Yes, I know, I am not being consistent at all with what I am posting here based on the stated theme, but part of me is still trying to get a handle on the best way to learn this game, so I am going all over the place. For those few readers I have hopefully you will understand and bear with me, otherwise by blog becomes simply a place for me to try to organize my own study which is okay as well.
Opening Roll Source Material
Most of the information I am using for my study of opening rolls is coming from the opening information at http://www.bgonline.org/., these are often referred to as “Stick’s” rollouts because bgonline is maintained by Stick Rice. Timothy Chow, who comments here frequently, has published a very handy summary of 2nd roll information which can be found at http://www-math.mit.edu/~tchow/2ndmove.shtml. You will also find on Timothy’s page links to information on nactation, a link to a similar summary of opening moves using standard notation, and a link to the opening information on Tom Keith’s Backgammon Galore site. I will not bother to duplicate those links here at the moment.
These charts are very handy, but I am finding that to get a grasp on the material I need more than that, so I am attempting to group and offer some reasoning for the plays in an attempt to more easily learn what to do rather than rely on brute force memorization. I am also trying to get more comfortable with using nactation, so I am using it mixed with traditional notation and simple descriptive text (eg, make the 20pt) below.
There are basically two options for playing the opening 21, slotting (21$, 13/11 6/5) and splitting (21S, 13/11 24/23).
My tendency has been to play 21S except at gammon-go scores where I tended to the slot. The rollouts indicate that 21$ is a slightly better play than 21S. One thing I did find surprising is that according to Stick’s rollouts 21$ is best even at gammon save scores, Keith’s rollouts differ from this but those are cubeless rollouts. However the difference in slot and split at GS in Stick’s rollout is very small, probably not statistically significant.
I have started playing 21$ instead of 21S as my typical 21 opening. I am still struggling with this in a couple of respects, one is mentally dealing with getting hit, especially after a roll of 64 where you end up with two checkers on the bar. More difficult for me at this point is playing my second roll when I am unable to cover the slotted checker. This is an area I need to work on.
Replies to 21$
Hit the slotted checker if possible except with 11. This is pretty easy to remember as it seems quite logical. The only question that remains is what do with the rest of the roll, of course with 31 you don’t have a rest of the roll after hitting.
11: Is the one exception to the hit the slot if you can rule. The best play with 11 is to make your 5 and 7 points. (nactation: N). Hitting here is around a 0.03 error. Without doing a lot of work to try and understand this one it seems that the value of making the 3 prime and having a good shot at a quick 4 prime must outweigh the value of hitting. Still this seems like a less than obvious best play to me.
22: This one can gives me pause OTB as it is very tempting to make the 20pt – given all we hear about the value of doing that, but the best option here (based on Keith’s data and bot evaluations) is to hit the slot and make the 4 point. (nactation: e)
41: Play 24/23 with the second checker, the two other options of slotting the 5 or 7 pts leave too many return shots. (nactation: U)
42: Play the second checker down to the 11 pt, it gives you a builder and can only be hit with 65. (nactation: S)
43: Stick’s rollouts (which for 2nd rolls do not have any at score information) gives a very slight edge to playing 24/21 with the second checker, Keith’s are the same except at GG Keith’s play is down (13/10). This makes sense as you need to contain checkers for the gammon and getting the extra builder down improves you chances of doing this. (U, except at GG S)
44: Pretty easy, make the 20 pt and the 9pt. (B)
54: A very slight edge goes to bringing a checker down to the 8pt (S), running the checker out after the hit ( R) is not far behind although I find it surprising that R is not better at least at GS scores)
64: Easy, run your checker to the 14pt hitting both blots in the process. (K)
Split Against The Slot. At first blush splitting when you cannot hit the slotted checker may not seem the best thing to do since you are giving your opponent two blots to shoot out and the slot gives them more ways to hit. However, some of the hitting plays that present themselves after these splits are not necessarily all that good for your opponent as they either bury checkers, force them off their 5pt, and/or leave good return shots.
