Neil Kazaross vs Bob Zavoral Annotated Match
Michigan BMAB 2022
Again, I just want to say thanks to Roberto and Dmitriy for organizing this BMAB. Their efforts make it possible for me to spend all this time on this series of annotated matches.
Bob Zavoral is obviously synonymous with leather backgammon boards and Neil Kazaross is a Giant of the game, so this seemed like a match worth reviewing. After the additional rollouts and analysis I performed, Kazaross had played a 2.34 PR and Zavarol a 5.74. It should be noted that, in selecting this particular match, I’ve selected Bob Zavoral’s worst match of the Michigan BMAB. His PR’s in the other 4 matches were 0.92, 2.84, 2.96 & 4.42. An excellent run of play.
One point for the format below, if I am not going to spend much time elaborating (pontificating) on a particular position, there will be splits next to the position showing Blue’s wins, Blue’s gammons and Red’s gammons after the roll. I decided to keep the player to whom the winning odds applied fixed throughout for ease of tracking the changes. Kazaross is Blue (bottom) and Zavoral is Red (top) and I will provide an indication of the quality of the analysis after the split (Rollout & # of games, ++, +, etc.). Here we go:
Game 1 - Kazaross 7 Away Zavoral 7 Away
Blue rolls 61 - 13/7, 8/7 (53.6%/16.0%/12.7% - Rollout of 10,368 games)
Red rolls 66 - 13/7 (2), 8/2 (2) (53.6%/16.3%/15.8% - Rollout of 10,368 games)
I like this play, not because it is particularly tricky or anything like that, but because I like the gammon values of 13/7 (4). At 2 Away 4 Away, Red would be correct to bring 4 down from the mid, leaving a blot on the second roll of the game. Somehow, that results in fewer gammons than a play that makes an extra point in the innerboard and leaves an indirect shot. That, to me, is counterintuitive at first glance. And I get how it works that the gammons are lower, but it still seems worth noting. Moving on.
Blue rolls 52 - 24/17* (57.2%/13.8%/13.3% - ++) Kazaross hits and claims an early advantage,
Red rolls 54
I thought it worth giving anyone reading this a look at one without an indication of the correct play (aside from what is in their own head), as this looks a bit like something that might come up in one of those “hit or anchor” quizzes. If it were a quiz, you might go down a checklist in your head of anchor vs hit factors. First, does Red have a particularly strong board? Not really with the seven and deuce points made and the lack of connectivity between them and the mountain on the 6. Second, does Blue have a strong board? Not really, but it’s better positioned than Red’s, since it has a “purer” setup. Third, is the point you’re hitting worthwhile? Blue isn’t losing much ground and slotting the 8 isn’t particularly additive to Red’s plan. All that strikes me as a combination that shouts “Anchor”. Of course, I get to look at this from the comfort of a couch, not over a board with a clock ticking an an opponent on the other side of the board. Much easier.
Red rolls 54 - Bar/21, 13/8* (54.6%/15.5%/16.3% - Rollout of 1,296)
Blue rolls 52 - Bar/20, 6/4* (54.6%/15.7%/17.6% - ++) - Kazaross throws 52 for the 2nd straight roll and enters on the 5 points while also hitting Red’s blot on the other side of the board. Kazaross’ advantage is tenuously perched for the moment.
Red rolls 42 - Bar/21*, 7/5* (51.1%/14.4%/21.5% - ++) - Zavoral enters with a hit and hits on the other side of the board for a double hit and his gammons reflect the opportunity.
Blue rolls 53 - Bar/22, Bar/20* (61.2%/19.3%/11.6% - ++) - Forced play for Kazaross, but an excellent roll.
Red rolls 11 - Bar/24, 8/7, 6/5* (2) (49.9%/13.3%/18.1% - ++) - Speaking of excellent rolls! Zavoral responds with one of only two rolls which leaves him has a favorite (33 being the other). He enters, makes the Bar, makes the 5 points and buts Blue on the Bar in the process.
Blue rolls 51 - Bar/24, 13/8 (46.9%/13.6%/19.9% - Rollout of 2,596 games) - A rollout was required simply to determine the difference between the play Kazaross made, which is the preferred play, and the 2nd best play, which is to exit the front checker from the back (22/17). The problem with the 2nd play is the lack of connectivity leaves two checkers stranded in the back.
Red rolls 62 - 24/16 (47.9%/15.0%/19.3% - Rollout of 5,184 games) - Zavoral’s play is the 2nd best play, with 24/22, 21/15 being the preferred play. Zavoral’s play is high on duplication and connectivity, which gives it a ton of merit, but it also leaves checkers in places that play into Blue’s preferred gameplan, which is priming. The deeper Blue has to hit if it wants to attack Red’s blots in the inner board, the worse for Blue’s priming gameplan.
Blue rolls 66 -22/4*, 13/7 (43.3%/13.0%/20.2% - ++) - Just when it seemed this game would settle into a mid-game…. Kazaross throws 66 and thrusts it directly back into a high-volatility hitting game.
Red rolls 32 -Bar/23, 24/21* (40.0%/10.4%/21.4% - ++) - Red enters from the Bar and hits right back, but leaves four blots spread out in the process. With a checker on the Bar, Blue’s weak inner board and Red’s structural strength still gives Red the distinct upper hand.
Blue rolls 53 -Bar/17 (40.8%/10.6%/21.9% - ++) - Kazaross enters from the Bar and exits into the outfield.
Red rolls 63 -24/21, 16/10 (43.7%/10.6%/19.7% - ++) - Zavoral is unable to hit that blot and Kazaross’s winning chances get a boost. The anchor is obvious, and then the 6 comes naturally.
Blue rolls 63 -24/15* (51.1%/13.2%/19.0% - ++) - Blue gets a shot from the back and once again the game swings back to hitting for a moment.
Red rolls 41 - Bar/21, 23/22 (53.1%/12.5%/15.7% - Rollout of 5,184 games) - Zavoral enters, but fails to hit, which makes this a disappointing roll. His play is the preferred play in makes a subtle choice, which is an important one for Red.
Red plays 23/22 after entering, rather than 6/5. Inching forward in the back may make Red a more attractive target for Blue’s many spares that have accumulated from the 8 to 6 points, but it also allows for that checker to escape and gives Red a greater possibility of hitting an outfield shot (or exiting) on a future roll, if one avails itself.
