How is the gambler’s fallacy not a logical paradox? A flipped coin coming up heads 25 times in a row has odds in the millions, but if you flip heads 24 times in a row, the 25th flip still has odds of exactly 0.5 heads. Isn’t there something logically weird about that?

Question

I know it’s true, it’s just something that seems hard to wrap my head around. How is this not a logical paradox?

In: Mathematics

Answer 1

I have always been god awful at math and things like this.

So my question is this. Lets say the coin is a perfect 50/50 “fair” coin. It was flipped until it hit either heads or tails 24 times in a row. You have to pick heads or tails. I know its 50/50 on the flip.

They offer you the information on if the last 24 were all heads or all tails if you want it. Is there ANY benefit to this?

I am going to say maybe for fun I would choose the opposite. But I know its still 50/50. The sequences in coin flips if you flipped them a billion times or whatever im sure you would have some strange patterns according to humans.

Is there such thing as betting against the sequence continuing, and does that give me better odds in any theoretical way?