There are now over 10 000 qualifying games. I've also improved the rating algorithm, and disqualified all games involving the bottom 10 players of all time.

Here are the new stats.

The neutral line seems to be: c3 - d3 - e3 - f3 - g4 - h5 - i5 - j6 - k7 - L7 (or is that - k6 - L6?)

There might also be some neutral spots in the mostly unexplored b12 region, for the more adventurous.

Seeing how the stats have jumped around, let me add a grain of salt. Even the stats for d3 have come down considerably since my last post – so, okay, maybe its death was greatly exaggerated. To some extent, this is all just a reflection of how we play, and improving the stats becomes like chasing ghosts. There is a lot of random stuff going on, and some of the spots have numbers I don't trust at all. (-197 on g11? No way. Even the -28 on f5 is dubious. +128 on j5? That'll probably come down.)

Still, it's pretty clear that the board in general is very red, indicating that a lot of players are playing overly strong first moves. This is okay if you're willing to bet that your opponent won't swap it. But against strong players, keep that neutral line in mind. And if you're feeling adventurous, try to boost my stats in some of the dark regions, please! My stats do include the 1-on-1 games that Little Golem does not rate.

Have fun!

Thanks for doing all that work, Alan! Uh, could you use brighter and more varied colors?

How are swaps handled? i.e., if the black player swaps, is that swapped position then logged as being an initial move for the black player and tablulated accordingly based on the win/loss results of the black player ?

If there is a swap, the 1st move belongs to the 2nd player, and then it's a matter of whether the 1st player or the 2nd player won.

For example, 1.e3 2.swap … 40.resign is a loss on the e3 spot, because the 2nd player took the e3 peg, and lost with it.

LittleGolem confusingly reflects the board, but 1.e3 2.swap is still considered an e3 start, not c5, because a c5 start would be different - the peg would be closer to its own side.

It would be great, if the number of swaps would be included! And *please oh please* use different colors. ;)

Any *specific* suggestions for better, brighter, more varied colors? Picking colors is not one of my greatest talents (as you might have guessed) …

How about, instead of going from red to blue, use more of the spectrum. Go from red through orange, yellow, green, blue, to violet. I'm not sure how that would translate into rgb values, but there ought to be some reference about that. Maybe use just 10 or so “region” values instead of a continuous spectrum. This may mean you won't be able to use a green font throughout. Also, have just 3 or so levels of brightness. I recommend most of the board could be much brighter. Use two darker values for “debatable” and “highly questionable.” The user can read the number of games and judge how valid the data for that hole is. Just a suggestion of course.

Fall colors.

That's what you get if you go the other way around the color cube, Red - Orange - Yellow - Green - Blue. Fall colors. It's very pretty. Couldn't use the green font anymore, though; I experimented a bit before settling on a golden color. Some combos are still hard to read, but most of them look good (on my high-end LCD monitor).

I also added swap percentage statistics, in brackets []. Good suggestion, technolion.

Also, I messed with the rating system. Now the numbers look very much like win percentages, even though they're not really: 50 = even chance, 60 = strong move, 100 = you win if you play this, guaranteed ;-) (Hey, would statistics lie to you?)

The idea is that the old scores were just an average of win expectancies. To illustrate a major defect in this, imagine if a strong player beats a weaker player (let's say the weak guy's win expectancy is .2) – it drags the average down toward .2. A win's a win; the score should go up.

Now, the main thing is that we want to find the neutral spots. The 0 point represents a neutral spot, so as far as neutral spots are concerned, it doesn't matter much what we divide by, as long as it's not 0. (Of course, I'm now renormalizing afterwards, so it's only 0 internally, but 50 on the final board, but you get what I mean.)

So, let's consider an edge case. Suppose a spot wins all of its games. What should its final renormalized score be? 100, I think, no matter what the win expectancies were along the way. Likewise, a spot so terrible that everyone loses on it should get a 0.

There is an obvious and easy way to accomplish this. Instead of dividing by the number of times the position was played (speaking again of the pre-normalized score), divide instead by the sum of the absolute values of the win expectancies. In other words, if you're adding .2 to the numerator, add .2 to the denominator. If your subracting .3 from the numerator, add .3 to the denominator.

Finally, renormalize this score, which will be from -1 to 1, to be 0 - 100. You might think of this result as your probability of winning a match with a player equal to you, if the first peg is yours and it's on that spot. It's probably pretty close to that. On the other hand, these numbers were created by observing as many games as possible, often with unequal players, and trying to compensate for the inequalities, and I can't guarantee the method of compensation is perfect. But I think it should be very close.

Have fun!

Oh, almost forgot! There's a new URL, so a new link:

Fall Colors

I think colors are better now.