>From pattib@netcom.com Tue Jan 10 11:11:30 PST 1995 It's interesting, really. I've been on FIBS for a year and a half now, played thousands upon thousands of games, and probably watched another several thousand. I'm quite familiar with the phenomenon of selective memory, especially when it pertains to "luck", and I maintain a healthy skepticism about RNG flaws. Nonetheless, I've probably at least ten people tell me independently that they think FIBS rolls too many doubles. Whenever I hear a story about a particularly quirky string of doubles, I always ask some flavor of the following questions: Was it early in the game? Middle game? Bearing off? Did you have "double" set so that you weren't asked? Did you have "automove" set so that forced plays were made automatically? In all but one situation, I've gotten the same answers: it was during the bearoff, and both players had things set so that both rolls and plays were happening automatically. In other words, several moves happened with nobody touching the keyboard. I spent several years of my life doing formal software testing, and I've seen all sorts of strange things from computers. To me, this smells like it might be an actual system quirk that causes doubles to occur more often when there is no player intervention. I can come up with a few plausible theories as to why this might occur, although I'm not familiar with FIBS internals, so they're all shots in the dark. Proving or disproving this theory is a little bit beyond what I'm willing to do at this point. It would require me to record hundreds of games, including which rolls happened automatically-- "oldmoves" output won't cut it, which makes things much more compicated. In addition, I can think of several factors which might be relevant: number of players logged in, number of games being played, number of watchers, and several others (some of which I couldn't even measure easily.) On the other hand, let's assume for a moment that my theory is exactly correct, and that the number of doubles rolled in that situation is higher than normal. What is the impact? Does it make the game unfair? No, I don't think so. I think this particular hypothetical phenomenon affects all players equally (and it will if I've guessed at the conditions correctly), so over the long run it won't affect anyone's rating. I certainly wouldn't use FIBS games as data for bearoff analysis, but there are far better ways to do this anyway, so that's no big deal. ----------- And now for some numeric guessing games ---------- The excellent "dicetest" command doesn't show any huge anomalies, but the hypothetical phenomenon I mention could well be in the noise. Actually, I would expect it to be. Just for fun, can anyone give me the following numbers: - Average number of rolls in a game played to completion - Average number of rolls for an unopposed bearoff - Average number of rolls in a game ended by a cube - Percentage of games that are played to completion - Percentage of games played to completion that end in an unopposed bearoff by both sides. I'll make some numbers up (rolls are per side): 40, 10, 10, 50%, 10%. Using these numbers, for every thousand games played (total/affcted): 500 end after 10 rolls 5000/0 450 end after 40 rolls 18000/0 50 end after 40 rolls, 2000/500 and 10 rolls show the phenomenon If my guesses are anywhere close to correct, the phenomenon affects 500 out of every 25000 rolls. Of these 25000, 4166 will normally be doubles (83 of which are in the affected group.) Let's say that our hypothetical phenomenon causes doubles to be 50% more likely than normal to occur (a number I consider REALLY high.) This gives us an extra 42 doubles, for a total of of 4208. In normal circumstances, 16.67% of rolls will be doubles. Our extra 42 doubles causes this number to rise to 16.83. CONCLUSION: If this phenomenon really exists, and my wild-assed guesses are anywhere close to correct, the phenomenon only changes .17% of rolls. I will gladly rework this analysis if anyone can provide me with more accurate numbers. I really did make all of these numbers up, and I wouldn't put any faith in them, although I'd guess they're all within an order of magnitude. :-) ------------- And now for some actual live numbers ----------- I just logged in and did a dicetest, which showed 66519 rolls, of which 11127 were doubles (16.73%.) To see how this compares, I added up each row and column (convenient groups of six). Here are the sorted percentages: 16.44 16.54 16.57 16.57 16.68 16.68 16.69 16.71 16.72 16.73 doubles 16.75 16.83 16.85 In this particular sample, doubles occurred slightly more frequently than average, but certainly not outside of what one would expect. (The two highest numbers above are for the column x-3 and the row 4-x, and the low number is for the column x-4.) CONCLUSION: In this particular sample, doubles occurred slightly more often than average, but not outside of the bounds of reasonableness. Many more samples would be required to show a real trend. MAJOR DISCLAIMER: I am *not* a math weenie, and I haven't done any statistics work in many many years. I also haven't checked my math above, and I'm willing to bet there's at least one error somewhere. For somebody who is better with statistics than I, how many samples would I need in order to prove or disprove that doubles are more likely than normal to occur? Would ten samples of > 50000 rolls be enough? Twenty? I'll be happy to grab them at random (making sure none overlap) and repeat this analysis to see what's going on. -Patti (whew. this is a lot longer than I'd expected.) -- Patti Beadles | pattib@netcom.com | Algolagnia abounds! pattib@ichips.intel.com | or just yell, "Hey, Patti!" | One bad cube can ruin your entire day.