--- In [email protected], "John O'Laughlin" <[EMAIL PROTECTED]> wrote: > > On 5/10/07, Steven Gordon <[EMAIL PROTECTED]> wrote: > > > As I understand the Quackle scheme as explained in this thread, AE > > would be less highly valued than EE and ERN would be less highly > > valued than ERR, whereas both Sheppard's approach and mine would both > > prefer AE and ERN, respectively. So, Quackle must have some > > additional synergy factors to account for this - right? > > Quackle's actual leave values were created through a more complicated > process than I'd like to fully describe right now, but I will try to > explain it in the near future. Quickly: > > The first step is to come up with "leave values" for all 3.2 million > racks. BaSiC values with synergy and v/c are part of the estimates for > the values, but I also take into account whether the rack has a seven > or eight letter bingo (and how many) and what possible nonbingo plays > are likely to be available. The estimates are tuned to minimize error > with a million-ish sample of simmed random racks. > > Then for zero- to six-tile leaves, I compute the leave's expected > value based on the values of racks it can draw (weighted for > probability). > > John
I can confirm that when your rack evaluator has synergy values then the value assigned to an isolated E is lower than when you don't incorporate such factors. Of course, John's listing derives from the ultimate evolution of synergy; Quackle has a value for every rack, so synergy is incorporated into every aspect of the evaluator. John's explanation is spot on: the E derives situational value from its positive synergy with a lot of other tiles, like ER, EN, ES, ED, and so on. Positive synergy with every consonant, IIRC. When you have synergy values, those can come to dominate the overall eval, particularly for racks with >= 5 tiles. For example, in ABCDE there are only 5 parameters for individual tiles, but 10 for pairs of tiles and 10 for triplets. Ballard and Carroll's Basic model suggests that ABCDE should be a lot better than ABCD, much more than the fraction of a point that you would figure if you used John's Quackle data. As far as using John's parameters in games: I am uneasy about it for a few reasons: 0) Theoretical: using 100 values that have been tuned in the context of 3.2 million values is hard to justify. (In theory.) 1) Theoretical: these parameters were optimized to be used *alone*, whereas human players want a system where the parameters are *added*. 2) Observation: without synergy values, the tile values seem "compressed" towards 0. John's recommendation of tweaking the vowels and consonants helps somewhat, but IMO some values are still out of line. (Q and E stand out.) 3) Experimental: these values differ from the values that Maven finds when it tries to optimize a fixed, small set of patterns that were designed to be *added* together. I must refrain from a definite opinion, since I cannot devote the time necessary to studying this issue. But: perhaps you are better off using Basic, or Maven's values or something, along with a V/C balance adjustment. Best and Warmest Regards, Brian