Blue rolls 31 - 17/14, 15/14 (54.1%/11.3%/13.7% - Rollout of 5,184 games) - Kazaross makes the second best play in this situation and it provides a couple interesting variants. Here is the play Kazaross makes in the match with Zavoral:
The preferred play is to make the 5 point and there are two important factors involved. One, Zavoral is stripped at the mid-point. It’s hard to over-state the importance of this. Any other play, but Kazaross’, becomes a Blunder if we take the spare from Red’s 21 point and put it on their mid-point.
Red rolls 43 - 7/3, 6/3 (61.0%/14.2%/11.9% - Rollout of 5,184 games) - Zavoral blunders (-.098) here as he decides to make the 3 point (exposing a blot on the Bar point in the process) rather than bring two down from the mid-point. While losing the mid-point is not ideal, the gameplan for Red has turned to containing that lone checker in the back and providing Blue this shot/exit combination does not fit neatly into that gameplan even though it gives Red upside when Blue doesn’t roll a 6.
Blue rolls 61 - 24/18*, 18/17 (64.4%/14.8%/9.0% - ++) - Blue responds with a 6 and really tilts the scales towards its side.
Red rolls 65 - Bar/20, 22/16 (67.2%/12.6%/7.3% - ++) - Red responds with a 65 and is forced to enter on the 5 point. The question is then where Zavoral should play his 6 and he opts for 22/16 (-.060), though 21/15 is preferred. It seems to me that the point of playing 21/15 is to maximize contact. If you manipulate the position by putting Blue’s back check all the way back on the 24 point and by giving Blue spares on the mid-point (and consequently removing the “second” mid-point) 22/16 becomes much more viable, though still 2nd best (-.014). Because Blue is so likely to expose checkers and its primary threat to Red is clustered around its own Bar point, Red should play for contact and perhaps control of the outfield. If anyone is reading this and wants to chime in on the reasoning, do it in the comments.
Blue rolls 11 - 8/5*, 6/5 (72.8%/16.4%/5.5% - Rollout of 5,184 games) - Kazaross makes the 5 point a very fine roll.
Red rolls 32 - Bar/23, 16/13 (74.8%/11.6%/4.4% - Rollout of 2,592 games) - Red enters on the 23 point and safeties its blot.
Blue Cube Decision - Blue Doubles. No Double -.071 Error
Red Take Decision - Double/Take. Double/Pass is +.009 Error after 5,184 game Rollout
This is a borderline Take/Pass position for Red, but Zavoral correctly finds the Take. Red is down 21 pips (157 to 136) and has the liabilities of a blot on the two point and an “impure” innerboard that may be tricky to fill. Still a 4 point board is strong and Blue’s points are stripped, plus that checker on the two point can be a bother to Blue even though it can be a liability to Red. Given that, on the next roll, Blue rates to safety their blot and give themselves a spare with all 3s & 4s except 43 (18 rolls) as well as 21, 65, 66, 11 and 22 (7 rolls). Then you have 61, 51, 52 and 62, which give Red an indirect shot, while clearing the blot from the outfield and 55 which is a very good roll while still leaving a blot in the outfield. 43 is really a weak roll for Blue. That means that 11 numbers leave a shot of some sort on the next roll and it there are some weaker safetying numbers that could potentially be misplayed. All in all, the near term opportunities are good enough that Red can decided to stick around knowing there may be opportunities later on as well.
Blue rolls 54 -17/8 (75.8%/10.7%/3.4% - Rollout of 2,592 games) - Little thought should be given to hitting here. For one thing, Blue has a nice race lead and wants to safety its checker. For another, there is no need to give Red an opportunity to re-enter on the ace point where he can be a much larger hassle to Blue as he bears in. I’ve looked at similar plays in this post.
Red rolls 51 - 23/22, 21/16 (73.9%/14.4%/4.2% - Rollout of 10,368 games) - Zavoral picks the 2nd best play here by a very slight margin (-.004), by playing a spare out into the outfield and stepping a checker from the 23 up to the 22. The preferred play is to leave that back blot alone and play 21/1. How close the plays is a testament t how weak the “2 point goalkeeper” game really is and how Red is already nearly better off abandoning it entirely rather than risking additional gammons. Regardless of the step-up, the critical element is coming out with the 5, not play 13/8. Red wants contact and this is how to invite it.
Blue rolls 62 - 8/2, 7/5 (70.6%/11.2%/5.5% - Rollout of 5,184 games) - Blue misses the shot and plays safely.
Red rolls 32 -13/8 (70.3%/18.1%/7.1% - Rollout of 10,368 games) - Zavoral fails to clear his blot, so he simply plays 13/8 and waits for more contact.
Blue rolls 66 - 14/8 (2), 13/7 (2) (83.5%/17.8%/1.1% - ++) - Red was expecting to lose this game at this juncture, but that gives Blue an overwhelming lead as Kazaross clears the two mid-points one one roll.
Red rolls 32 - 13/10, 8/6 (83.3%/20.2%/1.0% - ++)
Blue rolls 66 - 8/2 (2), 7/1 (2) (85.2%/28.9%/1.0% - ++) - Kazaross keeps the party rolling with another set of 66s.
Red rolls 61 -22/15 (89.4%/18.5%/0.5% - ++) - Zavoral extricates his blot from the back quadrant, leaving just an anchor on the 4 point. Zacoral is in good shape with a 70 pip lead at this point!
Blue rolls 44 - 7/3 (2), 6/2, 5/1 (81.4%/22.0%/1.7% - ++) - Kazaross throws his 2nd worst number and has to make an awkward play. Nevertheless, his gammons go up as he gains further in the race.
Red rolls 51 -16/11 (82.4%/24.4%/1.7% - ++)
Blue rolls 11 - 8/6 (2) (92.8%/23.5%/0.0% - ++) - Kazaross throws his fourth consecutive set of doubles which bring him into the homeboard without issue.
Red rolls 66 -15/9, 12/6, 11/5, 10/4 (93.4%/4.6%/0.0% - Rollout of 10,368 games) - Zavoral throws big doubles which eliminates almost all of Blue’s remaining gammons.
Blue rolls 65 - 6/1, 6/Off (93.7%/4.5%/0.0% - ++)
Red rolls 32 -9/4 (93.6%/5.9%/0.0% - Rollout of 5,184 games) - Zavoral fills his board and waits to see if he gets lucky.
Blue rolls 53 - 6/3, 6/1 (95.3%/3.0%/0.0% - ++) - Kazaross has one more point to clear and then its just a question of whether he can pull off a miracle Gammon.
Red rolls 21 -21/18 (95.2%/6.6%/0.0% - Rollout of 5,184 games) - This is the preferred play by .014.
