decisions and not at all equivalent to the first case.

For instance, I might want to bet you that the next 10 throws in a row will all be heads. If you know the coin is fair, this is a good bet - but without data on the coin, it could be a trap.

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The goal of polls is not to determine if an election is or is not a fair election. The goal of polls is to predict the final outcome of the election.

You state the case of no knowledge vs knowing 50/50 probability are equivalent, but they are clearly not.

If you have no data but one side is actually heavily favored to win, you cannot determine how much you should bet on that probability even though there is an opportunity to make good sized bets. If neither side is favored to win, then you can still make good sized bets if the payout is not 1:1.

The Kelly Criterion formulates all this - the probability of win/loss does in fact matter, and if you don't "know" that, you cannot make a good bet. Knowing it is 50/50, you can bet on it.

50-50 event with no edge, the Kelly Criterion suggests not to bet. (ChatGPT)

And this is exactly why you should not rely on AI without fundamental understanding.

That would only be true if the payout odds are even. And in my comment I explicitly say not 1:1 payout. Go ahead and ask the AI for clarification, I’m sure it can explain it to you. On Wikipedia, the factor is “b” - ie 2:1 payout and you would bet on a 50/50 event.

The intuition should be incredibly obvious here. I have a fair coin and will pay you 200 dollars for heads and take 1 dollar for tails. You would flip that coin as many times as I let you.

Even in your reply to this - ChatGPT is telling you in one situation you should not bet because the expected gain is nothing, and the other you don't know what to do - which is not equivalent. But the edge it is talking about is the expected gain over the probability of the event with the payout odds. If there is no edge, you won't bet. But you can have an edge with 50/50 odds, and if so you would bet.

Fails to see any difference other than "N/A" and "unpredictable":

     In the 50/50 case, the Kelly Criterion does provide an answer: don’t bet, because there’s no edge and no expected growth.

     In the unknown probabilities case, you can’t apply the formula at all, and you don’t have enough information to make an informed decision. You're essentially in the dark about how much to bet, and thus you cannot use the Kelly Criterion.

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