One of the position Tim posted from the othello quiz intrigued me. It's the one that Stick next'd and that Tim only posted to point out that it is obvious now but wasn't then. Of course I got it wrong, and I didn't really understand why. I've been palying with the bots to try to figure it out, and I'm sharing my thoughts in case anyone else here is confused or wants to correct any of my misconceptions.
Here's the position with gnu's opinion (4ply):
The score (after 0 games) is: white 1, blue 2 (match to 5 points)
| white | 147 |
|---|---|
| |
| blue | 164 |
Position ID: jM/BATDQc+QBMA Match ID: cAm2ABAAEAAE | |
| # | Ply | Move | MWC | |
|---|---|---|---|---|
| 1 | 4 | 13/9 13/8 | 54.75% | |
| 0.455 0.131 0.005 - 0.545 0.210 0.023 | ||||
| 2 | 4 | 13/9 11/6 | 54.21% ( -0.54%) | |
| 0.439 0.125 0.005 - 0.561 0.201 0.017 | ||||
| 3 | 4 | 13/8 11/7 | 53.72% ( -1.03%) | |
| 0.431 0.112 0.004 - 0.569 0.213 0.019 | ||||
| 4 | 4 | 13/4 | 53.63% ( -1.12%) | |
| 0.442 0.119 0.005 - 0.558 0.232 0.028 | ||||
| 5 | 4 | 24/20 13/8 | 52.82% ( -1.93%) | |
| 0.437 0.115 0.005 - 0.563 0.245 0.017 | ||||
The big surprise for me here is not that 13/8,13/9 is right, but that the natural looking (at least to me) 13/8 24/20 is so far off. I'd likely have played that and so I want to figure out what I am missing. My first thought/hope is that this is somehow match score related since I've been focusing on money play only for now that wouldn't bother me. It's hard to believe though given the score. Just to check, here's the money version:
| white | 147 |
|---|---|
| |
| blue | 164 |
Position ID: jM/BATDQc+QBMA Match ID: cIkSAAAAAAAA | |
| # | Ply | Move | Equity | |
|---|---|---|---|---|
| 1 | 4 | 13/9 13/8 | -0.257 | |
| 0.455 0.130 0.005 - 0.545 0.211 0.023 | ||||
| 2 | 4 | 13/9 11/6 | -0.303 ( -0.046) | |
| 0.438 0.125 0.005 - 0.562 0.202 0.018 | ||||
| 3 | 4 | 24/20 13/8 | -0.354 ( -0.097) | |
| 0.435 0.114 0.005 - 0.565 0.241 0.017 | ||||
| 4 | 4 | 13/4 | -0.364 ( -0.107) | |
| 0.439 0.118 0.004 - 0.561 0.230 0.028 | ||||
Ok, so that's not it. Things changed more than I would have guessed, but 13/8,13/9 is still best and much better than 13/9, 24/20. Ok, time for a new theory. Maybe it's about the blots? Maybe being behind in the race with two blots that can't easily be cleaned up means it's time to prepare for a possible deep anchor holding game or backgame.