Blue rolls 32 - 5/3, 5/2 (100.0%/2.1%/0.0% - ++) - Kazaross clears the 5 point and ensures victory.
Red rolls 64 - 21/17, 18/12 (100.0%/0.7%/0.0% - ++)
Blue rolls 11 - 1/Off (4) (100.0%/1.9%/0.0% - ++)
Red rolls 64 - 17/15, 12/6 (100.0%/0.9%/0.0% - ++)
Blue rolls 33 - 3/Off (4) (100.0%/4.5%/0.0% - ++)
Red rolls 42 - 15/9 (100.0%/7.9%/0.0% - ++)
Blue rolls 55 - 2/Off (4) (100.0%/30.6%/0.0% - ++) - Oh man! Is Kazaross going to do it! From less than 1% gammons 5 rolls ago to this.
Red rolls 62- 9/3, 2/Off (100.0%/0.0%/0.0% - ++) - Nope. No Miracle here.
Blue rolls 21- 2/Off, 1/Off (100.0%/0.0%/0.0% - ++)
Game 2 - Kazaross 5 Away Zavoral 7 Away
Red rolls 43 - 24/21, 13/9 (49.9%/13.9%/14.4% - Rollout of 31,104 games) - Zavoral actually makes the second best play, which is the result of the match score. Instead, he should be playing 2 down, 13/10, 13/9. However, the equity “lost” is .011, so doubt anyone is losing sleep over this.
Blue rolls 32 -13/10, 6/4* (48.1%/14.0%/16.9% - Rollout of 10,368 games) - 24/21, 6/4* is the preferred play by a thin margin (.008), while the double hit is well off and not a true candidate play in this scenario.
Red rolls 33 - Bar/22, 24/21*, 21/15* (39.2%/8.1%/23.1% - ++)
Note that Red’s raw wins are roughly 60% after this checker play that sends a 3rd and 4th checker back, while also semi-escaping one of its back checkers. It’s well below the 70% we might expect after both checkers are escaped and Red has establish a 10% pip lead, mostly because Red hasn’t yet escaped its checkers and it hasn’t established any inner board points or any outfield points.
Blue rolls 32 -Bar/23, Bar/22 (39.4%/8.2%/22.7% - ++) - Forced.
Red rolls 61 -22/21, 15/9 (39.4%/8.1%/20.4% - ++) - There might be some temptation amongst certain players to play the double hit (9/3*, 3/2*), but it would be wrong because of what Red has the opportunity to do. With the preferred play, Red makes an outfield point, thus fully escaping a checker, and pushes the other back checker up to prepare for its escape in the future. Given Red’s 41 pip lead prior to the checker play, this gameplan makes far more sense then the uber-agressive double hit or even making the 15 point, which is the 2nd best play, but still a Blunder.
Blue rolls 53 - 8/3, 6/3 (36.6%/7.9%/22.6% - Rollout of 5,184 games) - Kazaross makes the 3 point, though slotting the 5 point (13/5) is close (-.031) and is preferred if Blue has a 3 and 1 point multiple anchor game and (narrowly) if Blue has an anchor on the 3 point and blots on the deuce and the ace points.
Red rolls 52 -21/14 (37.3%/7.8%/17.7% - ++) - Zavoral continues his attempt to escape his back checker, but doesn’t make it all the way to the mid-point.
Blue rolls 65 -24/18, 23/18 (35.3%/6.6%/18.2% - ++) - Kazaross anchors and its easy to see why Zavoral’s winning chances are short of where they would be in a traditional holding game with such a large pip lead (36 pips after the checker play). Zavoral is lacking any innerboard points and still has to safety the blot on the 14 point.
Red rolls 51 - 14/8 (36.6%/6.9%/14.9% - ++) - Zavoral safeties his checker. Now, his focus will turn to making an innerboard point. Unfortunately, 31s, 42s, 53s, 64s and doubles don’t grow on trees, so he may be forced to take some risks.
Blue rolls 33 -13/10 (2), 8/5 (2) (39.0%/9.3%/15.0% - Rollout of 5,184 games) - Kazaross super-charges his board with 33s, making Zavoral’s ability to build his own board that much more difficult. Any risk Zavoral might consider taking must now be informed by the much improved strength of Kazaross’ board.
Red rolls 41 - 13/8 (39.9%/8.9%/11.9% - ++) - The 2nd and 3rd plays, both of which are Blunders, are 6/1* and 9/5, 6/5. Importantly, 9/5, 6/5 would be the preferred play if Blue had rolled a lesser number previously and had a much less impressive board. For example, had Blue rolled 41 and played 13/9, 6/5, this 41 from Red would demand a play of 9/5, 6/5.
Blue rolls 33 -10/4 (2) (41.7%/10.7%/12.0% - ++) - Kazaross fills in his 4 point, further strengthening his board and making Zavoral increasingly desperate for one of those point-making rolls.
Red rolls 52 - 13/6 (42.9%/11.4%/10.1% - ++) - Zavoral makes the risk-free play, simply biding his time. That said, with his mid-point now stripped, the 9 point stripped and mountains on the 8 and 6 points, things are getting hairy.
Blue rolls 42 - 13/11, 13/9 (42.6%/12.5%/11.6% - Rollout of 5,184 games) - Kazaross clears his mid-point, though that is the 3rd best play by a very small margin (-.008). The preferred play is 22/18, 13/11.
Given Zavoral’s lack of flexibility, anchoring on 22 point really isn’t a candidate play as that would open up a whole host of rolls that would otherwise be obviously unwelcome for Zavoral.
Red rolls 44 - 13/9 (2), 8/4 (2) (24.4%/2.4%/12.0% - Rollout of 3,790 games) - Zavoral gets what he needs…finally. Red clears the mid-point and makes an inner-board point while unstacking the mountainous 8 point. 55 & 33 are the only rolls that are better or comparable, respectively.
Blue rolls 42 -24/22, 11/7 (25.0%/1.8%/5.6% - ++) - Kazaross anchors and slots the back of the prime.
Red Cube Decision - No Double
The race is 104 Red to 138 for Blue prior to the roll and Red has 9 rolls which will makes it 5 point, improving its ease of bear-in markedly and likely leading to a Pass on the next roll if the Cube is not turned now. Additionally, Red has a good deal of time to roll these numbers because all its spares and its ability to play behind Blue’s 3 point anchor. Rolls like 63 and 64 will shorten that timeline, but many other rolls simply end up with spare Red checkers on the 1 and 2 points. On the other side of the board, Blue has just two crossovers left until a 6 will force it to break one of its anchors, so there are sequences where Red rolls nothing special on its immediate roll, but ends up in a better position because Blue moves so quickly.
