Quote:
Originally Posted by EscapedArtist
This is easy to test so don't write me off just by the subject.
Can anyone give me the odds of rolling a pair of dice 57 times and NOT getting doubles? That is what happened in my GNU BG when only counting the opening roll.
I first noticed an anomaly because it seemed that my GNU BG was giving really crappy opening rolls...consistently. I'm aware these things are usually psychological and I suppose it could still be the case here...I am a novice at statistics and backgammon. But, I became so curious that I started writing down my first rolls.
Now I see that I don't get crappy first rolls, rather, I hardly every get doubles on my first roll. I've now been monitoring this and I've gotten 6 doubles on my opening play out of 125 games. That is averaging 1 in 21 not 1 in 6...hmmm.
So, am I misunderstanding the nature of statistics? Is 125 games enough to expect a near 1/6 ratio or is this just one of those reasonable runs of bad luck. Can someone else monitor this and see if they have similar findings? My GNU BG version is 1.05.000-mingw 32-Bit 20150725. My seed is 803903184 and my trials are 1296 (I have no idea what trials are). All of this was set in the default install.
The odds of getting a double 6 / 125 times is 0.00498%. That probability is misleading though, since if you win the starting roll, it can't be a double. Assuming you win half of the starting rolls (63), it's 4.466%. If you also consider situations where you roll fewer than 6 doubles in 63 tries, it's 8.175%.
Getting no doubles in 57/2 ~= 29 tries (again because it's your opening roll) is expected at 0.505%. Unlikely, but not as remote as you may think.
If you want to play around with these, use the BINOM.DIST function in Excel.