Do you play safe or hit, thereby leaving a blot?

What possible advantage is there to leaving a blot? Gammon chances are minimal and you're already a big favorite.

5/2 4/3*

Yes, you are leaving a blot, but you are making your own 5 point board. Your opponent has 11 numbers to stay in this game. Even of those 11 numbers he does not win all of those games, as you will have 11 immediate numbers right back. If you come in immediately, you are a slight favorite. So let's assume he wins 8 to 9 of those games after he hits.

Additionally, while the gammon chances are small, there are some gammon chances when you hit. He can fan then you have 20 numbers to cover the blot. And if he fans for several rolls after you start clearing, you can win a gammon. Even if you only win 2 gammons in 36 games, this gives you the value of roughly winning 28 - 29 of 36 games.

Playing safe has it's own problems. You are only up 11 pips and only rolled 4 pips and buried another checker on your ace point, which would average 2 more wasted pips in the bear-off. After his average 8 pips, he would be within the doubling window if the cube was still centered. Meaning he will win at least 9 of 36 games in a race.

Hitting is the +EV play, with greater variance since the gammons go up 8x for both sides.

A more interesting set of questions is:

What do you do at 5-0? 0-5? 5-5?
Does it make a difference if it's a money game, not a match?

Here are some possible advantages to hitting and leaving a blot:

1) You win some gammons. If you play safe with 5/1, your gammon chances are nearly zero. If you hit with 5/2 4/3*, Black will dance 70% of the time and you'll win a few gammons. Not a huge number, but probably in the 10% range. That matters.

2) When he dances, you gain enormously in the race. If you play safe he'll trail by 15 pips, but he's on roll and owns the cube. His winning chances are far from trivial. When you hit and he fans (again, 70% of the time) his winning chances do drop to nearly zero.

3) The safe play isn't safe. If you play 5/1 instead, you leave a blot next turn with 6-5, 5-5, 5-3, and 6-1. (7 shots, almost 20% of the time.) Many other rolls (5-4, 5-2, 4-1, 3-1, 2-1 at least) force you to break your board while staying on the 8-point. You lose ground in the race while you're breaking your board.

4) Getting hit isn't a loss for you. You come in 30% of the time on the first roll and the game goes on. You win a few of those.

What you're doing here is conflating 'being a favorite' with 'always winning' and 'getting hit' with 'always losing'. It's a common problem and it leads players to making apparently safe plays when a little risk could pay off big. Here's the cure: Take this position and play it out by hand 50 times each way. Sure it will take an evening, but you'll learn a lot about how much play is left in the position.

Thanks, everyone. Appreciate the detailed replies. I gave little thought and ran the 5 only to be surprised to see the sizable error under 2-ply.

Gnu 2-ply yields a 160-error for the "safe" play of 5/1 versus 5/2 4/3*, while 4-ply yields an 80-error. Robertie and jjpregler are correct that hitting gives you about 10% gammons. Running the 5 gives you almost no gammons; although, the win percentages of "safe" versus hit are about the same.

By the way, 19 being open instead of, say, 24 or 22 makes all the difference. Not hitting would be the clear favorite otherwise.

At 5-5 and especially 0-5, I would consider not hitting to be a very bad decision. At 5-0, I think it's closer. Upon checking Gnu at that score, not hitting is "doubtful," though I'm not sure how much Gnu considers the score and the cube. I don't know.

In a money game, I think hitting is an all day, every day decision.

Thumbs up for Bill's advice. It might look abstract at first glance (why waste so much time?), until you actually try it. You really open your eyes to some features of the position.

I actually mostly use a limited version of this. I put the position into the bot, set up manual players, but don't actually make every play myself, but rather push "Hint" and click the top move. It still shows you what and how often is going on, you can truncate this at, say, 6 moves as the position will be rather decided by then. This speeds up the process considerably, and you can still stop at some interesting plays when you spot one. My typical 100 trials test take about 60mins per position. I find this to be a profitable investment.

I accidentally put the position into XG as a money game the first time around, and it's a terrible blunder to hit. 5/1 was the overwhelming favourite.

I don't understand that at all.

XG on money game setting makes 5/2 4/3* a clear winner, and playing safe is a blunder. You made a mistake somewhere.

Oops, sorry abut that. I didn't save the position so can't identify what was done wrong.

You probably had the cube in the middle.

Backgammon is all about taking calculated risks to improve your overall winning chances.