So, does Blue have enough wins to Take this Double and how might it reason that over the board? The most common variant in which Blue snatches a win likely features Red sending checkers deep on consecutive rolls and Blue managing to maintain both anchor. If we consider the 27 rolls that don’t make the 5 point for Red to be likely to send checkers deep then we can estimate that roughly 60% of the time Red is going to end up sending checkers deep twice. I round it up from 9/16 because when Red rolls certain numbers, like 66 or 55, it loses certain numbers which previously made the 5 point. Then we can see that, between its 3 spare checkers Blue has 19 combined pips to use before it must break an anchor. That means it can play 26 of 36 roll twice. So, 60% of the time Red will send checkers deep twice and 52% of the time Blue will play a couple rolls without having to break an anchor. That means the two variants will happen together roughly a third of the time. This is a bit too much for me to try and wrap my brain around, particularly over the board and it would just come down to pattern recognition and accounting for match score. The most common variants see Red either making the 5 point over the next two rolls and having a much easier time clearing past Blue’s bar point anchor or Blue breaking an anchor or cracking its innerboard, making the multiple anchor game much weaker.
Essentially, this may come down to a scenario where one is bearing in against a multiple anchor game and would often be waiting for an anchor to break, but that the likelihood of occurrence of a good thing (making the 5 point) happening for the player bearing in or a bad thing (losing an anchor or cracking the homeboard) for the player playing the multiple anchor game is so high over the next few rolls that one can feel confident in passing the Cube prior to an anchor being broken. With that framework in mind, it is the match score that pushes this towards the epitome of borderline Take/Pass for Kazaross.
Red rolls 32 - 9/4 (24.8%/2.0%/4.2% - Rollout of 1,296 games) - Zavoral does not Double, so we did not get a chance to see what decision Kazaross might have made. However, Zavoral throws a pretty nice roll, which improve his distribution.
Blue rolls 61 - 9/2 (24.9%/2.1%/4.3% - Rollout of 1,296 games)
Red Cube Decision - No Double
Zavoral decides not to Double once again, though it is important to note that this position is less favorable for Red, so if he did not think the last position amounted to a Double than it adds that he would not consider this a Double. The change in wins gives us an idea about the important aspect of this position, which is the ability for each player to hold its position longer than the other.
Red rolls 52 - 6/4, 6/1 (26.8%/2.4%/3.4% - Rollout of 1,296 games) - Zavoral unfortunately selects the 3rd best play, though the mistake is narrow. The preferred play is 9/2 and the 6/4, 6/1 play is a -.031 error.
Blue rolls 52 - 7/2, 6/4 (26.8%/2.3%/4.1% - Rollout of 1,296 games) - The rollout tells us that Kazaross should break his 18 point anchor by playing 18/11. It doesn’t add many rolls that wouldn’t be market losers for Red anyways, it brings in the possibility of misplays and it provides Red additional flexibility on the next roll.
Red Cube Decision - No Double
Again, Zavoral decides not to Double Kazaross and, again, we can note that the position has improved for Kazaross since Zavoral’s last Cube decision.
Red rolls 54 - 9/4, 6/2 (31.0%/2.7%/3.4% - ++)
Blue rolls 42 - 18/12 (31.4%/2.8%/3.2% - Rollout of 1,296 games)
Red Cube Decision - Double/Take
Zavoral finally pulls the trigger and passes the cube to Kazaross who Takes. Zavoral seems to have been waiting for Kazaross to break one of his anchors. Paradoxically, this position, of the past four cube decision positions for Zavoral, is the weakest. The breaking of the 18 point does not help Red much since there is only one roll (11) that allows Red to hit and cover its inner-board blots.
We see that a position which will have many opportunities to roll at a specific market loser (in this case making the 5 point) will likely see its winning odds decline with each passing failed attempt, so long as its opponent retains its strength. This is the general idea that I was trying to get at in my length (long-winded?) write-up of the first Cube Decision in this series for Zavoral.
The irony, of course, is that this position is “technically” not a Double at this match score. This position, however, is a borderline No/Double/Double.
Red rolls 64 - 6/2, 6/2 (37.4%/5.1%/2.7% - ++) - After this roll, with all points stripped, Red is quite likely to volunteer a direct in the near future.
Blue rolls 21 - 12/9 (37.6%/5.5%/4.7% - Rollout of 2,148 games)
Red rolls 41 - 9/8, 9/5 (47.9%/6.2%/3.0% - ++)
Blue rolls 54 - 18/13, 9/5 (32.5%/3.6%/2.8% - ++) - Kazaross extricates its blot from the 18 point.
Red rolls 42 - 8/6, 5/1 (24.7%/1.2%/2.6% - ++) - Zavoral picks up his blots bit playing 5/1 and moved a checker onto the 6 point by playing 8/6.
Blue rolls 64 - 13/7, 5/1 (24.7%/1.2%/2.1% - ++)
Red rolls 61 - 8/7, 8/2 (36.3%/1.5%/2.6% - ++) - Zavoral throws a bad number and gives Kazaross another shot.
Blue rolls 33 - 7/1, 6/3 (2) (8.0%/0.0%/2.8% - ++) - Kazaross misses and cracks his board in the process. Tough roll.
Red rolls 32 - 7/4, 2/Off (6.7%/0.0%/2.5% - ++)
Blue rolls 11 - 4/1, 3/2 (6.3%/0.0%/5.2% - ++)
Red rolls 54 - 6/1, 4/Off (6.3%/0.0%/4.1% - ++)
Blue rolls 31 - 5/4, 5/2 (4.6%/0.0%/9.2% - ++) - Kazaross clears the 5 point and his homeboard gets worse, as he cannot escape a back checker. An unlucky roll.
Red rolls 21- 2/Off, 1/Off (2.9%/0.0%/9.8% - ++)
Blue rolls 64 - 22/12 (3.1%/0.0%/5.5% - ++)
Red rolls 61- 6/5, 6/1 (11.4%/0.0%/0.9% - ++) - Zavoral with a poor roll that breathes some life back in to Kazaross. Zavoral opts for the 2nd best play here, witht the preferred being 6/Off.
Blue rolls 66 - 22/4, 12/6 (5.2%/0.0%/0.0% - ++) - Kazaross misses and that all she wrote.
