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PR match strategy
Posted By: Bob Koca
Date: Tuesday, 29 January 2013, at 2:02 a.m.
Are there any "tricks" to help in a PR tourney where the winner of a match is decided by the XG PR? Yes there are. The PR is essentially total errors divided by number of decisions (and then multiplied by a constant). Understanding exactly what constitues a decision is important. Note that a play which results in you having more decisions than your opponent may win you the PR battle even if you had a greater error total.
From the XG help pages one can almost (what does very negative mean?) see exactly what is considered a decision.

5. Decisions A decision is a checker move or a cube double that is considered nonobvious by the computer. Considered obvious are the following:
A forced moved
A move for which the best choice and the worst choice have an equity difference of less than 0.001.
A double action where the equity before doubling and after doubling is the same (optional double)
A double action where the equity before doubling is 0.200 larger than the equity after the double (obvious non double)
A double action where the equity before doubling is 0.200 larger than the equity after a drop (obvious too good to double)
A double action where the equity before and after a double is very negative (This corresponds to a loss of position when trailing in the match by a lot)
Are never consider as a obvious:
A double decision resulting in a double
A take decision

Here are a few cases where one can boost ones chances.
1) In an easy to play position avoid forcing forced moves.
White is Player 2
score: 0
pip: 41 point match pip: 7
score: 0
Blue is Player 1XGID=AAAd:0:0:1:21:0:0:0:1:10 Blue to play 21
eXtreme Gammon Version: 2.03
Many would mindlessly play 2/0 1/0 and indeed it is theoretically correct. In a PR match though the equally theoretically correct 2/0 4/3 is better. On 18 rolls (any 1 or 2 except doubles) your next play is not forced and you will probably play it correctly. You have a good chance of adding 1 to your denominator.
Another example is the 61 to play in the following position. Both legal plays are theoretically optimal but leaving 36 is better than 45. The difference next turn comes on the roll of 65 not being forced.
White is Player 2
score: 0
pip: 41 point match pip: 16
score: 0
Blue is Player 1XGID=ABd:0:0:1:61:0:0:0:1:10 Blue to play 61
eXtreme Gammon Version: 2.03
2) Races usually have easier checker plays. If you are in a race where opponent may have forced plays it may be worth a small theoretical error to get the larger denominator. In this game your opponent got lucky with escaping 66 from a crushed ace point game and is now redoubling:
White is Player 2
score: 0
pip: 299 point match pip: 51
score: 0
Blue is Player 1XGID=ACCBCBdfe:1:1:1:00:0:0:0:9:10 White on roll, cube action?
Analyzed in XG Roller++ No redouble Redouble/Take Player Winning Chances: 78.313% (G:0.000% B:0.000%) 78.215% (G:0.000% B:0.000%) Opponent Winning Chances: 21.687% (G:0.000% B:0.000%) 21.785% (G:0.000% B:0.000%) Cubeless Equities +0.5663 +1.1693 Cubeful Equities No redouble: +0.8694 (0.1306) Redouble/Take: +1.0092 (+0.0092) Redouble/Pass: +1.0000 Best Cube action: Redouble / Pass eXtreme Gammon Version: 2.03, MET: Jacobs & Trice
Even if you knew you are making that small error by taking it is probably worth it. For the .01 error you get several non forced easy race plays to add to your denominator. Your opponent probably gets only a couple unforced plays.
3) You should consider playing on in an optional TG/D position
In the position below your opponent was cruising to a gammon but had a bad double 66 after which you hit from the bar. In a real match doubling now or waiting a bit are of course equally good. In a PR match doubling is nearly as costly as a genuine blunder. Waiting until there is a chance of a turnaround makes no errors and gives you about 6 nonforced plays while bring your checkers around. Suppose you had a PR of about 5 based on 200 decisions in a long match. Adding 5 extra decisions without error lowers it to about 4.85. That is the same as avoiding a .06 error somewhere else in the match.
There is another drop of poison in doubling immediately. It does not count as a decision for you "A double action where the equity before doubling and after doubling is the same (optional double) " but does count as a decision for your opponent. Waiting until there is a chance of a turnaround makes it no longer an optional double and you get your decision from it.
White is Player 2
score: 0
pip: 489 point match pip: 63
score: 0
Blue is Player 1XGID=aBBBBBBAddc:1:1:1:00:0:0:0:9:10 Blue on roll, cube action?
eXtreme Gammon Version: 2.03
4) Delay your post crawford odd away cubes.
Doubling immediately is of course optimal but if you have no market losers then it is an optional double and does not count towards your denominator but does add one to your opponent's denominator. If the game is a blowout in his favor when you never had a chance never doubling saves a net of 1 decision. If you wait until there is a chance of a market loser then you are indeed credited with a decision.
5) Know the resignation rules. In the position below you have 0 equity after the roll. Playing the game out though may give your opponent a non forced play which would lower his equity so you should resign now (which is not an error). In general once you have 0% win chance you will not have any decisions ("A move for which the best choice and the worst choice have an equity difference of less than 0.001. ") but your opponent very well might. Stacking the ace point instead of using numbers to bearoff could well be an error of more than .001 meaning additioanl decisions for him.
White is Player 2
score: 0
pip: 151 point match pip: 15
score: 0
Blue is Player 1XGID=Oaaaaa:1:1:1:65:0:0:0:1:10 Blue to play 65
1. 3ply 1/Off(2) eq: 1.0000
Player:
Opponent:0.00% (G:0.00% B:0.00%)
100.00% (G:0.00% B:0.00%)eXtreme Gammon Version: 2.03, MET: Jacobs & Trice
In a "hopeless" race it may even be correct to give up some equity with a "wrong" resignation
White is Player 2
score: 0
pip: 171 point match pip: 15
score: 0
Blue is Player 1XGID=Oaaaaa:1:1:1:65:0:0:0:1:10 Blue to play 65
1. 3ply 1/Off(2) eq: 0.9999
Player:
Opponent:0.00% (G:0.00% B:0.00%)
100.00% (G:0.00% B:0.00%)eXtreme Gammon Version: 2.03, MET: Jacobs & Trice
For a .0001 error you likely take away a non forced play from the opponent.
6) Don't double without a market loser at 2away 2away.
If you double without a market loser it is not a decision for you but the take is one for the opponent. This is especially relevant if your oponent uses the (theoretically correct) strategy of doubling at first opportunity. It will be you instead of him who gets the cube decision. Usual warnings apply of course about the dangers of overdoing this and then actually making a cube error by waiting.
Two final thoughts:
i) Is a good rule set one which encourages a player to make some intentional theoretical errors when one of the reasons for the tournament in the first place was to increase the importance of skill in the tournament?
ii) Have a fun time if you are in the dual duel event.

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