Backgammon, Part 5

Now, things can get more complicated fast. Say you have the following board. You can say whatever you like about this layout, but let’s pretend that Red has gotten bad dice while trying to start a running game, while White has been luckier. If we count points, White has 110 and Red has 135 (Red: 1×3 + 1×4 + 1×5 + 4×6 etc.) White is in a somewhat stronger position than Red, so it’s to Red’s advantage to bide his time, leave the stones on 18 and 13 and try to build blocks with the other stones.

(White leaves a blot on point-15.)

However, White rolls something plus a 3. He moves a stone from 12 to 15, leaving it as an unprotected blot on 15. Is he stupid, or what?

As I wrote in the last entry, there’s more than one kind of risk. Red would need a 3 to hit White’s blot from the 18 point. Because there’s a block on 17, Red needs 1-2, 2-1, or a 3 on one die (3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 1-3, 2-3, 4-3, 5-3, 6-3) = 13/36 = 36%. One out of every three turns should let Red hit that blot. So, yeah, White is stupid, right?

Well, White gets on the bar and in the next turn needs anything other than 6-6 to get back onto the board. In fact, landing on the 3-, 4- or 5-points will hit one of Red’s blots and put him on the bar instead. What are the odds? White needs any roll with a 3, 4 or 5 in it, or something starting with a 1 or 2 to get on the board plus a 1 to hit the 3-blot. In fact, the only roll where Red won’t get hit are 6-6, 1-6, 2-6, 6-1 and 6-2 = 5/35 = 13%. Or, rather, 87 out of 100 times, White will hit AT LEAST one of Red’s blots. For 3-1, 3-2, 1-3, 2-3 and 1-1, Red will get hit TWICE (there’s that 13% probably again, but now, it can cause some real damage).

Here, we’re seeing two kinds of risk. The first is that White gets hit on the 13 point and sent to the bar. Second is Red’s getting hit in return and not being able to return to the board. Look at White’s “wall” on the 19-22 points. Red would need a 1 or a 2 (33% chance) to return one stone to the board. If White hit two stones, Red would need 1-2, 2-1, 1-1 or 2-2 (11%) to get both back on the board in one turn, otherwise White gets at least one round to bring in the stones on 12 and 17 and block the entire region from 19-24, preventing Red from getting on at all.

White is BEGGING Red to hit that blot on 15. It would destroy Red’s chances of winning. If things remain the way they are and White puts blocks on 23 and 24, he could continue bringing in his remaining stones at his leisure and start bearing them off the board. Red could get lucky and hit White one more time, but the odds for it are low.

The risk to Red is so great that White expects a 0% chance of that blot on 15 getting hit. In business terms, this is an “opportunity cost”. The impact of getting hit versus not being hit. As you play the game, you have to continuously weigh both.

Earlier, I mentioned taking risks at the start of the game and how this helps you build up blocks. As shown on the board above, having those blocks later on can offset the cost of being hit in the first 1 or 2 turns. Later on in the game, taking bad risks becomes much more costly, as in the case for Red here.

To be continued.


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