Red rolls 21 -2/Off, 1/Off (7.4%/0.0%/0.0% - ++)
Blue rolls 21 -2/Off, 1/Off (4.6%/0.0%/0.0% - ++)
Red rolls 53 -5/2, 4/Off (5.5%/0.0%/0.0% - ++)
Blue rolls 63 -6/Off, 3/Off (4.2%/0.0%/0.0% - ++)
Red rolls 54 -4/Off (2) (2.3%/0.0%/0.0% - ++)
Blue rolls 42 -4/Off, 2/Off (1.2%/0.0%/0.0% - ++)
Red rolls 41 - 4/Off, 1/Off (0.8%/0.0%/0.0% - ++)
Blue rolls 53 - 4/Off, 3/Off (0.3%/0.0%/0.0% - ++)
Red rolls 65 - 4/Off, 2/Off (0.0%/0.0%/0.0% - ++)
Blue Resigns the Game
Game 3 - Kazaross 5 Away Zavoral 5 Away
Blue rolls 62 - 24/18, 13/11 (50.7%/13.4%/14.1% - Rollout of 46,656 games)
Red rolls 65 - 13/7*, 6/1* (50.0%/13.5%/15.7% - ++) - Zavoral opts for the double hit, which is the obvious best play.
Blue rolls 62 - Bar/23 (44.6%/11.2%/21.4% - ++) - Forced
Red rolls 54 - 7/2*, 6/2 (47.0%/12.8%/21.3% - Rollout of 1,144 games) - The only other candidate play was to cover the blot on the ace point and split in the back, but that is roughly a -.015 error.
Blue rolls 62 - Bar/23 (42.0%/10.3%/26.1% - ++) - Forced
Red rolls 55 - 13/3, 8/3, 6/1 (35.5%/7.9%/34.1% - ++) - Zavoral’s onslaught on his offensive side of the board continues. The weakness to his game is that his back checkers remain unsplit.
Blue rolls 42 - Bar/21, 13/11 (38.3%/8.8%/34.0% - ++) - Entry is forced and the 2 is straight forward.
Red Cube Decision - No Double
Zavoral had an opportunity to apply a framework for unsplit doubles, which I’ve written about before. Typically, in passing one of these doubles, you want to see an innerboard point advantage of two points and have blots to aim at to continue an attack. Here, adjustments must be made, as the innerboard point advantage is 3 points and both blots that are available for attack are in the innerboard. Still, the extra innerboard point makes any attack particularly dangerous and Red has 26 numbers that hit at least one blot (5 of which hit two checkers).
This framework, which I discuss in this piece detailing a match between John O’Hagan and Kit Woolsey, is pretty effective for evaluating this position.
Red rolls 54 - 13/4* (39.0%/9.2%/33.1% - ++) - Red hits from the mid-point and hopes Blue dances.
Blue rolls 53 - Bar/20, 13/10 (47.4%/10.8%/16.8% - ++) - Kazaross anchors and can now turn his attention to priming Red’s unsplit checkers.
Red rolls 51 - 24/18 (50.8%/12.7%/14.7% - ++) - Red splits and waits to see what will happen next. The balance of odds have changed as this game has become a veritable coin-flip over the last few rolls.
Blue rolls 61 - 13/7*, 8/7 (51.1%/12.8%/17.8% - ++) - Kazaross make his Bar point, but breaks and exposes a blot on his mid-point in order to do so.
Red rolls 65 - Bar/20,13/7 (63.8%/19.7%/12.3% - ++) - An unfortunate roll for Zavoral, who enters but is forced to open up a blot on the other side of the board and to send a checker deep into is homeboard.
Blue rolls 55 - 20/5*, 10/5 (70.3%/20.5%/8.5% - ++) - Kazaross with an excellent throw from the Bar to hit and make the Bar. He leaves behind a checker in the back, but his game is looking promising from here.
Red rolls 11 - Bar/24,13/12*, 6/5*, 5/4 (52.4%/14.9%/23.2% - ++) - An excellent roll for Zavoral turns things around significantly. He puts two on the Bar, but leaves a blot on the 6 point to do so. Blue’s structure is now far superior and the next roll will tell us a good deal about the direction this game is headed.
Blue rolls 32 - Cannot Move (39.1%/8.4%/33.7% - ++) - Kazaross dances and it’s Zavoral’s turn.
Red Cube Decision - Double/Pass - Once again, we could use the framework we discussed earlier, but this game is a bit further along and I think we are better of looking at market losers and most common variants.
There are 26 rolls that make the 6 point, though some (66) are weaker than the rest. The remaining 10 rolls put Red in some questions positions, so Blue can think of things this way: 30% of the time Red is going to have a fairly tough time with its board; it will be fragile and unlikely to improve upon its innerboard. The other 70% of the time they will improve upon their homeboard to create a 5 point board, typically a death sentence when once has two checkers on the board, but Red has to get itself around Blue’s 4 point prime, which may not be the easiest task in the world. Between those two variants, I’d be inclined to Take this double, particularly at Money, but even at this match score. That’s easy to say when you’re running roll-outs on the positions leading up to the position and we can all understand how scary this position would seem over the board.
Of course, Kazaross Passed and the two players moved on to the next game.
Game 4 - Kazaross 5 Away Zavoral 4 Away
Blue rolls 51 - 24/23, 13/8 (50.1%/13.9%/13.6% - Rollout of 46,656 games)
Red rolls 52 - 24/22, 13/8 (52.7%/14.8%/11.8% - Rollout of 5,184 games) - Zavoral splits in the back and brings an additional spare onto the 8 point.
Blue rolls 33 - 8/5 (2), 6/3* (2) (65.6%/25.8%/7.3% - ++) - Kazaross throws 33s and goers on the attack.
Red rolls 22 - Bar/23, 8/4, 6/4 (59.3%/23.1%/11.3% - Rollout of 10,368 games) - Zavoral’s play is actually second best and it would be preferable to step-up to the 21 point, while making the 4 point on the other side of the board (Bar/21, 6/4 (2)).
Blue rolls 41 - 6/2*, 2/1* (55.9%/23.9%/12.5% - ++) - Kazaross continues the attack with a double hit. All other plays are blunders.
Red rolls 65 - Cannot Move (63.2%/34.0%/9.6% - ++) - Zavoral dances.
Blue Cube Decision - Double/Pass
Here is a very nice instance of match score impacting what would normally be a Take. The reason the position is a Take at Money or normal scores is because though gammons are high, gammon values are their normal 0.5 and wins aren’t all that high. Here, at 5 Away 4 Away (Blue trailing), gammon values are elevated, which means that the gammon value adjustment will be much greater than it will be at Money. As a result of that larger adjustment, Red must know, over the board, that this isn’t such an easy decision.
