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Game Plan Selection 5: What Now, and What Next? - Part 2
by Mary Hickey - September 2006

Mary Hickey
The following position arose later in the same game as last time’s problem, after the first player incorrectly attacked and made his ace point.

Problem 1

Priming two or more checkers, the principle we explored two articles back, may be the best play to win this game.  The rollout below makes that aspect of our decision too close to call, meaning that either play would be OK at double match point (“DMP” to the cognoscenti) or in a one-point match. If we were instead at a match score where gammons hurt us but not our opponent, it would be clearly correct to play 17/11, 6/5, to the point where any other play would be a massive blunder.

 

So, why don't we stay out of trouble, play 17/11, 6/5 for money also, and be happy?  Because we'll be even happier if we win a gammon!  This roll gives us a great opportunity to try for one, without excessive risk.

 

It's true that after the aggressive 10/4*/3*, our game could begin to unravel if White rolls a 3 and we flunk.  However, it's not over even then, since White still hasn't covered the 3 point or hit another of our checkers.  He may not even have both his men in from the bar yet!  So a lot has to go wrong before we have to pass a recube.

 

How can we know if a risk like this is worth taking?  The general rule is that you need to win twice as many added gammons as you lose added games.  If the cube is in play, we have to take that into account also, and be sure we have counted the lost games we might have won had we not been doubled out after a dice-barf or two.  We also need to add in the cost of any additional gammons we might lose.

 

Over the board, the opponent having six blots scattered around the board suggests aggression by you is appropriate.  If you play passively, almost anything he rolls will let him consolidate in some way.  This is generally true of “pure” positions, since the reason people create so many blots in the first place is to give them more good options on the next roll.  However, since the opponent gets to play first, when there’s significant contact in a position it’s usually wrong to have that many blots.  Even five blots is questionable; six is too many; and seven or more are is beyond the pale!  If a play that leaves several blots looks good but leaves you feeling vaguely uneasy, there’s often a good reason for that.

 

The rollout below shows that we gain 25.2 additional gammons, at the cost of 0.2 additional games lost, and 6.9 additional gammons lost.  This is obviously a favorable tradeoff, and so the equity play is to do it.  

 

How do we know over the board?  It's often hard to calculate, and comes down to experience rather than formula.  However, when in doubt, here are a few things to consider:

 

1.  Does he have a five point board or a powerful prime?  If so, he may be able to win with the cube after just a single hit, and this means you need to be a bit cautious.  In the position shown above, if White had his 3 point already made, 17/11, 6/5 would be better by .179, says a 3-ply evaluation.

 

2.  Will you gain enough if your play works?  It's easy to overestimate your chance of actually getting a gammon.  If only two of his checkers are in play, he needs to have a few extra outfield crossovers before he's home, or your gammon chances may not be that good even if you close him out, and especially if he manages to anchor.  That doesn’t mean it will always be wrong to pursue the gammon, but it’s definitely less “juicy” in the more doubtful cases.

 

3.  Do you have so many blots of your own in play if you attack, that one bad sequence could leave you in severe danger of getting gammoned yourself?  If that's so, maybe you'd better pull in your horns for this roll, and re-consider attacking next time if the opportunity is still there.  In the position above, this is a consideration but not an overriding one.

 

4.  Is the safe play actually safe?  If he's threatening to bolt into an equal or winning race, you may have to attack not just for the gammons, but to increase your chance of winning the game, too.  Yes, you might be hit back and lose, but the overall risk may be greater if you hold off.  Losing slowly isn't any more fun than losing quickly - it just delays the start of the next game!

 

The only time you would even consider making the priming play here for money would be if you were playing with the Jacoby Rule, and for some reason you had forgotten to double before you rolled.  In that case, you’d tighten everything up, not let him have any really good rolls, with the intent of doubling next turn.  We'll look at this concept in more depth another time. 

 

But you wouldn't have waited to double this game, would you?  Your double was huge, based in a large part on your looming gammon threat.  He would have had a gi-normous pass, so big that if you already owned the cube, you'd be too good to redouble (unless, of course, you thought he would take!)  In the actual game, Red had doubled earlier and so wasn't able to blunder by forgetting to jack it up here, nor was White able to blunder by taking.


Problem 1 with rollout:

 

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