The three difficulty levels of backgammon

Backgammon is not one game, but three games with increasing difficulty level.

LEVEL 1: matches to one point

You and your opponent roll the dice, move the checkers until one of you have won. It’s a tricky game already, with very different strategies to cover holding games, back games and such. If you master it well you’re ready for…

LEVEL 2: money games

Enters the doubling cube, maybe the most fiendish device created in any board game. Before every single move you must estimate whether you are more than 75% likely to win the game, and whether this assessment is likely to change next move.

I’m fairly good at level 1, regularly play on “advanced” level. But after years of backgammon my cube handling is still on “beginner” level. Sometimes I do well, sometimes I fail completely.

LEVEL 3: matches

Once you believe you have mastered the cube, proceed to level 3 and play matches. And all of a sudden, much changes. You play differently if you’re leading or if you’re far behind, and the cube’s value changes madly.

Yesterday (that’s why I’m writing this today :-) ) I reviewed a match I played on DailyGammon and came across this position:

 

 

Blue's move. Cube action? Redouble or play?

This is a match to 20 points (yeah, really), I'm leading 13:5. I hold the cube at 4, can redouble to 8. What should I do?

On level 2, this is an easy double. I need three rolls to bear off my checkers, he needs 3 rolls to bear off his checkers. 

So I doubled. And XG tells me "you were a really, really, REALLY dumb fool doubling." (okay it tells me I lost a full 0.83 points of equity, which (assuming a blunder costs you 0.08 points) is a tenfold blunder. 

At the same time XG confirms that I was correct with my "level 2" assessment: I'm 80% likely to win this game, so I should double, and white should pass.

 

Money game analysis - redouble/pass

But the thing is: I'm leading 13:5, and I'm 80% likely to end this match leading 17:5. XG says that in this situation I'm 90% likely to win the match before doubling. If I double to 8, white will redouble to 60. making this a "double match point". And as the figure above says: I'm 80% likely to win this match, so I reduced my match winning changes from 90% to 80% by doubling. Good move.

 

 

Match analysis (using match winning changes instead of equity)

 

Much left to learn to master level 3, the match play.

 

Which Back Game is how good?

tl;dr - avoid back games involving the ace point. Seek back games with two consecutive points (eg 34) - better if they are in the middle of your opponent's home board, maybe also with a single point owned by your opponent.

 

"Which Backgame is how good?" -  That's a question I was asking me for a long while? I know, some back games are actually fairly good for the defender. Some are not. But I didn't find good info on the internet.

So I'm trying them all out and log my results here.

I'm using three variations of the same position: one with maximum timing, one with minimum timing, one with a bit more than minimum. It's always white to move, with a roll that doesn't give blue an immediate hit. 

There's probably also an "optimal timing" which would be interesting, but which is too much to find out with my limited skills.

So here's the three positions, for an 21 backgame:

A backgame with little timing (35 pips behind)

In my "A" positions, blue has poor timing; his board will crumble in the next move.

 

A backgame with a lot of timing (80 pips behind)

 (In my "B" positions, blue has a lot of checkers to move before the board starts to crumble. Note that for some back games this is probably too much timing.

 

And finally, for the "C" position I moved the third checker on 20 in the "A" position to the 11 point for another 9 pips more timing.

A position in between the big alternatives (44 pips behind)

 

What I did then was feed the A and B and C positions for every single backgame of two points into XG2, analyze the move that it found best, initially, at Roller++, and looked at equity, winning chance for white, Gammon/Backgammon chance for white.

If I was analyzing a back game where the blot on 10 couldn't easily move to safety with the 32 roll (e.g. a 54 back game), I changed the roll to 31, and in the special case of a 65 backgame, to 42, so that white always has a roll that doesn't give blue a shot.

 For clarity here's position "B" - much timing for a 43 back game.

Findings

More timing, more gammon losses

Totally trivial Finding: much timing will lead to more gammon and backgammon losses. Only for an 12 back game this doesn't make a difference. A well timed 13 backgame already gives you 5% more gammons, and this percentage increases continuously until for a 65 backgamme the additional 5 checkers cause a 35% difference of gammon wins for white.

The reason is of course that 5 checkers on 12 and 11 need to be brought home, which adds a lot of gammons. In a 21 back game this is not critical, but e.g. in a 43 back game it is.

You don't want a back game with your ace point

The questions that made me embark on this mighty analysis mission were: 

 

1. "if I can choose, which back game should I go for?"

2. "is this a backgame worth playing (or e.g. dropping)?"

To answer this question, let's have a look at the equities in our test positions. In normal games you only have limited control over how your timing evolves (and then you get that 66 when you really don't want it). Therefore I've simply taken the average of the equities of the three positions A, B, C. Here they are.

"What is this supposed to mean?" you ask? 

It's simple. To find out what average equity you get for a 42 back game, look at the row labeled "2" and the column labeled "4" and you'll see the figure 0.71 (it's German excel so you see a comma instead of a dot). 

 

This means that if you take the equity for position "A" (low timing), and the equity for position "B" (much timing), and the equity for position "C" (in between), then their average is 0.71. A 42 back game is not the worst you can have. You might even take a cube.

 

Result: 

• The worst five back games here are the 61, 51, 41, 31, 21 backgames.
  Probably you don't want to play a backgame involving your ace point.
  
• your best chances with a back game are the 43, 54, 53 back games.
  Good back games: two consecutive points in the middle of your home board.

If you're at the end of a match and gammons don't count, then not this equity but the pure winning chances for white (and blue) are most interesting:

The situation is similar, but not entirely the same.

Again: don't play a back game with your ace point.

Best: go for the 3 point if you can. 32, 34, 35 are all good.

If you have A LOT of timing, go for at most 1 point between your points

Let's have a look at the equity for only the "B" position in which you have 5 checkers to move home, plenty of timing.

 

Please note: timing is relative - the pip difference that is great timing in one position might be too little or too much in another position, so please take this with a grain of sault.

First you notice that all 65..61 back games are poor here. But as the 6 point is and stays in white's hand in pretty much every game, let's mark them in a greyish pink and ignore them.

Results:

• The best back games are 31, 32, 42, 43, 53 - go for adjacent points or for points with only one point in-between.
• The worst back games are, again, involving the ace point - 21 and 51 (and 61 which we ignore)

The full monty

If you want to do some analysis on the raw data as well, here's a link to the excel (hopefully will easily open as a google table):

The spreadsheet with all the info

 

Disclaimer: I am not good at back games. Watched Michy vs. Dirk yesterday playing a back game on Backgammon Galaxy's YouTube channel. Had no clue why they made some moves. XG2 knows back games, but if I asked it the wrong questions, it certainly gave me the wrong answers.

If you're good at back games and think all this is nonsense, just drop me a comment.