In order to determine whether it’s a Pass or perhaps a Take, we can go one of two routes. First, we can put some estimates to wins and gammons and, if we are fairly confident, can make a decision based off that process. This requires knowing the gammon values and, at least roughly, the take points. Second, Red can walk through a most common variant analysis and look at Blue’s rolls that are immediately detrimental.
For the second option, Blue has 9 rolls that could make the ace point and another that makes the 4 point (22), which gives it 10 rolls that are fairly damning for Red on the immediate roll. Blue has then has 13 rolls that are above average in size that will bring checkers around the board to support the attack and put it in good position to continue the attack in most instances on the following roll. Finally, there are 13 rolls that are small and require a bit more luck in order to sustain the attack. Looking at the 26 rolls that don’t make a new point in the innerboard, there are 13 responding rolls by Red (All 1s, 44, & 22) that hit or anchor and 9 rolls that dance entirely. When Red dances after those 26 rolls, it’s worse off than it is now. That makes for 6.5 games out of 36 (26 * 9/36). There are also 12 rolls which enter one checker and which will require Red to roll again to enter regardless of what Blue does on the following roll. That means that you have another 2 games out of 36 in which Red is in particularly bad spot. Since we are already at 18.5 games out of 36 games that are quite bad for Red, it stands to reason that, with elevated gammons at play, there might not be enough upside in the remaining games to warrant a take.
Personally, I prefer the estimates for a position such as this where I think it’s possible to be pretty close.
Kazaross Doubles and Zavoral Passes.
Game 5 - Kazaross 4 Away Zavoral 4 Away
Blue rolls 63 - 24/18, 13/10 (50.5%/13.5%/14.0% - Rollout of 46,656 games)
Red rolls 62 - 24/22, 13/7* (50.5%/13.5%/14.0% - Rollout of 1,828 games) - Zavoral responds by hitting and splitting.
Blue rolls 55 - Bar/20, 8/3* (2), 6/1* (58.3%/25.6%/10.8% - ++) - Kazaross rolls 55s from the Bar to go on the attack.
Red rolls 51 - Bar/20, Bar/24* (50.9%/15.6%/14.1% - ++) - Forced. Zavoral enters both checkers and hits back, a pretty good roll all things considered.
Blue rolls 43 - Bar/18* (50.0%/14.7%/14.4% - ++) - The hitting game continues with another hit from the Bar.
Red rolls 54 - Bar/20, 24/20 (50.0%/9.1%/11.6% - Rollout of 1,969 games) - Zavoral opts to anchor and give his anchor a spare rather than continue the hitting sequence. After the play, Zavoral trails by just 4 pips, so the thinking will go that Blue has so many blots to clean up that this play puts the onus on him to do so and that Red can attack those blots with spare checkers on all its points on the next roll. All those spares are what make the play close because normally the combination of trailing in the race and an inferior board would be a good reason to choose the more aggressive play. Still, Zavoral’s play is -.021 error. The issue with it is that is consigns Zavoral to a likely mutual holding game when there is a much higher upside play available. When Red hits it is making it very likely that Red will anchor on the following play, but has the possibility of escaping a checker on the following roll. All of this with a race lead.
Blue rolls 64 - 10/4, 8/4 (48.9%/10.8%/13.0% - Rollout of 2,381 games) - Kazaross opts to make his 4 point behind Zavoral’s anchor to make any loose hit Zavoral may consider in the future a bit more dangerous. Unfortunately, he underappreciates that Red will double hit with almost everything that doesn’t make a new point and some of the numbers that don’t (52 & 43) do escape a checker from the back. Kazaross’ play really leaves Red dreading 32 and 54, but perfectly happy with 63, 62, 54, 21, 41 and even 51.
Kazaross should instead secure his own anchor and slot his 4 point, once again proving Michi’s axiom, as detailed in Opening Concepts, of matching your opponent’s anchor with one of your own. The error isn’t enormous for the reason that I imagine was on Zavoral’s mind over the board.
Red rolls 63 - 13/7*, 8/5* (47.9%/13.1%/14.3% - ++) - Zavoral double hits. It’s really the only candidate play.
Blue rolls 52 - Bar/23, Bar/20* (57.7%/19.3%/8.7% - ++) - Force. Kazaross enters both checkers and hits while doing so.
Red rolls 44 - Cannot Move (62.4%/26.0%/6.7% - ++)
Blue Cube Decision - Double/Pass
First, we should discuss whether Kazaross even has a Double here. He has 4 numbers that don’t hit Red’s blot, so the vast majority of sequences will result in a 2nd checker on the Bar for Red. Even still, with three checkers to move around the board and no outfield points, Kazaross cannot have much above a 65% chance to win, and probably slightly below. Then the question becomes what Kazaross must have in the way of Gammons. The near guarantee of a 2nd checker is counterbalanced by Red’s 5 point, so we can easily assign Blue something in the 20’s maybe as high as 30% gammons given its current 3 point board. Wirth those estimates, Blue is comfortably within the range to Double.
Should Zavoral take? Yes. He should. This one may seem scary, but it isn’t like the Game 3 Pass by Kazaross because Zavoral has a 5 point anchor. That anchors will tether him to this game and keep him away from gammons in the majority of instances and will be a significant deterrent to Kazaross if Zavoral can get both checkers off the Bar in short order. Unfortunately, Zavoral drops for his lone Cube Blunder of the match.
Game 6 - Kazaross 3 Away Zavoral 4 Away
Red rolls 65 - 24/18, 13/10 (47.1%/13.1%/12.2% - Rollout of 10,368 games)
Blue rolls 43 - 24/21, 13/9 (44.6%/11.8%/13.2% - Rollout of 1,296 games)
Red rolls 62 - 24/16* (41.2%/10.0%/12.2% - ++) - Zavoral hits with an 8 and is off to a good start in this game.
Blue rolls 62 - Bar/23, 13/7 (38.2%/8.7%/13.6% - ++) - Not a great response from Kazaross as he enters, but fails to hit back or anchor and he ends up with blots strewn about. Zavoral, on the other hand, is semi-escaped and has a 20 pip lead after the checker play.
Red rolls 11 - 6/4* (2) (33.1%/6.7%/15.2% - ++) - Zavoral points on Blue and makes the 4 point simultaneously. Kazaross is in need of an anchor or a retaliatory hit.
Blue rolls 43 - Bar/22, 13/9* (37.4%/9.1%/17.9% - ++) - Kazaross gets what he needs and stops Zavoral’s escape for the moment.
