The epic, ultimate non-random series
Part 1: 51 vs 42
Do you also remember the awful feeling you get if the damn Gods of Backgammon luck decide to give you the same roll twice, thrice, four times? How awkward your positions get if you roll 51, and then you roll 51, just to roll ... 51?
What would happen if we would confront the top AIs with not only this situation, but with an eternal non-random series of always the same roll? And who would emerge victorious if one side always rolls, say, 51, and the other 42?
Let's find out.
The first game is 51 vs 52. Both rolls bring you 6 pips ahead, so the game might be balanced. I have more warm and fuzzy feelings about rolling 42 than 51, so I would bet my money on "42 wins".
Here we go.
Setup
As I can't create DLLs for the life of me (which is what XG2 wants as custom dice generator), and as I was too lazy to manually roll 51, 42, 51, 42, 51, ..., I let BGBlitz play against itself, on strongest TachiAI V settings. BGBlitz can take text files that contain the rolls after each other. So I create a huge text file with endless iterations of 51 42 51 42, let BGBlitz play a money game against itself, and then analyze it with XG2 on Roller++ level (because XG has this nice PDF position export).
I'm only an advanced player (although my checker play is expert most of the time), but I'm trying my best to help interpret XG's analysis.
(btw both players are BGBlitz TachiAI V, that "andara" name is just a bad German pun)
The game. 51 vs 42
1. White 51: 24/23 13/8
2. Black 42: 8/4 6/4. So far nothing unexpected
For the next 51 white faces the first interesting situation.
My favorite move here is 24/18, doing something reasonable with the roll; I just can't imagine stacking another man on the 8 point, and as the 17 point is stripped, hitting me with an ace wouldn't be all that bad for me. It turns out that XG's top two moves both contain 13/8. BGBlitz played 23/22 13/8, and XG2 agrees to that. My 24/18 was rated as a -0.045 error. Not too horrible.
3. White 51: 23/22 13/8
Another interesting one. Black to move 42. Split the back men or not?
It turns out that 24/20 13/11 and 13/11 13/9 get exactly the same value. BGBlitz didn't split and played
4. Black 42: 13/11 13/9
(Curious, I did a rollout of this position with XG2 which was not conclusive but preferred splitting the back men by 0.008.)
Now 51 is an anti-joker with -0.42 luck.
5. White 51: 24/23 13/8
6. Black 42: 11/7 9/7
That's the nice thing about always rolling 42. You split men from the 12 point in one move and can make a point 6 away with the split men in the next move :-)
By now, white is seriously behind, and rolls another awful 51.
7. White 51: 23/22 8/3
Not much of a dispute here - sometimes there's only poor moves, and this is the least poor one. Rather place a builder on the 3 point than giving up the 13 point and improving nothing. If you're interested: XG2 ranks 23/22 13/8 worse by nearly 0.2 points.
8. Black 42: 24/22* 22/18
Just as good (-0.012) is 24/22* 24/20
9. White 51: Bar/20 8/7*
10. Black rolls another 42. Quite as expected.
Here the question is whether to move the back men only or whether it makes sense to get one man off the 6 with 6/4, distributing the attackers a bit better.
10. Black 42: Bar/21 24/22
Bar/21 6/4 is an error (-0.035), probably because it lowers the chances to make the 5 point, and with a white anchor on 3 the builder on 4 doesn't make too much sense.
11. White 51: 20/15 8/7
12. Black 42: 22/16
Trying to bring home a back man as long as there's no prime.
13. White 51: 15/9*
Now what should Black do with its 42?
Bar/21 is clear, but where should the deuce go? 13/11 or 6/4?
14. Black 42: Bar/21 13/11
The reasoning is like before: A blot on 11 is fairly save and can act as a builder for the 5 point. A 3rd man on 4 is not very useful. No blunder but a -0.064 error.
15. White 51: 9/3
In the next position it took me a while not to blunder seriously.
16. Black 42: 13/9 11/9
(11/5 would have been a -0.25 blunder)
17. White 51: 13/12* 8/3
18. Black 42: Bar-21 6/4
No other option for the deuce if black wants to keep its prime.
Now white has many similarly good moves for its 51. Can you find the best one?
Obviously, white wants to unstack its 6 point and do something about the two blots who can be hit with 8 numbers out of 36. But should it slot the 5 point?
I didn't find the right move, went for 13/8 6/5 (-0.008, okay, I'm fine with that). The best move, is, unexpectely for me, the totally conservative
19. White 51: 13/12 6/1
It achieves the two goals, but at what price? No flexibility anywhere, and a man on the ace point?
20. Black 42: 6/2 4/2
White again faces a difficult decision.
So, which one is it?12/11 6/1? 6/5 6/1? or maybe 12/7 6/5 or even the save but passive 6/1 3/2?
BGBlitz played 6/5 6/1 and XG says everything else is a 0.050+ error.
I must confess that I'm still not entirely sure what's going on here. The dice distribution shows that 6/5 6/1 isn't that bad, because many rolls where black hits on the 5 cause it to give up the prime, for example a 21. Therefore XG believes only 6 black rolls are really bad for white (14, 15, 16) because it allows the checker to hit and escape. Others like 12, 13 are not a big deal.
On the other hand, if white would play 12/11 6/1, then every roll that hits on 11 or 12 is horrible for white. And there are 8 of them. And while 6/5 3/2 doesn't leave a blot, it gives black much freedom to improve its position because of the two blots in black's home.
