Thank you to Chicago Point , then as now a prime source of backgammon information and it's editor Bill Davis, whose contribution to our wonderful game over all these years is incalculable.
In every position, Black is on roll. You can assume that you are playing an equally strong opponent to yourself. Five positions today, five tomorrow.
Position One. It's a 9 point match and Black holding the cube leads White 6-2. What's the correct cube action for both sides?
Position Two. Money game, Black to play 3-1.
Position Three. It's DMP, how should Black play his 1-1?
Position Four. It's a 7 point match, White leads 5-2 What's the correct cube action for both sides?
Position Five, money game, Black to play 1-1.
An interesting feature of this quiz is that it was composed at a time when bots were in their infancy. The best available was Tom Johnston's Expert Backgammon, a weakling compared to today's heavyweights but a remarkable program for it's time, particularly considering that it was the work of one man. In their answers Bill declared that only positions 6 and 10 were at all debatable, but ExtremeGammon has something to say about that, as we will see. Nevertheless, kudos to both men for an excellent quiz.
Post your answers to these five in the comments section please and I'll put up the next five tomorrow.
Oh yes, what is the prize? The winner will receive a backgammon book! Don't get too excited, it's minute and almost valueless, but it is very old and very cute and will look well on your trophy shelf.
Enjoy the game!
15 comments:
I have removed Timothy's answers so that they dont help anybody else. However Timothy, I messed up and put the score wrong in Question 4. It is correct now and White leads 5-2, so you may like to answer that one again! Sorry about that.
...now that I've given my answer, I've read the other comments...
I hope you'll show Tim's comments at some time - I always find his views enlightening.
How does it work?
leaving the answers as a commen?
reasons included?
How does it work?
Just posting the anwers as a comment, reasoning included?
Yes, please post your answers, with or without reasoning, but I may remove the comments as I go along so that others don't see them first!
Ok, thx!
1) First i allways calculate TP.
White can pass for 7-1 away,
that´s 9,3% MWC or take and redouble and win for 100%. So TP is
9,3%.
Black hasto throw no Dbl exc, 11
and roll 66,55,44 thats 3x30/1296
so roughly 90/13 7%. He might Gain on two 21 by black 5,55x5,55% and on 21 31 same gve him another 1% for that. So he´s about ~8%.
Clear Pass , no need to calculate Give Point
Double/Pass.
2)Tricky 12/9 11/10 gets most doubles and numbers working on the next 2-3 rolls
3)I nearly allways fock up this one. You need the second Blot.
If he consolidates on the ace
Youre below 17%. 2/1*, 10/7.
Moight be a bit to conservative but my first thought.
4)My andvantage on this Quiz is: i
know all take-, give- and redoubling points in a 5 point match
according to RK mat. :-)
5-2 away has an extreme low TP gammonless: 17,35%. Trailer Givepoint is very high: 69,5%.
Black bears off with all 6,5 and 5-
27 exc. the ones-6 thats 21 +33ans 22 a total of 23. 18 is 50%
5 is 13,88. So he has a total of 63,88%. IT´s beloe GP of 69,5%.
No Double/Take.
5)Try the simple way, only adjust when difference is small.
If he shifts all Checkers on the ace, he will nearly allmost win and gets a gammon (exc 11 dance-2,77 no Double 83.33 hit 30,55)
wich cost minimal gammons and still leave him +95% Facorite to win the game) he even wins some BG´s her on 21,31,41,51,32,42- 16,66% followed by a Double 16,66%
and 11 danceand a double. so he earns a bit more than 400 in 100 games.
If he bears off 2, opp. hits 14 times and escapes 3 time off bg (44
55,66) hits save the gammon
14 is 38,33% single losses.(i ignore the few wins) 3 Doubles
loose gammon 8.33%G´s.
Reat is 53,34% id BG.
This are round about 391 points in 100 games. No need to go further
:-)
3/1, 2/1(2)
Nice christmas.
boop says
1) i wonder if a double and redouble is too risky for black as white would would win the match with 44 55 or 66. if white gets the lucky dice and wins it goes to 6-4 rather than 6 - 10
no double/redouble
2) unless white gets a double in the near furture, i have 2 more throws after this 3-1. so i need to get at least 1 home next move to stop the gammon. 12/9 11/10 leaves 2/1 as a failure in that respect. so 12/8
3) 10/7 2/1 hoping to get all 3 of whites pieces pn the bar.
4) black is better than 50% and a double kills the cube. all 1s lose = 11 plus 2-3 = 13 = 63.9% to win. i'm looking forward to reading other's comments that take into account match equity - can't wait till those calculations are possible for me.
so i'm guessing double/pass (not very certain)
5) well, are we going to risk our certain 4 point gammon to win a 6 point backgammon? can i do the maths?
taking 2 off the 2 point leaves any 3 to hit = 14 chances … so 38.9% to win only 2 points, 61.1% to win 6 points barring a lucky 44 55 66 from white. <-- actually i think that that should be taken into account in the calculation as the win would then only be for 4 points. At this point my brain is throbbing and I think the best thing to do is admit that I need to learn some methods to help calculate these positions. Still, with an almost certain 2 points in the bag and just a bit less than 61% to win 6 points, i'll play 2off(2)
now let's go see what the others say! and Merry Christmas to you all + a big thanks to you Dorbel for putting the effort into this blog :-)
this is a day late, but heck i've been busy. I have not looked at the other comments, so here goes.
