I am not a master, just a patzer, but this isn't true. The masters rely heavily on engine analysis in their prep and in their evaluation of their play post game. They certainly run the game through an engine and extensively analyze it based on advice from the engine. They may disagree with certain moves the computer suggests if those move rely on some super deep calculation that isn't humanly possible, but in general they respect the advice of engines.

I have very little else to contribute to this thread as I don't feel qualified to question the advice of XG. If it tells me to double I am going to assume doubling was the best play and try and learn why I didn't make it. I think it takes everything you are saying into account up to 3-ply when it makes it's evaluation.

Thanks again. While strong chess players rely on bots to ASSIST them in their study, they don't just trust them out of hand. One of the main uses strong players like Caruana make of bots is having a team of seconds search for positions that the bots get wrong. The other use is more like what I think you were thinking of, looking for positions that the bots say are even but the inferior side needs to play 'like a god' to hold the draw. The bots are obviously not infallible or in bot v bot games they both wouldn't chalk up wins or in BG people wouldn't run rollouts on complex positions of timing.
I noticed I didn't give my reasoning earlier. It seems reasonable to assume that a game where one player misses good double/take opportunities several times in a row is probably, but not certainly, a low volatility series of positions.
If a human player was 200 elo better than XG, demonstrated by winning around 75% of their matches (75% is from chess not certain what the exact number is for BG) over a long series of matches, XG analysis would insist that the player played like an idiot and was very lucky. XG's standard is itself. If you disagree, even when you're right, it considers you wrong unless it failed to examine your play and upon deeper analysis sees that it is in fact better.
I don't think I'm better than XG. When it tells me I made a checker error I usually agree instantly. I usually didn't even consider its move. But acknowledging that it is better is different than accepting that it is infallible. I get outplays sometimes. Not as often as I get blunders but sometimes
Regarding cube decisions you could be correct as I can't always understand what XG is telling me when it is right there to study.

I forgot the best situation. It is currently a double/drop but not quite a too good to double position. Even though you can currently mark up the win by taking the double/drop route (which has a positive equity) if there is less chance of dropping into the double/take range than there is of moving into the too good to double range nothing is lost by waiting until next roll. In essence you are too good for a double/drop. You can allow your position to deteriorate somewhat and still have a double/drop. If you are 95% to win and wait until next turn and your probability of winning drops to 80% you have lost nothing by waiting, you get the same one point for cubing now that you would have gotten last turn.

That is just not a thing. If it were "too good to D/P", then it would just be too good. That's literally what too good is. If you're supposed to cash in, then that your position is simply not worth more than 1 point - ie there IS more to be lost by waiting then there is to be gained. If there weren't, it would be too good!

Sorry, I disagree. Your equity when you are too good to double is > 1.0. You have a double/drop if your equity is .75 < equity < 1.0. If your current equity is .95 you are not too good to double. If the probability of your equity changing to > 1.0 is greater than the probability of it falling to < .75 then you are correct in waiting to double. All equity values between .75 and 1.0 are equal as you can double your opponent out. If your equity falls from .95 to .76 you have lost nothing while if it grows to greater than 1.0 you should play on. If it is still between .75 and 1.0 after the next set of rolls you reassess. I would guess that with a current equity of .95 the probability of it dropping to about .9 would be the same as the probability of it growing to about 1.0. Granted there would be an array of values but that should be very close or the current equity wouldn't be .95. That leaves a significant amount of wiggle room justifying waiting to see what happens rather than doubling your opponent out. I'm not saying that doubling your opponent out is a mistake. I'm saying that you have a valid choice. I haven't looked at backgammon for 20 years. That was the math back then. Has someone refuted it since I last studied?

If you are correct to play on, then your equity will be, BY DEFINITION, >1.0. I think that you are conflating win % and equity, since you are claiming that equity .76-.99 is a double-drop.

The double decision and the take decision are two separate things. If a position is correct to double, that simply means that the equity of the position increases by the turning of the cube. That can happen either because you get to cash in OR because you're forcing your opponent to play a bad position for higher stakes. If it is incorrect to double, that simply means that, by the turning of the cube, the equity in the position goes down. That can be because EITHER your position is not good/not volatile enough, OR because you are too good due to the chances of winning gammons as compared to losing chances (this is somewhat simplified but should suffice) As for the take decision, it is correct to take if the equity, after taking, is <=1.0. If the equity after taking is >1.0, then it is a mistake to take, but that in and of itself has nothing to do with the D/TG decision.

On a related note, contrary to another point you made, the chances of various equity chances are not linear. Some positions are MUCH more volatile than others, and doubling is one way we cash in on volatility.

Firstly, I didn't say that equity/winning percentage was linear. I very specifically said that it wasn't. I said that the variance from .95 would be roughly in the range of .9 - 1.0. It is actually the probability * the value so the values below .9 would need to have a lower probability of occurring than the values above 1.0 for the current value to be .95. It is an average. Technically the variance isn't relative it is just an understandable way to state the reasoning. What actually matters is the count of cases where it improves to above 1.0 and the count of cases where it deteriorates to a below .75 (taking into account that some of the below .75 cases may be gammon losses) as all cases from .75 to 1.0 are equal.
Secondly, where do you get that winning percentage doesn't equate to equity? What is your equity when you have a winning percentage of .74? By your reasoning I guess you would say that it is ~98% (assuming there is a reasonable amount of volatility in the position, I included this again just for you). And I guess that you would say that your equity hits a plateau of 1.0 while your winning percentage is any where from .75 to 1.0 and then starts moving into the to good to double range. If that is the case I'll stick with my understanding.
Lastly, I'm sorry if I didn't include a caveat about volatility in every sentence. The repetitive inclusion makes any discussion unreadable and is normally left to the reader to understand. A single reference should suffice.

You're welcome to get defensive and be a **** if that's the only way you know how to communicate. I was trying to nicely inform you of some areas where your understanding is just plain off. I'm done now as I have better things to do for my mental health than continue this.

Sorry you took offense. I was just pointing out that you were misrepresenting what I said and quibbling over semantics.

P.S.
So as not to confuse anyone. Adept was correct in saying that I was misusing the world equity. My statement/accusation (as he apparently took it) that he thought a winning percentage of .74 was about an equity of .98 (with the cube centered, it drops to about .66 [1/3 * 2] if you pass the cube) all things being equal, is correct. The numbers not necessarily his opinion as he didn't actually make it known.

If I understand him correctly, Alexander is claiming that the PR calculation tends to favour whoever has fewer decisions. I think it’s worth engaging with this claim in a bit more detail.

As Alexander points out, having very few decisions can harm you a lot. In particular, if you play worse than usual, and then don’t get any more decisions (e.g. because you are on the bar), then your PR will be higher than usual. This is true, but misses the fact that having few decisions can also help you! In particular, if you play *better* than usual, and then don’t get any more decisions (e.g. because you are on the bar), then your PR will be *lower* than usual.

How does this average out? We need assumptions to answer that, but it seems reasonable to view a player’s equity loss each move as independent draws from a fixed distribution. In that case, it’s easy to show that one’s expected PR is completely independent of the number of decisions! On the other hand, having a small number of decisions does inflate the variance of one’s PR.

In summary: having a small number of decisions does not reduce your PR on average. However, it does make it more variable.