First, here's the original position posted on Facebook from Joshua Riddell that you can tackle before scrolling down where there will be spoilers/rollouts.
                        |
| ||||
| XGID=--BBB-C-C---cBb---bccb-A--:1:-1:1:13:0:0:0:7:10 | |||||
| Blue to play 13 | |||||
eXtreme Gammon Version: 2.10
There is bound to be a lot of rambling many of you don't need so feel free to skip to the rollouts. (TLDR) However, if you want the entire reasoning and process behind breaking down a problem read on.
First, it's a pet peeve of mine to post something that could be posted for money at some score where it won't matter. Why? Because what do we really want to know here? We want to know what the correct play is in general and while in general will equate to 7a 7a even with the cube turned about all of the time for checker play it introduces a variable we don't need introduced. It makes people like myself have to do double work to make sure the score has no effect. I realize the position arose at 7a 7a so it's easiest to copy & paste and present as is but it would be better for such scores where it's a checker play to make it unlimited and call it a day.
Next, the position itself. Let me assure you that I make the 5pt and I made it rather quickly ... and you should too. That's right, the geniuses who got this correct in the FB thread (Hi Neil! Hi Wil!) I would argue should have also made the 5pt even though in this case they got it right and I got it wrong.
I will delve into the actual analysis now far more than I did at first glance. Let's start with stepping up, 23/22 8/5.
- Great numbers: [55 44 43 42 32 22] While [11] technically is a pointing number, it switches and not makes it outright, so I won't include it in this set of rolls because I'm only concerned with the best of the best. That's 9/36ths of the rolls where we are on the bar against the best four point board and if we don't perform almost immediately it will be lights out. Also, those few times we do hit back either immediately or a roll or two down the road, we will still have that annoying blot on our 5pt.
- Solid numbers: [66 33 11 53] As you can tell, depending on the roll it either makes the 5 prime, switches points, or is simply a buttload of pips that we'll happily accept. That's 5/36ths of the rolls.
- The rest: 22 numbers left. These vary a little in equity obviously because something with more pips or something that hits off the front of the prime is better than a complete dud but overall I'm lumping them into the same category. Everything of course leaves us a clear favorite as we have a close race with the opening having his checker trapped behind a solid four prime with not too many clean freeing rolls.
Now we turn to making the 5pt, 8/5 6/5. It needs to be directly compared to the above.
- Great numbers: [66 55 44 33 53 43] I am including [43] but not [54] because while [54] does point on his 2pt the same as [43], it leaves four indirect shots which are absolutely crushing. Also not included is [22] even though it switches as it's a weaker switch in my eyes. 8/36.
- Solid numbers: [54 32 22] 5/36.
- The rest: 23 numbers with the same stipulations as stepping up.
So on the surface it seems like they should be close with the slight edge if there is one going to making the 5pt straight out. What we have to remember though is that "the rest" is a lump of what are average rolls for that particular group of rolls. In other words, it's entirely possible that the grouping of the rest after making the 5pt has a lower equity than the grouping of the rest after stepping up and slotting the 5pt.
Other than the extra vig I get out of trying to give Neil and Wil a hard time, why should we be making the 5pt when the rollouts below show the correct play to be stepping up?! Because you aren't good enough. I know I'm not good enough and I was able to do all that garbage you read above, separating accurately the rolls into different groups to arrive at a general consensus of what was going on. Even with that I'm still left shrugging my shoulders not knowing for sure.
By making the 5pt we are, at worst, making a small error.
This of course makes some assumptions that you're a decent enough player to realize when Play B in a position is screaming out to be made over making the 5pt. When you're at a crossroads though between making the 5pt and Play B, make the 5pt. I've seen countless times in my own play and countless times cubed in other people's play where they make Play B and BAM! BLOOD RED. In the few spots where making Play B was correct making the 5pt was a small error at most.
Here are the rollouts. First AtS (7a 7a), unlimited, and dmp. They are all rolled out on the same settings with the same seed. (5184 trials) You will notice that 7a 7a and unlimited are very close in their results but not exact. I don't need that noise. Lastly, I included an unlimited rollout with moves and cube XGR++ to see if there was likely to be any difference due to the level of play in playing it out. It's only 1296 trials because it takes quite a while until I get a new computer. It shows there is really no difference. (as we would expect) There will be at least one more paragraph after the rollouts so don't miss it.
Original (7a 7a)
|
| ||||
| XGID=--BBB-C-C---cBb---bccb-A--:1:-1:1:13:0:0:0:7:10 | |||||
| Blue to play 13 | |||||
| 1. | Rollout1 | 23/22 8/5 | eq: -0.550 | |||
| ||||||
| 2. | Rollout1 | 8/5 6/5 | eq: -0.570 (-0.020) | |||
| ||||||
| 1 5184 Games rolled with Variance Reduction. Dice Seed: 38374579 Moves: 3-ply, cube decisions: XG Roller | ||||||
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
Unlimited
|
| ||||
| XGID=--BBB-C-C---cBb---bccb-A--:1:-1:1:13:0:0:3:0:10 | |||||
| Blue to play 13 | |||||
| 1. | Rollout1 | 23/22 8/5 | eq: -0.546 | |||
| ||||||
| 2. | Rollout1 | 8/5 6/5 | eq: -0.568 (-0.022) | |||
| ||||||
| 1 5184 Games rolled with Variance Reduction. Dice Seed: 38374579 Moves: 3-ply, cube decisions: XG Roller | ||||||
eXtreme Gammon Version: 2.10
DMP
  |
| ||||
| XGID=--BBB-C-C---cBb---bccb-A--:0:0:1:13:0:0:0:1:10 | |||||
| Blue to play 13 | |||||
| 1. | Rollout1 | 8/5 6/5 | eq: -0.312 | |||
| ||||||
| 2. | Rollout1 | 23/22 8/5 | eq: -0.314 (-0.003) | |||
| ||||||
| 1 5184 Games rolled with Variance Reduction. Dice Seed: 38374579 Moves: 3-ply, cube decisions: XG Roller | ||||||
eXtreme Gammon Version: 2.10, MET: Kazaross XG2
Unlimited XGR++
|
| ||||
| XGID=--BBB-C-C---cBb---bccb-A--:1:-1:1:13:0:0:3:0:10 | |||||
| Blue to play 13 | |||||
| 1. | Rollout1 | 23/22 8/5 | eq: -0.551 | |||
| ||||||
| 2. | Rollout1 | 8/5 6/5 | eq: -0.573 (-0.023) | |||
| ||||||
| 1 1296 Games rolled with Variance Reduction. Dice Seed: 38374579 Moves and cube decisions: XG Roller++ | ||||||
eXtreme Gammon Version: 2.10
Did we notice at dmp the results turned to making the 5pt? Now that isn't important concerning who would have got it right/wrong because it's a tiny error even for dmp. The point of it is that nobody who got this play correct in the original position would have been able to give you the proper explanation as to why it is right. It seems to be because of the jumbled gammons won/lost tradeoff. Stepping up will force more immediate hitting situations which both wins and loses you a certain amount of gammons more than quietly staying back.
Stick