That's easy enough to check - let's make the 5-point with a checker from the 6, and move the blot on the 11 back to the midpoint. That only changes the race by one pip, but clears up all of the blots. That gives:
| white | 147 |
|---|---|
| |
| blue | 165 |
Position ID: jM/BATCwc/ABMA Match ID: cIkSAAAAAAAA | |
| # | Ply | Move | Equity | |
|---|---|---|---|---|
| 1 | 4 | 13/9 13/8 | +0.182 | |
| 0.551 0.169 0.007 - 0.449 0.146 0.008 | ||||
| 2 | 4 | 13/4 | +0.104 ( -0.078) | |
| 0.534 0.161 0.006 - 0.466 0.158 0.010 | ||||
| 3 | 4 | 24/20 13/8 | +0.096 ( -0.085) | |
| 0.537 0.150 0.007 - 0.463 0.161 0.005 | ||||
Well, that made blue's position much better, which is hardly a shock. It didn't do much to the relative merits of 13/8,13/9 and 13/8, 24/20. If anything, I'm more confused by this position as it looks a lot less complicated. Time to guess again. I know I have a tendency to advance my back men even when so far behind in the race that staying back would be better. Maybe this is just another example of that? In other words, maybe trying to make the 20-point is a mistake because this far behind in the race the 24-point is simply a better anchor to have. That's not too hard to check either. Let's just advance the anchor to the 20 point and give white a balancing 8 points in the race by moving a checker from the midpoint to his 8 point and from his 6 to his 3. This is a somewhat awkward distribution for white, hopefully it won't cause too much trouble. That gives:
| white | 139 |
|---|---|
| |
| blue | 157 |
Position ID: HM+DATCwc/ABAw Match ID: cIkSAAAAAAAA | |
| # | Ply | Move | Equity | |
|---|---|---|---|---|
| 1 | 4 | 13/9 13/8 | +0.548 | |
| 0.632 0.173 0.006 - 0.368 0.076 0.002 | ||||
Fortunately this seems clear: 13/8,13/9 is still the best play, but blue's equity has increased by around .350. Even if some of that comes from stripping white's midpoint, the 20-point is still a vastly superior anchor here. That is a relief as far as not having to unlearn everything I think I know, but leaves no explanation for the original position.
Next theory: it's the priming side, stupid. In other words, while 24/20 starting the 20 point is a good idea it simply isn't nearly as urgent as bring down another builder. This makes some sense - if blue can contain white's back men then the racing lead will turn into a timing problem, and bringing men to aim at the 7 and 4 points (and starting the 9) are the way to do this. We can check this theory too - from the position one back (before we gave blue the 20 point), let's let blue play 13/9, 24/20. Obviously not a legal move, but it does both the stated goals. That gives this position (with white on roll):
| white | 147 |
|---|---|
| |
| blue | 157 |
Position ID: sHPhASGMz8EBMA Match ID: MAEAAAAAAAAA | |
According to gnu 4-ply, that has an equity of .073 for blue. Compare this to the legal play of 13/8, 13/9 where blue's equity evaluates to .182. So this latest theory is wrong too - 24/20 isn't just less important than 13/9, it's just plain bad. How can that be if the 20 point is a huge improvement over the 24 and gives extra outfield control? The only explanation I can see is that the danger of being hit is too great. This seems hard to believe - white only has the spares on the 6 and 8 points for attacking, and is ahead in the race. Given that both boards are equally strong, all of this would seem to mean that an exchange of hits in white's board is just what blue wants. To check, I looked at the distribution of rolls for white after 13/8, 24/20.
Finally, a theory that seems to check out. It's not a surprise to me that white often hits here - that's normal with the 5 point slotted. It did surprise me that white double hits with 41,43,53, and 51 - the last two in particular leave a lot of return shots in a position where the race lead is all that white really has going for him. Perhaps even more surprising to me is that white hits loose on the 1 point by itself with 52 and 54. However, all of these rolls are below the average equity for white. In fact, the bulk of white's equity here comes from the four moves that let him make the 5-point on blue's head and a few other doubles that play nicely.
With hindsight being 20/20, I think that points at an explanation - while white is ahead in the race his position is quite awkward - the only thing he's accomplished from the starting position is moving 2 men from the midpoint to the 3 point. That's nice for the race, but has put those checkers somewhat out of play. He has very little constructive to do, and by splitting we would give him several plays that hit or double hit in his board to gain time to develop something more flexible. It's better to just focus on building our position and further isolating his back men, and wait for him to get one of many rolls that play badly.
(btw - in looking this over I realized that my simplified position is just 31P-55P-54, so this must really all be completely known to anyone who has studied the opening rolls in depth, so I apologize for the long post that butchers something you all know already. Hopefully someone else can get something from it.)