Thank you yuri, dnikeeb, timothy, ah clem and markx for your illuminating reasoning, heroes all.
Let's look at these again, with hindsight and the benefit of a computer! This first one was a misplay of mine.
"Should I hit him on the bar? That's a waste of a good number, I'll just play the solid 13/11(2), 6/4(2). I didn't even consider 6/4(2), 3/1*(2) but it is easily the best play, very like the position after an opening split (for White) and a 5-5. When White dances you can cash the game. You won't be too good. When he enters, well at least you have a three point board and often two or three blots to shoot at. If White enters with a 6, you can probably double and get a take, although weaker positions than this are passed every day. Any other play is a BIG blunder.
This play came from 23 years ago. White is Alan Steffen, Black is Joe Sylvester and Joe took half an hour to make his play. Joe played 10/1, 4/1. He eventually did this as the best anti-gammon play. Danny Kleinman commented that he would play to win 11/8*, 11/5, 10/7. There were almost as many other ideas as there were experts! In 1988 of course, there wasn't anybody with a laptop and a bot.
Both the best play include 21/18(2). This seems so obvious to me, because it gives White no "safe" points. If you stay back she can leave blots on the 13, 12 or 11 pts and only risk an indirect shot. After that you pick up the blot on the 10pt and play 7/4 or 4/1. The two plays are roughly equal. How did Joe's "gammonsaver" play do? It's probably fourth best, winning about 29% and losing 10 gammons. Danny's "play to win" approach wins 33% but loses 20 gammons! The winningest play is 21/18, 11/8*(2), 10/7, earning 36 wins but losing 28 gammons!
Finally this one.
It's double match point. 13/9(2) is the clear winner, putting you just one roll away from making a 6 prime. Even when White rolls a 2, you are far from dead of course. making the point 6 pips away from a straggler is always strong, so that he can't jump out with a single die. To many people's surprise I am sure, this is also the right play for money. You cash when he doesn't roll a 2 and you are still in the game when he does.
How did our brave correspondents fare? One fell nobly on his sword after feeding the positions into Gnu, another had three wrong answers, another one right, another two right and dnikeeb nailed all three. Kudos to dnikeeb of course, but equally kudos to the others for sharing their thought processes here, from which we and they can learn a lot. We only learn from mistakes. Our successes teach us nothing.
I'll find something else for you tomorrow. Don't forget to order your copy of Mochy v. Falafel, annotated and with comments from the players, the most instructive match I have seen for ages with many tough plays. dorbel(at)gmail(dot)com for PayPal and/or queries. $10.
Until next time, enjoy the game!
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In position 1, your comparison with an opening 5-5 blitz is obvious in retrospect but I didn't think in those terms; that was helpful.
I'm not surprised that I got position 2 wrong. Does the match score make any difference? What rollout settings did you use? This is one where I think strong rollout settings are needed, especially for cube play. When I analyzed the position I linked to in my previous comment, XG misjudged things so badly on evaluation that sometimes the top checker play wouldn't even make it into its top 32 plays on 1-ply! This position is complex enough that I wouldn't trust the bot on the basis of just one rollout; I'd have to play around with variants and make sure (for example) that it isn't misplaying the next roll or two on either side.
The match score is White 21-away, Black, 18-away, so I don't think that that is a factor. I used XG's default rollout setting, which is 3-ply checker play with XG roller for cube decisions.
All bots sort small doubles badly at 1-ply. 1-1 and 2-2 are prone to this, 3-3 and upwards less so. XG looked at 35 plays at the 3-ply level.
After a 324 game rollout, 21/18(2), 10/7, 4/1 and 21/18(2), 10/4 are tied. The next best play is 0.1 behind, so I don't envisage it catching either of the above, although you are welcome to try. Extending the rollout might sort the top two, but I don't believe that it will make a hitting play correct.
I believe that the range of choice here is confusing. 21/18(2) to cover the outfield and 10/7 to pick up the blot are so clear that I don't know what Joe was thinking of. Getting involved in a blot hitting contest where you are outboarded and have a blot inboard is just against all common sense.
It might just be a redouble after 11/8*, 7/1, 4/1 which helps, but the quiet play will lead to more powerful cubes later I think.
Thanks, Paul. I studied this position with the bot a bit and thought I'd share some of what I found.
First of all, although a 3-point lead at 21-away might seem indistinguishable from an even match score, I've been dinged before for making that assumption. Of course, as you point out, it's not going to make up for a 0.100 equity difference!