1. I'm sure it's a double and I think it's a drop. DD
2. 11-7. nothing you do gets better than double threes for the next play so, this looks best for the turn after.
3. 10-7, 2-1*. I know the hit is right, I.m not sure about buttoning up, on the back side, but that's my play.
4. DD no question in my mind.
5. I can figure everything except how often do you escape after getting hit and how often do you lose after getting hit. The rest of it seems to point to going for the BG, but even though I suspect that losses might swing it back the other way, I would take two off and go for it. two off, final answer.
now to read the other comments and on to part two.
1) Double-drop
2) 12/9 11/10 - all doubles wash; 11/7 leaves an extra flunk after 23 next time; 12/7 leaves an extra flunk after 31 next time.
3) 10/7 2/1*, otherwise you run out of time to pick up an extra man.
4) Close double, clear take.
5) 2/off(2). You elevate backgammon chances from about 1/6 to about 2/3, at the cost of 1/3 singles and a tiny % of losses. White can't cube you out unless he completes the close out and then gets 8 men off while you dance.
Not sure I'll have time to do problems 6 to 10, but at least I'll redo problem 4.
Black bears off with 23 rolls and misses with 13 rolls. Suppose Black doubles. If White drops then she will be at 2a4a with 67% MWC; if she takes and loses then she will be at 2a3a with 60% MWC; if she takes and wins then she wins the match. Thus she can take with 17.5% game-winning chances, and 13/36 is much better than that, so the take is trivial.
What about the double? If things go well for Black then, as we saw above, a double will take him from 33% to 40% and if things go poorly for Black then a double will take him from 16% (his MWC at 5a1a) to 0%. Thus by doubling, he's risking 16% to gain 7%, and he has to be a 16-to-7 favorite or better to double. 23-to-13 is worse than 16-to-7 so Black should not double. ND/T.
Of course if you think White doesn't understand match equities and may drop, then you might want to double anyway.
1. double pass
2. 11/7
3. 2/1* 10/8
4. double/take
5. 3/1 2/1(3)
The following comment was posted Dec 20th, but removed pending the answers being posted.
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1) If white passes, it's 7-away crawford and her ME is 9.1%. If she takes, she has an automatic redouble and the game is for the match. This simplifies the take decision: if white has more than 9.1% GWC, it's a take, less than that is a pass. So let's see if I can calculate GWC:
Black wins immediately with a roll of double 2s or higher for 5/36 or 13.9%
Of the 86.1% of the games where White gets a shake, she has four shakes to win so she wins 1/9th of them. This gives us our GWC for White as 86.1/9 == 9.5%
So it's a take. Barely.
The doubling decision is harder - I can calculate the theoretical doubling window, but in most positions you actually need to be better than the theoretical value for the double to be correct. In practice, this is probably a double since many players will pass as white (I wouldn't be able to do the calculation above OTB). And I'm going to say it's a double since the take decision is so close. But I'm really not sure how to calculate this.
R/T
2) My first instinct is to just maximize the chance that Black will be able to bear in both checkers next roll - that play is 12/8, leaving tho checkers as close to 2.7 points apart as possible.
But Black doesn't have to bear in both next turn. He just has to make sure that he can bear off a checker the turn after next. So I'll play 11/7 which guarantees one bear in next roll. The worst possible roll, 21, still gives Black a chance to save gammon with any 4,5,or 6 or 33 (28 shakes) while an airball after 12/8 means Black will need doubles to save gammon.
3) Black needs another checker to have decent winning chances, so leave a blot on the ace to try to force a hit. 3/1* Then 10/8 looks as good as anything else.
3/1* 10/8
4) 13 rolls miss, giving White 36.1% GWC. That's usually enough to take, but at score maybe not. Let's calculate White's takepoint
If White passes, she is 2-away 4-away or 67% MWC. If she takes and wins, she's 100% and if she takes and losses she's 2-away 3-away or 60%. So, White is risking 7 to gain 40
TP == Risk/(Risk + Gain) == 7/47 == 14.9% So it's a pretty clear take for White.
Again, the double decision is not so easy to calculate, but risking 40 to gain 7 is usually not a smart bet, so I'll say no double here.
ND/T
5) The obvious play is 3/1 2/1(2) - this ices the gammon, but wins few backgammons. Taking off two now gives White 14 shakes to hit (and presumably save gammon), but should win a backgammon when White misses.
Let's simplify and say the safe play wins 0 backgammons and 100% gammons, and that taking off two wins a backgammon when White doesnt hit and wins a single point when white does.
E1 == 2 (100% gammons)
E2 == 1*14/36 + 3*22/36 == 80/36
So taking off two gives more equity. 2/off(2).
Thanks for the patience of anyone who bothered to read this - it's more for my own practice than for others, but if you get something out of it, great. BTW, I doubt I'd be able to do this OTB.
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