From: Backgammon Galore : Woolsey-Bagai Match

Kit Woolsey vs. Jeremy Bagai
Game 6

Annotated by Kit Woolsey, Jeremy Bagai, and TD-Gammon

Match to 9:   Kit Woolsey - 4,  Jeremy Bagai - 6

Kit Woolsey is playing Red.
Jeremy Bagai is playing White.
Jeremy wins the opening roll.

Position 1: White to play 31.

Position 2: Red to play 43.

Kit: Once again, I like this split better than 13/10, 13/9 in response to a made five point. I can use his four point for an anchor badly, and right now he doesn't have the ammo with which to attack. If I delay splitting just one roll, the builders come down from the midpoint and then splitting will be too dangerous.

Jeremy: A little surprising. I would have thought the match score would prompt Kit to play 13/10, 13/9 trying for a prime vs. prime game where the prevalence of gammons would give him more menacing threats. His actual play looks right for the player who is leading in the match and wants simple games where the cube actions are clear. Kit must think his play is simply stronger than 13/10, 13/9. I think the two plays are about equal so I would bring two checkers down.

TD: If Kit's reason for making his play is that it simply is the better play, he is right. Going after the advanced anchor quickly here is very important.

    24/21, 13/9      -.205
    13/10, 13/9      -.240
    13/6             -.281

Position 3: White to play 62.

Position 4: Red to play 32 from the bar.

Position 5: White to play 63.

Position 6: Red to play 31.

Position 7: White to play 33.

Kit: An interesting problem. Jeremy's play is certainly the natural looking one, but I'm not so sure it addresses the position. He is miles ahead in the race, but I have an anchor on his four point. This indicates that a priming approach won't work -- I should have sufficient timing if I can contain his back man. After his play his position is very stripped. Now let's look at 24/15, 13/10. This is great if he isn't hit. He will have escaped all his men and will have a big racing lead -- enough to claim with the cube or be very close to a claim. If he is hit it isn't so great, but he is still in pretty good shape. The one big argument in favor of Jeremy's play isn't so much that it makes a new blocking point for a prime, but the bar point is now a landing place for his checkers in the future. This of course assumes that he will be able to escape the back man -- if he can't, that landing place won't to much good. It's an interesting position and making the bar point could easily be right, but I would play 24/15, 13/10.

TD: Sorry Kit, but your play just doesn't rank in the top three. Looks like making the board improvement is more important. However there is plenty of value in getting the back man going somewhere and the three point isn't chopped liver, so I like 24/21, 13/10, 6/3(2).

    24/21, 13/10, 6/3(2)     +.377
    24/18, 6/3(2)            +.374
    13/7(2)                  +.368

Position 8: Red to play 54.

Position 9 before roll: White's cube action?

Jeremy: I have a five-prime, but it's no big deal against Kit's advanced anchor. A double would be premature -- especially at this match score where Kit will be very quick to recube. Overage is the issue here. I can't use all four points of a four-cube, while Kit certainly can. I also won't have the usual luxury of being able to redouble to eight if things go well.

TD: Equity is .409, and volatility is relatively low. Not even a money double.

Position 9: White to play 63.

Position 10: Red to play 43.

Position 11: White to play 51 from the bar.

Kit: Jeremy must risk getting hit with a 5-4. Dumping a checker onto the ace point here is very bad.

Jeremy: I should give some thought to the anti-positional B/24, 6/1 in order not to get with Kit's 5-4. But Kit's 5-4 plays very well anyway (makes his four point), so I make the more flexible play.

TD: Just examining going to the ace point almost caused my program to crash.

    B/24, 13/8      +.339
    B/24, 6/1       +.246
    B/24, 10/5      +.171

Position 12: Red to play 44.

Position 13: White to play 63.

Position 14: Red to play 33 from the bar.

Position 15 before roll: White's cube action?

Kit: This is obviously a huge double. Jeremy has four of my men trapped, and he is well placed to bring the position home safely. He doesn't have many gammon chances, but he is a big favorite to win. The match score shouldn't stop him from doubling positions like this one.

Jeremy: The match score shouldn't paralyze me!

TD: No kidding. This is a monster double.

Kit: It just isn't worth it. I'm not hopelessly behind in the race, but I would have to roll very well to make it a race. If I can't escape one of the back men quickly while still holding the advanced anchor my position will fall apart. I'm not likely to get a shot, and I may not be ready for the shot even if I do get one. While I would have big recube leverage available due to the match score, I simply don't have sufficient winning chances.

Jeremy: Clear drop for money; Kit's position stinks. I won't be leaving shots for a long while, and he may be crashing in two rolls. What does the match score do to this? The numbers look like this: If Kit takes and wins the score is tied, so his chances of winning the match are 50%. If he passes he needs five points while I need two, and the associated winning chances are 25%. If he takes and loses he needs five and I need one, which puts him at 15%. (these numbers come from a match equity table which you would need to memorize in order to do this sort of thing.) That means that by taking he would risk 10% (the difference between 15% and the 25% he would have by passing) in order to gain 25% (the difference between passing and winning.) 10% / (10% + 25%) = 28.6% which is the raw game winning chances Kit needs in order to take this double. It can be instructive to see how this logic works for money games: Taking a two-cube and winning earns you two points. Dropping a two-cube loses you one point. Taking and losing loses you two points. Your risk is one point, and your possible gain is three points. 1/(1+3) gives you 1/4, or the familiar 25% which you need to take a normal double (assuming no gammons). But this is only half the story. 28.6% is the *raw* winning chances that Kit needs. Kit can win the game another way -- with a recube. It turns out that Kit's recube is particularly powerful. When Kit redoubles to 4, my take point is 33.3%, which is pretty high. I also won't be able to recube to 8 because I only need 3 points. (It is usually on recube considerations that you get the intuitive result that the player behind in the match should be aggressive, while the player ahead in the match should be conservative.) So you have to integrate his high take point with the power of his recube. How to do this is a matter of some controversy. If this all seems a little esoteric, it is, but serious players need to master it. A great place to learn it is Kit Woolsey's How to Play Tournament Backgammon, which is all about match score considerations. In the current position none of this really matters. Kit's position stinks. He passed in an eye-blink, as I recall.

TD: Kit's position sure does stink. I make the equity -.709, surely not enough to take even at this match score. Once again your cube action has been flawless.

Match to 9:   Kit Woolsey - 4,  Jeremy Bagai - 7

Go on to next game: Game 7

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