Quote from: o_e_l_e_o on October 19, 2023, 09:54:59 AM

Quote from: larry_vw_1955 on October 19, 2023, 03:29:16 AM

so under the assumption that HT and TH have equal probability that method seems good for eliminating bias but there is that assumption.

That's not an assumption - it's pure math.

Let's say your coin is biased to 60% heads, 40% tails. The probability of HT is 0.6*0.4 = 0.24. The probability of TH is 0.4*0.6 = 0.24. The probability is identical. This is the whole premise behind von Neumann's algorithm - you know HT and TH are equally probable without the need to perform any statistical testing of your coin.

This finally hit me why it is wrong. The flipping must be done blindfolded and gloved to avoid a biased flipper that does not like your method.

Your assumption is that the coin is biased not the flipper. If it is the flipper your method is not good. Ie the flipper may subconsciously be able to take a neutral perfect coin and make it do heads 60-40

or tails 40-60 on any toss. So he would ruin the neumann method. unless he flips it gloved and blindfolded.