Quote from: LoyceV on Today at 09:36:51 AM

Quote from: o_e_l_e_o on October 23, 2022, 07:48:04 AM

Quote from: larry_vw_1955 on October 23, 2022, 12:16:15 AM

but then we get into other questions such as "what is an acceptable level of bias in an experiment where you perform it some number of times, be that 1000, or more?"

When considering generating private keys for bitcoin, then my answer is zero. I don't see why you would settle for anything less. This is why I advocate for using coin flips with von Neumann's algorithm, since by doing this you can be certain you have eliminated any bias in your coin, as well as not introduced any new bias by performing randomness extraction or other processes you don't fully understand on your data.

By coincidence, I stumbled upon an article about bias in coin tosses. It reminded me about this topic, hence the 10 month bump.

TL;DR: if you start a coin toll with heads up, there's a 50.8% chance you'll end up with heads.

Quote from: Coin Tosses Are Not 50/50: Scientists Toss 350,757 Coins And Prove Old Theory

"According to the Diaconis model, precession causes the coin to spend more time in the air with the initial side facing up," a new team writes in a pre-print paper that has not yet been peer-reviewed. "Consequently, the coin has a higher chance of landing on the same side as it started (i.e., ‘same-side bias’)."

Diaconis found, from a smaller ideal number of coin tosses recorded and analyzed, that coins land on the same side they were tossed from around 51 percent of the time. The new team recruited 48 people to flip 350,757 coins from 46 different currencies, finding that overall, there was a 50.8 percent chance of the coin showing up the same side it was tossed from.

Delving into the data further, they found that coin tosses are highly variable between people, with some showing a strong same-side bias and others having none at all – coin tosses may come down (ever so slightly) to the tosser.

Further reading: Fair coins tend to land on the same side they started: Evidence from 350,757 flips.

There are older articles also claiming a similar (51/49) distribution, but as far as I've found the recent research had the largest sample size.

So if you have a 51 to 49 percent bias on all your picks it still to the 24th power.

so effectively the bias mean a 24 word seed is more like a 22 word seed or am I wrong