Problem of the Week #148: July 29


Cash game, Black owns a 2-cube.




Black to play 1-1. Where does the blot belong?



Note: All ‘cash game’ problems assume the Jacoby Rule is in effect. That is, you can’t win a gammon unless the cube has been turned.

The obvious part of the answer is "not where it is now" because the rolls that crack the midpoint by force hit you. My gut is that minimizing the direct hits (18/14) is going to be correct because if he keeps the midpoint intact next turn, you're always hopping it to play the race if you can. Ignoring the combos where the path isn't settled after our next roll (he's hit, we've hit, no-contact race), each pip we stay back increases his shot-leaving rolls by 1 (an additional 6-x) and adds at least 1 direct hitting number. Since the additional direct hit is 2-3 times as important as the additional shot (it picks up ~.5 equity over the race when it's rolled, whereas we only hit 1/3-1/2 of the time when the shot-leaving number is rolled and race the rest). It's hard to imagine the funky combos can ever make up for that.

18/14

In a dead heat race like that and 2 closed boards, getting hit is just lethal. Black owns the cube, so doesn't have to worry about being cubed next turn.

White won't expose a blot unless he has to (any 6 but 6-6), he will crunch his board and play the cat and mouse game.

Since any 6 but 6-6 is bad for White, Black can't leave the blot there for sure, since it would then make those 6s good. You want to avoid being hit at all costs, so why not minimize shots against him with 18/14? Maybe 18/15 5/4 would be a good middling play. Leaves only two more shots but gives him a shot to a blot more often when White doesn't hit and leaves a blot behind (6-1 vs 6-1, 6-2). Is it worth it? I don't think so.

18/14

Edit: I like how TomCowley phrased it.

I play 18/14 here, I can't see anything else that makes sense to me.

I have worked myself through the 147 problems now, and i must say they are really tough. And as far as most of the doubling decisions concern, i rather throw a coin.
With this foreknowledge, i am sure that 18-14 is not right. So it must be something else.
After 1-1 white has a slight racing advantage. Now if black is in a naughty mood, he could stay. White will have to break up his board if he does not hit, and can't double out. If black throws a low number for a second time, he could remain on the 18 point for a second time.
If white hits he now has a little hole of opportunity to hit back with his closed board, and if white does not hit, white has to break up further, or leaves a blot even . The incentive to stay with uncooperating dice could become everytime stronger, and the doubling cube could do the rest.
Now on the 17 point this strategy is still a lot stronger, because white will leave a blot with every six, except 6-6, 6-5. So my choice is 18-17.
I didn't try this out over the board, but it could be a step in the right direction.

z=1/36 not hit * shot * hit shot fyi if no hits, black cant break contact
18-14, 24z 2z 12z = 576zzz, 4z 11 22 12
18-15 22z 4z 14z = 1232zzz, 4z 11 33 12
18-16 21z 6z 15z = 1890zzz, 7z 11 44 22 12 31
18-17 21z 8z 15z = 2520zzz, 10z 11 55 12 13 14 23

So is 18-17 the best over 18-16, I vote for 18-17 based on higher numbers are good for black anyway

otb play 18/14 without much thought but curious to learn if/why this is wrong as it opens up a series of perms I don't usually give that much thought to.

OtB I would play 18/14 to leave the least shots and play for the race.

Quiz factor and cube position tells me something else could be going on. 18/16 6/4 could be a choice leaving a bit more shots, but having benefits of its own. Only 66,55,33,65 get by the blot with both midpoint checkers and if he doesn't want to crash his board there are about 22 rolls that makes him leave blots. Maybe some of these variations (considering activated gammons and cube ownership) could tip things in favor of some middling play, but I would never come to it OtB.

I would play 18/14 without even thinking about it.
I guess I'm going to find out why this is wrong?

Whoever has a blot exposed is an underdog so 18/17. Make white expose a blot or lose ground in the race.

Hm 18/14 what else? The dangerous thing about this is i wouldnt even think a second about this move otb...

Lol. Indeed.

Before he plays this 11, Black trails by 2 pips, 71 to 69. When White gets the dice, White will trail by the same 2 pips. So the race is not quite tied. Were White on roll trailing by 4 pips, it would be a tie. White has buried a third checker, so the EPC (effective pip count) is even closer. That should be a sign for Black that safety is not his only concern. If he were substantially ahead after this roll, say 12 pips or more, he could opt for safety. Then he would play 18/14, and risk the minimum 12 shots.

Let’s look at some numbers.

Black Blot on 18pt

• 17/36 — White hits: 61 62 63 64 65 66 51 42 33 22
• 00/36 — White leaves shot: never
• 03/36 — White runs past Black, or safely advances: 55 44 11
• 16/36 — White retains the midpoint: 54 53 52 43 41 32 31 21

Black Blot on 17pt

• 15/36 — White hits: 51 52 53 54 55 56 41 32
• 08/36 — White leaves shot: 64 63 62 61
• 05/36 — White runs past Black, or safely advances: 66 44 33 22 11
• 08/36 — White retains the midpoint: 43 42 31 21

Black Blot on 16pt

• 15/36 — White hits: 41 42 43 44 45 46 31 22 11
• 06/36 — White leaves shot: 63 62 61
• 05/36 — White runs past Black, or safely advances: 66 55 33 65
• 10/36 — White retains the midpoint: 53 52 51 32 21

Black Blot on 15pt

• 14/36 — White hits: 31 32 33 34 35 36 21 11
• 04/36 — White leaves shot: 62 61
• 10/36 — White runs past Black, or safely advances: 66 55 44 22 65 64 54
• 08/36 — White retains the midpoint: 52 51 42 41

Black Blot on 14pt

• 12/36 — White hits: 21 22 23 24 25 26 11
• 02/36 — White leaves shot: 61
• 16/36 — White runs past Black, or safely advances: 66 55 44 33 65 64 63 54 53 43
• 06/36 — White retains the midpoint: 51 41 31

Hanging back gives White more hits, but also makes it harder for White to play safely. The problem is that being hit is nearly fatal. From the bar, Black can expect to win only 4% to 5% of all games. By staying back on the 16pt, for instance, Black is surrendering an extra hit in 8% of the games. Can he make up those losses by delaying White for one extra roll during the bear in? Remember that Black is delayed, too, when he hangs back.

I have seen the bots hang back, leaving at least a 1pt gap between a trailing blot and an opponent’s made point in the outer board. With the race this close, and facing a closed board, I don’t want to be any farther back than that.

My solution: R (Run) = 18/14.

For the Record
I am so often wrong that I like to post my record in these messages. It's kind of a truth-in-advertising thing. Grunch: I have been answering these problems without the use of a bot, and before checking the excellent solutions of others, since Problem 28. My record at this writing is 53%.

Thanks for the numbers, Taper_Mike.

Based on them I also say 18/14. Since we are dead if we're hit, I guess the priority is to decrease the chances of White hitting us and increase the chance of passing through opponents pieces.