Red Cube Decision - Double/Take
A nice Double by Zavoral and, in a way, an even better Take by Kazaross. There are so many blots around the board that it might be possible to talk yourself into a Pass given Red’s elevated gammon values. However, gammons are relatively low once you count out only 11 hitting numbers and Blue has a pretty good structure when Red doesn’t hit back. Plus, Blue anchors up in many variants when he is hit. One aspect that makes this quite “takeable” is that Red lacks the firepower to carry out a blitz on the offensive side of the board. The flag that would tell us that, aside from the obvious 8 checkers in the zone, is the mountain on the mid-point. With all that in mind, Blue has to swallow hard and accept the cube.
Red rolls 22 - Bar/23, 13/11 (3) (34.7%/7.6%/17.1% - ++) - Zavoral with a nice roll from the Bar, even though it doesn’t hit it does unstack the mid-point.
Blue rolls 44 - 8/4 (2), 6/2 (2) (39.9%/13.7%/17.6% - ++) - Kazaross rolls an attacking number and makes two innerboard points while putting Zavoral on Bar.
Red rolls 54 - Bar/16* (30.5%/6.9%/19.9% - ++) - Zavoral responds with a hit in Blue’s outfield and is, once again, semi-escaped.
Blue rolls 31- Bar/22, 6/5 (29.5%/6.8%/18.0% - Rollout of 6,209 games) - Kazaross anchors and then slots his 5 point. It’s too early to shift into a multiple anchor game and Kazaross is correct to prioritize the strength of his innerboard.
Red rolls 53 - 16/8 (30.2%/5.9%/14.1% - Rollout of 2,326 games) - Zavoral makes a slight error here as he safeties a checker. It seems that with the number of blots still in and around Blue’s homeboard, Zavoral can afford to take more risk in pursuit of gammons.
Blue rolls 52 - 23/18, 7/5 (30.3%/6.0%/15.4% - ++) - Kazaross makes his 5 point and steps out to the Bar point.
Red rolls 11 - 8/7*, 7/5, 6/5 (21.8%/2.7%/21.2% - ++) - Zavoral hits and makes the 5 point, spiking both wins and gammons for him.
Blue rolls 65 - Cannot Move (21.8%/2.5%/25.5% - ++)
Red rolls 52 - 13/6 (22.7%/3.0%/22.2% - Rollout of 5,184 games) - Zavoral brings another checker into the zone.
Blue rolls 61 - Bar/18 (23.5%/3.5%/24.7% - Rollout of 6,289 games) - Kazaross enters and steps back out, though settling into a multiple anchor game is also a viable candidate play and is actually the preferred play. Stepping out is a -.003 “error”.
Red rolls 44 - 13/9 (2), 11/7* (2) (21.4%/1.8%/30.4% - ++) - Zavoral rolls 44, which makes the Bar point and against boosts his gammons.
Blue rolls 31 - Bar/24, 13/10 (27.4%/2.1%/24.3% - Rollout of 5,184 games) - Kazaross manages to makes a multiple anchor game and brings another checker into the outfield.
Red rolls 51 - 11/5 (26.0%/2.1%/24.4% - Rollout of 5,184 games) - Zavoral puts a spare checker on the 5 point, but the preferred play is to slot the deuce point.
Blue rolls 65 - 13/7, 8/3 (23.8%/1.9%/26.1% - ++) - Kazaross slots the 3 point and the Bar point.
Red rolls 43 - 6/2, 5/2 (24.3%/1.8%/24.4% - Rollout of 2,592 games) - Zavoral makes the two point when, again, he should simply slot the point and hold back.
Blue rolls 41 - 10/9, 7/3 (27.0%/2.3%/24.3% - ++) - Kazaross makes a 5 point board.
Red rolls 32 - 9/7, 9/6 (22.0%/1.0%/24.9% - ++) - Zavoral clears his 9 point.
Blue rolls 31 - 9/5 (24.8%/1.4%/24.8% - ++)
Red rolls 42 - 8/4, 7/5 (20.9%/1.0%/27.5% - ++)
Blue rolls 65 - 22/11 (20.3%/0.6%/30.4% - ++) - Kazaross breaks his front anchor with what is, practically speaking, a forced play. Zavoral’s gammon’s spike as he has 25 pointing numbers.
Red rolls 66 - 8/2 (2) (28.1%/0.9%/17.1% - ++) - Zavoral is unable to point on Kazaross and throws a fairly awkward word.
Blue rolls 22 - 24/22 (2), 11/7 (14.1%/1.0%/11.2% - Rollout of 1,296 games) - Kazaross decides to limit gammons by putting all of his remaining back checkers on the 22 point. Unfortunately, this is the wrong idea because, though it does save quite a few gammons, it costs him so many wins. The preferred play of 11/7, 5/1 wins 28% of fames for Blue but Red wins 24.5% gammons as compared to the play that was made (a -.099 Blunder), which has 13.8% wins and 10.7% gammons for Red.
Red rolls 51 - 7/6, 7/2 (11.8%/0.0%/9.7% - ++) - Zavoral clears the 7 point.
Blue rolls 54 - 22/13 (11.2%/0.0%/7.1% - Rollout of 2,592 games)
Red rolls 53 - 6/1, 4/1 (13.5%/0.0%/5.0% - Rollout of 5,184 games) - Zavoral ignores the opportunity to bear off and instead opts for a purer bear-off.
Blue rolls 62 - 13/11, 7/1 (13.9%/0.0%/5.6% - Rollout of 2,592 games)
Red rolls 64 - 6/Off, 5/1 (14.5%/0.0%/5.3% - ++) - Zavoral is without spares now, so any deciding moment is forthcoming.
Blue rolls 62 - 11/3 (14.7%/0.0%/5.5% - Rollout of 5,184 games) - Kazaross maintains his anchor, which is the correct play. Gammons are quite low, as Red has only one checker off at this juncture.
Red rolls 53 - 5/2, 5/Off (16.5%/0.0%/4.6% - ++) - Zavoral clears the 5 point and Kazaross has a slightly better chance to get a shot.
Blue rolls 65 - 22/11 (15.8%/0.0%/1.7% - ++) - Kazaross breaks the anchor and runs.
Red rolls 41 - 6/5, 6/2 (33.2%/0.0%/0.9% - ++) - Disaster strikes for Zavoral, as he volunteers a shot. Here’s the position at this critical moment:
Blue rolls 21 - 22/20*, 20/19 (85.6%/0.0%/2.2% - Rollout of 2,592 games) - Kazaross hits! Now, can Zavoral roll back in on the ace?
