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Lots of votes to make the bar here, but it is wrong. 13/4 is the play. Typically, you don't want to make points that you will have to clear later and it is worth taking a small risk now to avoid later problems. That's enough to justify 13/4 on its own, but there is more. If we can pick up another checker on the way home it has to increase our gammon chances. 13/7, 10/7 is an awful play!

having been the victim of every available joker recently, i  chose the bar point, but also also because of a future 55 we may roll

We can  make the bar point or we can run either checker home.  

Running the back checker leaves 55 and 52 as shots, while running the other leaves only 55 as a shot.  Leaving one checker behind gives us the chance to pick up another blot.  Is the added gammon chances worth the added risk?  

Making the bar point pretty much ices the win, while still leaving good gammon chances.  Only 62  would be a bad roll for us (although 22 would be awkward.)

Over the board, I'd almost certainly make the bar point.  I'm not sure it's correct, but I like the almost sure thing.  
13/7 10/7

Quote from: dorbel on September 01, 2009, 09:40:23 AMLots of votes to make the bar here, but it is wrong. 13/4 is the play. Typically, you don't want to make points that you will have to clear later and it is worth taking a small risk now to avoid later problems. That's enough to justify 13/4 on its own, but there is more. If we can pick up another checker on the way home it has to increase our gammon chances. 13/7, 10/7 is an awful play!

Agree that you don't want to make points that are hard to clear later, but it won't be hard to clear the bar point.  Any roll without a 2 will clear it, and only 62 is actually bad.  Compare a 2/36 chance of us getting a bad roll next time, vs a 3/36 chance of being hit immediately if we play 13/4.  Plus, rkb is 25/36 to remain on the bar, so our "bad" 62 will most likely only offer an indirect shot with 5/2.  Meanwhile, 13/4 leaves us open to it's own bad roll - 65 will leave a direct shot.

So, I don't see 13/4 as being safer. The only reason I can see to play it is to pick up another blot, and with 4 of rkb's men back, I think we have enough.

Why are we so worried about fly shots? White's board is in poor shape and unlikely to improve soon, so even being hit with a fly shot and dancing (8.25% x 44% = 3.3%!) is hardly a disaster. Even so, it is a small risk so why take it? Partly of course to try and pick up another checker, but mainly because clearing the bar without any spares is trickier than you might think. All the twos play badly (check through them for yourself) and all the ones stack a spare on the 6pt, delaying the time when we can safely clear that.

This problem more often occurs in the form where you still have an outfield point to clear. If you make the bar point here, how do you play 4-2 if White stays on the bar? Clearly it is correct to play 7/1 and risk the indirect and in this slightly different form it is correct here too. Of course we may never throw a number that involves any risk at all, but you can't rely on that. Taking very small risks while the opponent is still on the bar pays dividends.

Quote from: dorbel on September 01, 2009, 06:00:18 PM
Why are we so worried about fly shots? White's board is in poor shape and unlikely to improve soon, so even being hit with a fly shot and dancing (8.25% x 44% = 3.3%!) is hardly a disaster. Even so, it is a small risk so why take it? Partly of course to try and pick up another checker, but mainly because clearing the bar without any spares is trickier than you might think. All the twos play badly (check through them for yourself) and all the ones stack a spare on the 6pt, delaying the time when we can safely clear that.

This problem more often occurs in the form where you still have an outfield point to clear. If you make the bar point here, how do you play 4-2 if White stays on the bar? Clearly it is correct to play 7/1 and risk the indirect and in this slightly different form it is correct here too. Of course we may never throw a number that involves any risk at all, but you can't rely on that. Taking very small risks while the opponent is still on the bar pays dividends.

I can't say I'm terribly worried about the fly shots.  I was more concerned about the 65 after playing 13/4.  Or at least equally concerned since it's also a low-probability event.

But I see where you're going here: all 2s play poorly after making the bar point. The only rolls that play poorly after 13/4 are 65 and 55 (and 55 is not that bad).  Us rolling a 2 is far more likely than rkb rolling one of the three jokers or us rolling one of the three anti-jokers.  So you may be correct that 13/4 brings the checkers home more safely.  I'm not entirely convinced, so I'm not changing my vote, but I'm also far from certain that making the bar point is best.  

I just want a shot at the second blot and to assure a gammon

I think making the bar point is pretty clear here. Even though small, getting hit is potentially devastating. We'd be trying to scramble home with all our other checkers out of play.

It's not even clear that we have to hit another blot to win a gammon here; he's buried in the race with 5 checkers to bring home. It's true that 2s are cumbersome, but there's always an awkward roll..........13-7, 10-7.

I think Bagai has an addage that says that typically you have the most to gain from Gammonish plays when the gammon rate is closer to 50%. If this is applicable, given that we have strong gammon chances (say over 30%?) and we're gammongo suggests that we shouldn't let up.

Just wondering if any of those in favour of 13/4 have any strong views against 10/1? I was quite partial to it, but once I saw the vote I went with my closest 'thematic' equivilent' (albeit with much more stress on gammongo, then long run bear in safety).