I spent most of my time looking more closely at my play of 11/8* 7/1 4/1. First I looked at what happens after 11/8* 7/1 4/1, dance. I still haven't purchased XG2 and am still using XG1. XG1 3-ply doesn't double here, but XG1 4-ply thinks it's a massive double. Rolling it out with 4-ply for the first few decisions produces about a 0.100 overall difference in the rollout equity! That is, the play is "only" about 0.100 back rather than 0.200 back (as a pure 3-ply rollout indicates). This illustrates my point that it's risky to take a single, isolated bot rollout at face value for such a complicated position. I'm guessing that XG2 XG Roller probably won't suffer from this problem, but it's always worth checking this sort of thing.
Next, I changed the score to DMP. Hitting then becomes mandatory. 11/8* 7/1 4/1 probably isn't the top play even at DMP, but it's pretty close. The non-hitting plays that come out ahead at a normal match score aren't anywhere close. For this reason, I feel that I cannot agree with you that 21/18(2) 10/4 or 21/18(2) 10/7 4/1 is "clear" or "obvious" in any human sense. Given that these two plays don't come close to winning the most, the assessment that they are best must be a result of weighing extra gammon losses against extra wins, which is not at all a trivial calculation for such a complex position. In this position which I mentioned before, moving out to the 18pt looks promising for the same reasons that it looks promising in Sylvester's position, but the tradeoff works out to favor the gammon-losing hit.
Finally, I played with a couple of variants of the position. For example, I tried moving Black's dilly builder on the 2pt back to his 11pt. Then 11/8* 7/1 4/1 seems to be the top play. In this variant position, 11/8* 7/1 4/1 doesn't create a blot on our 11pt, and doesn't permanently kill any checkers. Though of course moving that dilly builder back to the 11pt is a rather major change to the position, it does illustrate that there are many features of the original position that need to be taken into account to properly evaluate it.
After 11/8*, 7/1, 4/1, XG2++ thinks that this is a marginally correct redouble. If the scores are reversed, it becomes a very strong redouble indeed and only barely a take! This is not enough however to make this hitting play correct. There is an interesting hybrid hit play that I overlooked, 21/18, 11/8*(2), 10/7 which may well be the best way to hit, but even when trailing, 21/18(2), 10/7 are essential.
I think we are confusing two techniques here. With hindsight and unlimited time we can list the candidate plays and assign to them a win rate and a gammon rate and look at the positions where we might be able to cube. Over the board I don't believe that anybody plays in this way. Over the board in this position and in many others like it you do have to think about what sort of game you want to play and how you intend to go about it. Covering the outfield, so that White has no safe havens and lifting the blot so that White can't hit to help him get home appear to me to be simple and obvious. If this doesn't lead to the best play, that's a pity but we have done the best that we can.
Your play, which leads to a marginal double when White dances (16 rolls) also gives 19 return hits, some of them double hits and all of them gammonish. I couldn't price that up over the board, but I do know it isn't a place that I want to go! This is practically the same as hitting when you have two blosts inboard, sometimes necessary when it is Last Chance Saloon, but not here.
He usually gets lots more shots from here, hopefully at a time when he has a board to contain them.
Thanks again, Paul, for the extra info. I forgot to say in my previous comment that I switched to a money game so as to avoid the confounding effect of the score (which as you discovered can make a significant difference).
I'm not sure that it's true that nobody plays by trying to estimate wins and gammons and subsequent cube actions in complex positions like this one. Stick Rice at least claims to play this way when a critical decision comes up. Increasingly, I find myself trying to memorize reference positions along with estimated wins and gammons so that I have something to work with OTB.
In this particular position, as I mentioned I had recently studied a similar position. Therefore I knew right away that hitting would probably win more games and that I would probably have a cube after a dance, and that the critical question was the tradeoff between wins and lost gammons. I couldn't estimate gammons very well so I just guessed that the tradeoff would be favorable as in the other position. Of course I was wrong, but that just means I now have a new position that I can use to help me estimate more accurately next time OTB.
Obviously, there's no time OTB to think about every position in this way, but it seems to me that when a position like this arises where there's potentially a huge amount of equity at stake, it's worth trying to study the numbers carefully for future reference. I don't feel that I've done "the best I can" unless I make this effort.
Yes, there are a few players who think like this. For every one Stick there are 10,000 honest plodders who simply cannot do what he does. We can try and emulate the plays of the outstanding players who play with a PR rate under 3, but I don't think it is possible for most of us to use the methods that they do, or indeed achieve their results if we did. I think that most of us, me included, need a simpler approach, based largely on eliminating the mistakes that we already know enough not to make!
There are many ways to play well. Finding an approach that works for you as an individual is the first step. Your method wouldn't work for me, mine perhaps not for you.
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