(September 29, 2017 at 12:04 pm)Tiberius Wrote:

(September 29, 2017 at 12:01 pm)vorlon13 Wrote: drop coin on checkerboard

whatever color it most covers, red or black, corresponds to heads or tails

Haha, points for thinking outside the box. Let's add the additional constraint that you can only use the coin and the action of flipping the coin to get a result.

(September 29, 2017 at 2:15 pm)pocaracas Wrote: Hammy, the keyword was "simulate".

(September 29, 2017 at 12:42 pm)Tiberius Wrote: Each flip isn't the same chance though. There's the unfairness, which you can use to your advantage in the method which eliminates it.

(September 29, 2017 at 2:59 pm)Hammy Wrote:

(September 29, 2017 at 2:15 pm)pocaracas Wrote: Hammy, the keyword was "simulate".

Simulate by still using the same normal non-simulated coin lol.

Simulate a flip... or in other words... don't actually flip the coin normally.

So basically... it was a trick question

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(September 29, 2017 at 12:42 pm)Tiberius Wrote: Each flip isn't the same chance though. There's the unfairness, which you can use to your advantage in the method which eliminates it.

That's not what I mean.

Say it's 60% chance to be heads and 40% chance to be tails. Each flip it's that exact same chance. 60% heads, and 40% tails. It doesn't matter how many times you flip it. And redefining and equivocating by calling a bunch of flips a "throw" won't change the reality.

(September 29, 2017 at 12:53 pm)Tiberius Wrote: Ok, well here's the solution that Steel hinted at.

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Let's assume that the coin lands on "heads" with a probability of A, and lands on "tails" with a probability of B. We don't know what A and B are, we suspect they aren't equal.

If you flip the coin twice, there are 4 possibilities with the following probabilities (H = heads, T = tails):

HH = A*A
TT = B*B
HT = A*B
TH = B*A

Now A*B = B*A so the probability of flipping heads and then tails is the same as flipping tails and then heads.

Knowing this, we can ensure that we get a fair result by following this method:

1) Flip the coin twice. If the result is HH or TT, repeat this step.
2) If the result is HT, we say the overall result is "heads".
3) If the result is TH, we say the overall result is "tails".

To show this with numbers, let's say the probability of heads is 70% and the probability of tails is 30%. The results of flipping a coin twice would be:

HH = .7 * .7 = .49
TT = .3 * .3 = 0.09
HT = .7 * .3 = 0.21
TH = .3 * .7 = 0.21

So as you can see, when you disregard HH and TT results completely, you have a perfect 50/50 balance between HT and TH, making the unfair coin produce fair results.

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(September 29, 2017 at 3:33 pm)Tiberius Wrote: Your example of it being 60% / 40% every time is true, however when you group together multiple flips the percentages change. That's the key to the simulation, finding two different sequences of flips that have the same probability of occurring.

(September 29, 2017 at 12:53 pm)Tiberius Wrote: Ok, well here's the solution that Steel hinted at.

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Let's assume that the coin lands on "heads" with a probability of A, and lands on "tails" with a probability of B. We don't know what A and B are, we suspect they aren't equal.

If you flip the coin twice, there are 4 possibilities with the following probabilities (H = heads, T = tails):

HH = A*A
TT = B*B
HT = A*B
TH = B*A

Now A*B = B*A so the probability of flipping heads and then tails is the same as flipping tails and then heads.

Knowing this, we can ensure that we get a fair result by following this method:

1) Flip the coin twice. If the result is HH or TT, repeat this step.
2) If the result is HT, we say the overall result is "heads".
3) If the result is TH, we say the overall result is "tails".

To show this with numbers, let's say the probability of heads is 70% and the probability of tails is 30%. The results of flipping a coin twice would be:

HH = .7 * .7 = .49
TT = .3 * .3 = 0.09
HT = .7 * .3 = 0.21
TH = .3 * .7 = 0.21

So as you can see, when you disregard HH and TT results completely, you have a perfect 50/50 balance between HT and TH, making the unfair coin produce fair results.

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