Comment by lupire

4 years ago

Biased coins are *impossible" to make if the coin is flipped not spun.

I doubt any story about a biased coins in the real world.

4 comments

lupire

Reply
function_seven  4 years ago

If the coin was made from a thin magnet, and being flipped onto a weak magnetic plate, couldn't you bias the result? If the landing pad was a strong magnet, then you could trivially make it a "100% heads" coin. Just weaken the magnetic field so it's not strong enough to flip a coin flat at rest, but has enough oomph to take a coin landing near its edge to the preferred result.

  • lupire  4 years ago

    If you don't flip the coin within any reasonable definition of flip, sure.

    But if you flip a coin and it turns about N times, you can't make the sum (over all k) of the probability of N+2k turns substantially more likely than thr sum of probability of N+2k+1 turns.

    • function_seven  4 years ago

      If the mat that my coins are landing on is a strong magnet, I know I can make every single flip land heads. Even when the coin would otherwise land tails, it will instantly flip to align with the strong magnet beneath.

      So what if I dial the magnetic field back just a bit? So that only when the coin is oriented flat as it lands will it maintain that orientation in spite of the opposing magnetic forces. But if the coin's orientation is near vertical, then the forces are directed to nudge it "headwards" instead of "tailwards".

      Your math applies to weighting the coin. It makes sense in that context. I'm talking about a system of magnetic coin and matched magnetic landing pad.

    • shezi  4 years ago

      If you bend a coin, one side has larger area than the other and will prefer to land on that side accordingly. The turn-based argument depends on the fact that both sides of the coin are the same size, which is not true if you bend the coin.