61
Saving the Gammon
Fig 1 :

61 - Save the Gammon
What a state to get ourselves into.
Black has 4 checkers on her Ace point.
No matter where we move our checkers, if our opponent rolls any double her checkers are off and we lose 2 points.
So our opponent has 6/36 good rolls to win a Gammon.
So on the flipside she has 30 rolls (30/36) that only take 2 checkers off so lets see if we can play the 61 as efficient as possible.
Black has 4 checkers on her Ace point.
No matter where we move our checkers, if our opponent rolls any double her checkers are off and we lose 2 points.
So our opponent has 6/36 good rolls to win a Gammon.
So on the flipside she has 30 rolls (30/36) that only take 2 checkers off so lets see if we can play the 61 as efficient as possible.
Fig 2 :

61 - Save the Gammon
Lets see, 13/7 5/4 is the move in Fig 2.
How does 53 work with is move ?
53 works terrible, its leaves 2 bad rolls which isn't too bad at all but let's look for a more efficient move.
Hoping Black doesn't roll a double.
2/36 Bad Rolls - 34/36 Good rolls
How does 53 work with is move ?
53 works terrible, its leaves 2 bad rolls which isn't too bad at all but let's look for a more efficient move.
Hoping Black doesn't roll a double.
2/36 Bad Rolls - 34/36 Good rolls
Fig 3 :

61 - Save the Gammon
Remember the 6 is forced, we have to move it, its what we do with the 1 that matters.
Lets see, 13/7 7/6 is the move in Fig 3.
Now how does 43 work with this move ?
43 works terrible, there must be a more efficient move.
43 Leaves 2 bad rolls if Black doesn't roll a double.
2/36 Bad Rolls - 34/36 Good rolls
Lets see, 13/7 7/6 is the move in Fig 3.
Now how does 43 work with this move ?
43 works terrible, there must be a more efficient move.
43 Leaves 2 bad rolls if Black doesn't roll a double.
2/36 Bad Rolls - 34/36 Good rolls
Fig 4 :

61 - Save the Gammon
13/7 6/5 is the move in Fig 4.
How do 33 work with this move ?
33 works terrible but is better than the positions in Fig : 2 & 3
33 Leave 1 bad roll if Black doesn't roll a double.
1/36 Bad Rolls - 35/36 Good rolls
Is there another move ?
How do 33 work with this move ?
33 works terrible but is better than the positions in Fig : 2 & 3
33 Leave 1 bad roll if Black doesn't roll a double.
1/36 Bad Rolls - 35/36 Good rolls
Is there another move ?
Fig 5 :

61 - Save the Gammon
Yes there is 13/7 2/1 the move in Fig : 5.
You move the 1 from the 2 point to the Ace point (1 point), but this seems counter-intuitive right?
Yes it most certainly does but how do all of the numbers work with this move now?
43,53,33 works perfectly, As well as every other roll.
We still hope our opponent doesn't roll a double and if she doesnt, we've just Saved the Gammon.
This move leaves no bad numbers.
0/36 Bad Rolls - 36/36 Good rolls
You move the 1 from the 2 point to the Ace point (1 point), but this seems counter-intuitive right?
Yes it most certainly does but how do all of the numbers work with this move now?
43,53,33 works perfectly, As well as every other roll.
We still hope our opponent doesn't roll a double and if she doesnt, we've just Saved the Gammon.
This move leaves no bad numbers.
0/36 Bad Rolls - 36/36 Good rolls