Red rolls 44 - Cannot Move (90.7%/0.0%/0.3% - ++)
Blue Cube Decision - Double/Pass
Game 7 - Kazaross 1 Away Zavoral 4 Away (Crawford Game)
Red rolls 43 - 24/21, 13/9 (49.7%/16.0%/14.6% - Rollout of 20,736 games) - Zavoral opens with a tiny error (-.008) as he should paly the more aggressive 13/10, 13/9 in this scenario. A gammon for Red is especially valuable here as it takes away the potential need to win 3 consecutive games.
Blue rolls 53 - 24/16* (53.8%/13.9%/12.7% - ++) - A nice start for Kazaross with a hit and halfway to escaping its first back checker.
Red rolls 52 - Bar/23, 6/1* (56.6%/21.4%/12.1% - Rollout of 1,968 games) - Zavoral decides to enter and hit Blue off the ace point on the other side of the board. The preferred play is Bar/20, 6/4.
Blue rolls 31 - Bar/24*, 16/13 (54.9%/23.8%/11.8% - Rollout of 5,184 games) - Kazaross responds immediately by hitting from the Bar and safetying his checker as well.
Red rolls 21 - Bar/24, 23/21 (55.1%/23.3%/11.5% - Rollout of 5,184 games) - Zavoral enters and slips right into a multiple anchor game.
Blue rolls 54 - 24/15 (56.4%/16.3%/10.9% - ++)
Red rolls 54 - 13/4 (58.5%/22.0%/10.7% - Rollout of 2,592 games)
Blue rolls 63 - 15/6 (55.7%/15.5%/11.6% - ++) - Kazaross has brought his back checkers to safety but hasn’t done much else and will need a fortuitous roll on the next term in order to diversify his board. Zavoral will want to improve his home board as quickly as possible as he lies in wait.
Red rolls 44 - 13/5, 8/4, 6/2 (56.6%/14.1%/12.8% - ++) - Zavoral makes the 4 point and slots the 5 and the 2 points, which strikes me as an odd choice given the circumstances. The are various rolls that give a shot on the very next roll, so it might be wise to just make the 4 point and the 2 point and bring another checker into the zone.
Blue rolls 55 - 13/3 (2) (58.6%/15.9%/8.9% - ++) - Kazaross gets a nice roll to unstack the mid-point and make an innerboard point in one fell swoop.
Red rolls 61- 8/2, 6/5 (57.1%/14.8%/9.5% - ++) - Zavoral makes a 4 point board, so his gamble the roll before pays off.
Blue rolls 61- 13/7, 8/7 (61.8%/17.1%/6.5% - ++) - Kazaross makes the Bar point and his game looks a good deal stronger all of a sudden.
Red rolls 55 - 13/3 (2) (63.6%/15.3%/6.9% - Rollout of 1,296 games) - Zavoral opts to make the 3 point, but the rollout tells us that the preferred play is 21/16, 13/3. 8/3, which spreads Red out, but increases contact and provides more flexibility on future rolls. The critical aspect here is the creation of bad rolls for Blue. Sure, Blue has some pointing rolls that are ideal, but it has to deal with so much more contact and that contact is critical to Red’s most likely path to winning.
Blue rolls 41- 13/8 (65.2%/14.0%/5.7% - ++)
Red rolls 62 - 13/3 (2) (64.6%/15.0%/5.7% - Rollout of 5,184 games) - Zavoral breaks his front anchor, maximizes contact in Blue’s outfield and places a spare in the best place in his own homeboard. Nice play.
Blue rolls 64- 8/2, 6/2 (70.2%/16.0%/3.6% - ++) - Kazaross makes the 2 point, helping to unstack the 6 point.
Red rolls 33 - 24/21 (2), 4/1 (2) (74.3%/10.5%/2.5% - Rollout of 5,184 games) - Zavoral steps both his checkers up in the back, which surprised me as the preferred play. I would have, I am quite sure, made the 2nd best play (-.009) of 24/21, 6/3, 4/1 (2) in an attempt to maximize contact. Zavoral, however, finds the best play, but there isn’t much separation here.
Blue rolls 41 - 6/1 (71.1%/6.7%/3.0% - ++) - Kazaross immediately takes advantage of the ability to play behind Zavoral.
Red rolls 44 - 15/3, 6/2 (74.1%/3.6%/0.9% - ++) - Zavoral throws a large number that gives it a small amount of racing equity and drops the gammons for both players. The ability to win from a holding game has decreased as Red’s timing has been hurt.
Blue rolls 55 - 13/3 (2) (82.8%/3.9%/0.3% - Rollout of 1,296 games) - Kazaross rolls his own large number and ruins that racing equity. He clears the mid-point and Red will have to hope to hit a checker as Kazaross bears in.
Red rolls 53 - 21/13 (81.5%/1.7%/0.4% - ++) - Zavoral skips a spare checker out from the back and awaits Kazaross’ next throw while retaining his 5 point board.
Blue rolls 11 - 8/7 (2), 6/5 (2) (84.0%/1.3%/0.2% - Rollout of 2,592 games) - Kazaross makes a play that’s a bit awkward and ends up being a -.051 error. Interestingly, my play of 6/5 (2), 3/1 is a -.001 error and the preferred play is simply 7/5 (2).
Red rolls 42 - 13/7 (85.5%/1.4%/0.2% - Rollout of 2,592 games) - Zavoral continues around the board.
Blue rolls 51 - 7/6, 7/2 (86.6%/1.4%/0.2% - ++)
Red rolls 41 - 7/3, 2/1 (88.5%/1.2%/0.1% - ++) - Zavoral retains its anchor for one roll by burying its checker deep. A rollout shows that he is correct to retain that anchor even though the margins are thin.
Blue rolls 55 - 7/2 (2), 5/Off (2) (93.2%/2.7%/0.0% - ++) - Kazaross clears the 7 point and bears two checkers off the 5 point.
Red rolls 62 - 21/13 (93.4%/2.0%/0.0% - ++) - Zavoral breaks the anchor and this roll or the next should tell us how much more backgammon there will be.
Blue rolls 55 - 6/1 (3), 3/Off (100.0%/1.9%/0.0% - ++) - Kazaross wins!
Red rolls 21….. Resigns the Match
Blue wins the Match 7-3
Match Summary
There were a couple particular types of plays that I may revisit in later posts:
Hit and Split Decisions as Compared to Hit and Support
When to Break and Anchor
Additionally, the Cube Decisions that caused errors for these two exceptional players really required difficult over-the-board Most Common Variant Analysis and some match score adjustment. All the more reason to do a few more of these annotated matches.