Backgammon Game - Question about odds !

This is a question for backgammon lovers with better math abilities than mine, or for a combination of group working it together.

Points value: * single win - 1 point. (1pt)
* gammon win - 2 points. (2pt)
* backgammon win - 3 points. (3pt)

Description: * a single win is considered when one player manage to take all of his checkers out of the board, while the other player took out at least one checker.

* a gammon win is considered when one player manage to take all of his checkers out of the board, while the other player did not managed to take any of his checkers out of the board.

* a backgammon win is considered when one player manage to take all of his checkers out of the board, while the other player did not managed to take any of his checkers out of the board AND have at least one checker left in his opponents base quarter.

Assuming perfect play by both players, when starting a game both players have EQUAL chances:

* 36,26% for winning a single game,

* 13.15% for winning a gammon game,

* 0.59% for winning a backgammon game.

PS: Backgammon game is usually played with a cube called doubling cube but this does not affect my question so I will not detail.

If anyone is interested in a complete backgammon video tutorial, I invite them to give a search of "Backgammon tutorial by 1984Hunter" on Youtube and the first one showing is mine. (I did not posted a link because I am not sure if I am allowed or not)

Question: What are the odds to get a backgammon win (3pt value) WITHOUT hitting any of you opponents checkers ?

Quote: PlayHunter

Question: What are the odds to get a backgammon win (3pt value) WITHOUT hitting any of you opponents checkers ?

If you can't hit your opponents checkers then the only checkers left at the end of the game by your opponent would be the 2 left in your bearing off zone.

So, with 4 high doubles you could bear off and your opponent somehow has to roll so that his 2 checkers are left in your home zone. The odds of this would be extremely small coupled with the miniscule odds of having your opponent left with 2 checkers even though you haven't hit any of his checkers.

My guess would be around 1 in 10 million?

Incidentally, you can have a situation where both players are bearing off, player A is 15 pips ahead in the pip-count and he's first to throw ... during the bearoff, player A even throws a double and yet he still loses a gammon??

You would have to build your prime very quickly, while having your opponent roll combos that wouldn't let him run, or aren't typically used to split the 24-point (like 1). Most likely way is for you to roll a series of doubles that let you build the prime and run your checkers. Once your prime is built, it doesn't matter what your opponent does in the midgame, you can slowly move the prime into the home board. Then you need series of increasingly unlikely rolls for your opponent to not escape while you bear off.

For example, if you start bearing off with 3 checkers each on the 2-6 pts, and your opponent has 2 checkers on the 1pt with all others home, you only have a .2% chance of winning a backgammon if hits are allowed. Obviously less if not.

In summary, you need a very unlikely series of rolls to get to your prime without opponent escaping, then you have a free ride to move the prime home, then you have a 1000-1 shot or worse to bear off with a backgammon. Switch's 10million to 1 guess could be in the right ballpark

Quote: PlayHunter

Assuming perfect play by both players, when starting a game both players have EQUAL chances:
* 50% for winning a single game,
* 13.15% for winning a gammon game,
* 0.59% for winning a backgammon game.

Besides the rules I don't know much about Backgammon, but how can both players have a chance >50% of winning the game by either method ?

What OP means is a 50% chance of winning, of which 13.15% is a gammon, etc. You don't have a 50% chance of winning a single.

Quote: MangoJ

Besides the rules I don't know much about Backgammon, but how can both players have a chance >50% of winning the game by either method ?

You are right MangoJ there was a mistake on my side .. 50% are the chances to win with either method .. just edited my prime post.

Thank you Switch and dwheatley ! So it is about 1 (one) in 10 millions ! Think I`m lucky then :-) because I have got it on tape.

If anyone is curious to actually watch it, just search "Backgammon crazy Jokes" and the first video is mine. This is at 3:44-4:26

By the way, same area .. What would be the odds (before bearoff) of losing a backgammon with only one checker on the bar ?

What's interesting about your game is that your computer(?) opponent could have avoided a backgammon, but gambled and kept one piece back hoping to hit and turn the game around. I'm looking at 4:15, when it rolls 5/4, and only runs the free piece when it could have saved them both.

I plugged one of the late positions into GNUbackgammon, and it agrees with my instinct: your opponent made a 3% mistake by playing 21/12 instead of 24/19 & 21/17. At that point it would give up all chance of winning, but only by giving up a likely gammon. Then you had another game to go for the match.

So, a very unlikely feat, but yours was technically not against optimal play :)
I'm (mostly) teasing.

Losing a backgammon with only 1 checker on the bar depends a LOT on the pip count and quality of primes. For any specific position, the programs can tell you.

Now I did the same with that 5-4, putting it on GNU too. And says 21-12 is still the best move .. (think take score into account too)