Quote from: Dabs on August 02, 2013, 03:25:54 AM

Quote from: organofcorti on August 01, 2013, 01:12:11 PM

Not quite. The expected number of sequences until you exactly 5 losses in a row is 41772.04. The expected number of loss runs until you hit more than 5 losses in a row 3e05.

Keep in mind that the variance is large. If the expected number of loss runs is 1/3e05, then 95 times out of a hundred that you experiment, you'll hit a hit loss streak of 6 or more at between 7,595 and 1,106,661 sequences.

Quote from: Dabs on July 31, 2013, 01:32:21 PM

So, a loss run is any martingale sequence? Not including just 1 loss. That means at least 2 losses in a row? Or does loss run mean any sequence of losses, including a single loss?

"Losses in a row" can be any positive integer from zero up: 0, 1, 2, 3 .... For example loss, loss, win, loss, win, win is 2 losses in a row, followed by a one loss sequences, followed by a zero loss sequence.

So "Losses in a row" is basically how many wins, because that includes zero loss sequences, except if there are "Wins in a row" which are counted as one up to the next loss. Correct? This translates to approximately 87.7779% of the number of rolls? Or the other way around, about 13% of the number of rolls is the losses, therefore, the "Losses in a row" sequences.

No. You could think of the number of "loss runs" as the number of wins, though.

Try this. Let "loss" = 0 and "win" = 1. Consider the following 24 rolls:

Code:

0 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 1 1 0 1 0 1 1

Now split into the "roll number", "run (or sequence) number" and "losses per run":

Code:

Rolls: 0 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 1 1 0 1 0 1 1
Roll number: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Run number: 1 2 3 4 5 6 7 8 9 10
Losses per run: 3 1 2 0 0 6 0 1 1 0

I hope that's clear?

Quote from: Dabs on July 31, 2013, 01:32:21 PM

Also, 95 times out of a hundred, I will hit a loss streak of 6 or more after 7,595 sequences, but before 1.2 million sequences. Which means I'm almost guaranteed to hit the loss streak after a million rolls.

I think the debate now is whether just-dice is really memoryless or not, but that's another issue. We can all agree that it might indeed be actually memoryless. Or maybe that's just Gambler's Fallacy whispering in my ear again ...

Dung beetles navigate using the milky way galaxy ... (okay, just having some fun here.)

If the dice rolls at Just-Dice are not memoryless, then the pseudo-RNG it uses would have to be broken. AFAICT, it's not. It's also quite possible to prove (within certain confidence levels) that the RNG is or is not as random as it should be, but I don't really have time for those sorts of shenanigans.