A long overdue lesson on backgammon

I frequently play a poor game of backgammon, occasionally against strong competition. It's all good fun, but I've long been stuck in ... "I know i'm doing something wrong, just not sure what it is". Last night (*with much gratitude*) my opponent became my teacher and in the span of a few hours this beguiling game revealed how much I've been mis-estimating, mis-calculating and mis-playing.

To start with, I've been using the totally wrong model. This die matrix ...

... is fine for craps but wholly insufficient for BG.

This is the right way to think about the bg dice matrix. These are the rolls ...

... Each of the 36 spots is worth 2.78%. Frequently faced issues can now be solved with simple math.

I used to think having five points blocking my opponent was a massive advantage. I was not even in the ballpark. Leave one open spot for your opponent to hit ("I need a 1!!" they say) and and they have 11 outs; that's a 30% chance of hitting what they need. Or in other words, leaving your sixth piece open probably works only 70% of the time.

Leave two open spots ("I need a 1 or a 2!!" they say) and that offers a 56% chance to hit; 20 outs.

Three open spots and forget about it. Probability of success in need of three different numbers is 75%. That's hardly a big advantage.

I also mis-estimated safe distances to keep an open pip?

The 7 spot always brought me caution. Totally wrong. It's sheer luck to make the right choices with the wrong information. The 6 is the most dangerous. Leave an open spot 6 pieces away and your opponent has a nearly 50% chance of hitting it. Keep it 7 spots away and risk declines 65%. This is basic stuff to sound players. Now we all know.

The game offers little morsels that are a bit like portfolio management. Not every move carries the same weight, yet each one embeds some level of risk and reward, randomness and valuation. Furthermore, you can do everything right, and still lose. That's important to keep in mind when managing risk.

The way I see, no matter the field or diversion, the pathway to improvement is about honesty and growth and willingness to keep going until you get it right. With time, attention and intentional practice, anyone can improve anything over time. I'm excited to level up!

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