I realise the 13 point means we have further to go, and we're no means guaranteed to get by in one throw (But we are still  favourite to get home without getting hit - and even when hit, the setback isn't fatal as long as Rkb's 6 point is open).

On the plus side, 10/1 minimises first round fly shots (1 vs 3, which in 1296 games, first round hit minimisation results in 72 fewer hits on the fly. I didn't do the maths/counting but it didn't seem clear to me that this would be overturned given the parley necessary...) and provides a greater chance to pick up a second blot.

Any thoughts?

Well, the way I see it is, after 13/4 White has only a 30.6% chance of coming off the bar and needs the luck of the Devil to hit us, only an 8.6% chance.  And if that happens, we are more likely than not to re-enter (56.6% chance).  We'd still be ahead in the race, with possibilities of then picking up 1 or more chequers as we come round.  We're trailing 0-2 in the match and I rather like the idea of finding ourselves 4-2 up, so playing 3/4 and increasing our gammon chances gets my vote.

I thought about 10/1 but rejected it as likely to make the safe clearance of our 6 point more difficult.

The question about playing 10 - 1 caused me to take another long look at the position. First, I think 10-1 is pretty bad and would reject it. Then I spent another hour mentally playing the original 2 alternatives. I think now that making the bar point is inferior, the inflexibiliaty of the 2s is pretty rough. I change my vote.

A very  interesting position, perhaps the best puzzle we've had so far.

First, 13/4 is definitely the superior play. Props to Dorbel for pointing it out and swaying the forum. I'm glad we made the best choice rather than my choice. 

But I don't think it's best for the reasons given above.  Making the bar point wins more games, despite the awkward 2's, so 13/4 doesn't appear to be the safest way to bring the checkers home.  We can see this from the second rollout, where I set the match score to 3-3 - with gammons off the table, making the bar point is a .036 (1.8% MWC)  favorite to win.

The reason why 13/4 is so favored is the increased gammon chances (57.5% vs 50.4%) despite losing more games (7.4% vs 4.8%).  The magic "twice as many gammon wins as losses" threshold is crossed. (actually, the factor is somewhat less than 2 at this match score, but let's not get too technical here)

Despite getting it wrong, I don't feel too bad about picking the inferior move - it leaves us a better than 95% chance of winning and a better than 50% chance of gammon and I'll take that any day.




    1. Rollout          13/4                         Eq.:  +1.705
       0.941 0.575 0.004 - 0.059 0.001 0.000 CL  +1.719 CF  +1.705
      [0.001 0.002 0.000 - 0.001 0.000 0.000 CL   0.004 CF   0.004]
       
    2. Rollout          13/7 10/7                    Eq.:  +1.629 ( -0.076)
       0.956 0.504 0.001 - 0.044 0.003 0.000 CL  +1.640 CF  +1.629
      [0.001 0.002 0.000 - 0.001 0.000 0.000 CL   0.003 CF   0.004]

    3. Rollout          10/1                         Eq.:  +1.594 ( -0.112)
       0.914 0.542 0.003 - 0.086 0.006 0.000 CL  +1.613 CF  +1.594
      [0.001 0.002 0.000 - 0.001 0.001 0.000 CL   0.004 CF   0.005]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 867695693 and quasi-random dice
        Play: 0-ply cubeful prune [expert]
        Cube: 0-ply cubeful prune [expert]



Rollout at match score 3-3

    1. Rollout          13/7 10/7                    Eq.:  +0.913
       0.957 0.696 0.002 - 0.043 0.004 0.000 CL  +0.913 CF  +0.913
      [0.001 0.009 0.001 - 0.001 0.001 0.000 CL   0.002 CF   0.002]

    2. Rollout          13/4                         Eq.:  +0.877 ( -0.036)
       0.939 0.711 0.011 - 0.061 0.003 0.000 CL  +0.877 CF  +0.877
      [0.001 0.008 0.002 - 0.001 0.001 0.000 CL   0.002 CF   0.002]
       
    3. Rollout          10/1                         Eq.:  +0.827 ( -0.087)
       0.913 0.685 0.009 - 0.087 0.007 0.000 CL  +0.827 CF  +0.827
      [0.001 0.008 0.002 - 0.001 0.001 0.000 CL   0.002 CF   0.002]
        Full cubeful rollout with var.redn.
        1296 games, Mersenne Twister dice gen. with seed 867448849 and quasi-random dice
        Play: 0-ply cubeful prune [expert]
        Cube: 0-ply cubeful prune [expert]

I found this very interesting too...in all the cases where I have set up the poll, I have had to use gnu hint to make sure I covered all the options - and in doing that you see which move it picks as best.

To get around this problem, I have studied the position before using hint and decided on my move.  I then vote for that but stay out of the discussions.  In this case I saw the best move was 13-4, but had picked to make the bar point. 

Seeing how the vote went I still felt really strongly that I would make the bar point, but have really enjoyed seeing the discussion unravel - and felt I have learned something from this move.