32, 51, 52: S
21: Timothy’s chart gives both S and $ as options here, recent extensive 4ply XG rollouts by Neil Kazaross posted on the BGonline forum make it pretty clear that the $ is best, but the difference is still only 0.005 http://www.bgonline.org/forums/webbbs_config.pl?noframes;read=59007
62: Has 3 viable options S (24/18 13/11), Z (13/7 24/22) and N (13/7, 6/4). Running out with a back checker (R) and bringing two down from the midpoint (D) have also gotten consideration. Based on recent rollout data S is best with Z being close and N not totally out of the question. http://www.bgonline.org/forums/webbbs_config.pl?noframes;read=58683
63: Running a checker out (R) is the best play here rather than splitting, and the reverse split (24/22 13/7, Z) is slightly better than the normal split. None of the plays are huge errors (S being about –0.015 worse than R)
Rather Obvious Plays. 53, 55 both make your 3 pt, 65 always runs a checker on the 2nd roll except for against 61P where you can’t, and 66 is forced 61 make your bar point.
And Finally. 33: Make your 5 pt and the 22pt. This play is harder to remember than it seems because in many cases the 2nd 33 is not used to make the 5 pt even though that might seem like the logical play at first glance. My instinct with this play is to make my 5 and 3 pt because having two home board points seems like such a good idea. But that is behind the best play and the more typical 33 second roll play of making the 22 and the 10 (B).
Replies to 21S
Play Like First Roll. Many of the replies to 21S are played liked the first roll—or at least like of the main options for the first roll. These are:
31P, 51S, 61P, 32S, 42P, 52S, 54S, 62S, 63S (or 63R), 65R
21: Playing 24/21 (21U) has a very slight edge over 21S, but both are viable plays.
41K: Hit both blots in your home board.
53P or 53S: 53P gets an extremely small edge, but splitting is very close which is why I put it here rather than in the play like first roll group.
64H: Hit the checker on the 15 with 24/15
11e (6/5(2),24/22) – Against the slot 11 is played as N, but with the split playing N gives shots with 6s and 7s, so this requires a safer play
22N, make the 4 and 11 points.
33B, make the 21 and 10 points.
44B, make the 20 and 9 points.
33 and 44 are both difficult for me to keep in mind because I have to fight the desire to make the 5 point with them. Of course with 44 this is moving two from the 13, with 33 you still have 2 3s to play. While making the 5pt with a 33 on the second roll is right at times, making it with a 2nd roll 44 is almost never right.
55A, Hit on the 1 and make the 3, giving you a good start on a blitz.
66B Same thing for 66 on all 2nd rolls except after 61P, where you can’t, B with a 66 makes both bar points.
One thought on “Opening 21”
One thing that may help you remember how to play 22 is that making your own 4-point with a second-roll 22 is almost always right. This is for money-play; at GS, making the 5-point anchor is almost always right. An advanced anchor is usually the best insurance against getting gammoned. Thus, for 21$-54 at GS, keeping the 5-point anchor slotted is better than continuing to run. Running tends to be better at DMP.
Given the title of this blog, you should note that 21$-62 is discussed at length in Trice’s book. I don’t have the book on me at the moment so I’m not sure what page it’s on, but I think it’s in the section on duplication. Trice remarks that 13/7 6/4 was very popular for a while because it exploited the duplication of 3’s and 6’s. The bots have changed their minds several times over the years and may continue to do so in the future, but eXtreme Gammon, the reigning champion, seems to agree with Trice’s recommendation of 24/18 13/11.
Regarding 21$-21, I would still list both $ and S if the difference is only 0.005. On Stick’s forum it is regularly debated whether a difference of 0.005 should be believed. Nack Ballard and Paul Weaver consider plays whose equities differ by 0.010 or less to be “tied.” David Rockwell thinks that 0.005 is meaningful. The trouble with reading too much into a difference of 0.005 is that one can easily imagine bot misplays causing systematic errors of more than 0.005. For example, suppose Play A leads to a backgame 3% of the time and Play B leads to a backgame 8% of the time, and suppose that on average the bot loses a total of 0.100 equity in the course of playing a backgame. That’s 0.005 systematic error right there. My opinion is that, while 0.005 shouldn’t be completely ignored, it shouldn’t be taken too seriously either, and that other considerations are likely to be more important (such as whether the play is likely to lead to positions where you or your opponent are likely to make mistakes).