Blokus Strategy 2 – Bayesian Probabilities

This piece of Blokus strategy deserves its own post.

Let me introduce you to the concept of Bayesian probabilities. The math is pretty heavy, so I will just describe the concept.

In regular probability, you look at the frequency of how often something occurs. This works in playing card games. “What is my chance of drawing a diamond”.

Bayesian probabilities assigns probability based on an states of knowledge or belief. “What is the chance of someone playing in that square, given the other options they have to play”

This is pretty complex, so let me give you an example in Blokus. Suppose there are 4 different places that you are thinking about playing on the board. When you look at each one, the you gather the following information about each option.

  • Option 1: No one else can play on it. It is a perfect fit for your square piece
  • Option 2: All 4 players can play into this space. Once played there, it is isolated, so it won’t get you anywhere else.
  • Option 3: Only you and one other person can play here. The other player needs this space to avoid getting stuck.
  • Option 4: You and 2 others can play here. It leads to one other open space

How do you decide what to do? Bayesian probability tries to assign probabilities to each of beautiful-mindthese sites to decide the probability that you won’t be able to play there later. It seems complex, but your brain is already doing this when you think through where you should play. I’m going to assign probabilities the way my brain naturally thinks about it, without actually calculating probabilities. (No one has time for you to get your whiteboard out and Beautiful Mind the actual probabilities.)

  • Option 1: 0% probability of losing this space before your next turn. Wait for a later turn to play here
  • Option 2: 80% probability of losing this. Potential for this turn
  • Option 3: 90% chance of losing the space. Would really hurt the other player, and you won’t have a chance later
  • Option 4: 85% chance of losing the space. This will give you another play, so if you need the extra space, this may be your best choice.

At this point, you know you will probably lose two of the spaces, so do you want to use the chance to block someone out, or to sneak into extra space? Its up to you, just go in understanding the consequences.

Are there any other techniques you use to figure out where to play? Leave a comment.

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