21. White 51: 6/5 6/1
22. Black 42: 8/6 8/4
9/7 9/5 would keep a three-point prime but 21 and 22 are just too horrible. Blunder (-0.12)
And 51 proves again to be an awful roll. What to do now?
You can't cover the blot, and you can't move it out of danger. What's the best option?
I would actually have played 12/17 6/5; this gives me two builders for my blot on 6 in the next roll. Would be a small error (-0.038). The best play is
23. White 51: 12/6
Maybe because there's no double hit like with 12/11 12/7 (second best move, -0.018)
24. Black 42: 9/7 9/5
The alternative 6/2 4/2 is very ugly but so safe that it's only very slightly worse (-0.007).
25. White 51: 22/17 6/5
With black's blot on 20, now is a good time to try to escape. The alternative of 12/7 6/5 misses an opportunity and is a -0.15 blunder.
Now, all of a sudden, white is a favorite to win the game.But we all know the nice roll it's going to get
26. Black 42: 7/3* 5/3
Position after Black's move
And black is back.
27. White 51: Bar/20 12/11
The rule of thumb "the further away the blot in an indirect hit, the better" doesn't apply if a prime is in-between. Here black can hit white on 12 with 53, 62, and on 11 with 52, 61. And on 11 it has more safe landing points in the next move (at least that is what I - fairly clueless - believe the reason for this move to be).
28. Black 42: 7/3 7/5
29. White doubles.
If I can trust XG2's analysis and rollouts, then sometimes BGBlitz doubles poorly. Seems to be the case here. XG2 says "no double/take", doubling being a 0.077 error (XG rollout). And this is a daring double, against a 4 point board.
29. Black takes.
29. White 51: Bar/20* 17/16
Obviously, Bar/20* 11/10 is worse, 4/10 is a direct hit.
30. Black 42: Bar/21 3/1
Clearly the best move. Bar/23 doesn't have a single roll past white's prime; 3/1 starts a fifth point in black's home.
31. White 51: 20/15 16/15
32. Black 42: 6/2 4/2
33. White 51: 15/10 11/10
34. Black 42: 6/4 6/2
Black's board crumbles.
Now, white faces a number of interesting candidates for its next 51. Can you find the best one? I couldn't.
35. White 51: 7/6 7/2
My explanation (do you have a better one?): 15/9 leaves a direct hit which isn't reasonable given white's fairly big racing lead (-0.061). My choice, 8/7 8/3 doesn't slot an additional point and doesn't have any significant advantage over the best move (-0.053). I just happen to hate these point/empty/point/empty/point structures.
36. Black 42: 4/2
According to XG, this is slightly worse than 3/1.
37. White 51: 8/2
Makes the 5-point board and keeps the 15 point to keep an extra hit chance in case black wants to escape. Given black's weak board the blot on 8 is no big deal, and keeps gammon chances.
I must confess that I would have played 15/8 6/5 without thinking here (a -0.1 blunder!); I didn't see that this is now about a gammon vs. no gammon. With the stopper on 15, the gammon chances increase significantly (8/2: 88% win rate, 24% gammon, compared to 15/8 6/5: 89% win rate, 12% gammon)
38. Black 42: 21/17 3/1
39. White 51: Bar/20 6/5
40. Black 42: 21/17 3/1
41. White 51: 20/19 15/10
Now black (42) can either crunch his board even more (17/13 4/2) or risk two different direct shots against a five-point board (17/11).
The crunched board is bad, but not that bad.
42. Black 42: 17/13 4/2
And another unlucky 51 roll for white.
The 5 is clear: 10/5. But what to do with the 1? Move the back checker on the 19 into a direct hit at 18? Destroy the 5-point board with 3/2 or 2/1? Or something else?
I didn't find the best moe. I would, actually, never have selected the best move. Also, BGBlitz didn't find the best move. And I had to roll it out to believe it.
The best move would have been: 10/9 10/5, leaving two blots, either to a double shot from black, on 10 and 9, and another indirect hit on 19. Wow. The stuff you can do if you have a strong board and your opponent's board is crunched. But BGBlitz played what I would have played (please note: after rolling out the position the difference between BGBlitz's move and the best move is a measly 0.007).
43. White 51: 19/18 10/5
44. Black 42: 17/13 4/2
45. White 51: 10/9 10/5
18/13 3/2 would have been safer, but reducing the gammon chances significantly.
46. Black 42: 13/7*
47. White 51: Bar/20 9/8
48. Black 42: 13/7
Slightly better than 7/5* 5/1.
49. White 51: 20/19 8/3
XG recommends 20/15 8/7, but the differences are minimal (0.001 after rollout)
50. Black 42: 7/5 7/3
I'll end this game here; white kept its lead but couldn't prevent black from running home its back checkers. White won a single game.
Result: 51 beats 42 (51 starts) :-)
Alternatives...
In move 26, there was an alternative to black's 9/7 9/5: Play the ugly but save 6/4 6/2. Actually this is what XG Roller++ would have played, but the game ended boringly after
27. White 51: 22/17 6/5
28. Black 42. 7/3* 3/1
29. Double/drop
and white wins.
Up next?
I was not sure whether rolling always the same roll can lead to a reasonable game. But this was not all bad. Of course, the AIs, despite their I in the name, never considered that the next move of their opponent might be 41 or 52, and that therefore this blot 3 away would actually be safe.
Up next: 42 vs. 51.
And then? What rolls do you think could lead to interesting games? Looking for input.
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