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Setups

64bitscrabble

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What is a setup

A setup is when you make a play that sets up one of the tiles on your rack for a future high scoring play

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Factors to consider

How much does the set up play score?

How much could you score doing something else?

How much can you score if you get to use the setup spot on your next turn

How likely is it for your spot to stay open

Could your opponent use the setup spot themself (if you’re setting up your S, could they also have an S)

How big of a sacrifice does your opponent have to make to block your setup play if they choose to block it

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Math Example part 1

We can make a 10 point setup play or a 30 point standard play

We will score 60 if the setup stays open. It will stay open 80 percent of the time

We will average 30 if the setup gets blocked. It will get blocked 20 percent of the time at an average sacrifice of 10 points for our opponent

We will average 35 if we make the 30 point play on our next turn

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Math from slide 4

If we go for the setup, our EV is 10+(60*.8)+((30+10)*.2) or 66

If we don’t go for the setup, our EV is 30+35 or 65

In this case, the setup is a good idea

Notice that the sacrifice our opponent has to make to block makes the difference. Many players fail to account for this, but the sacrifice your opponent has to make to block your setup is part of your EV

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Math Example part 2

We can make a 20 point setup play or a 34 point standard play

If we make the 20 point setup play, we get an average of 50 points if the setup stays open, which it does 0 percent of the time

Our opponent has to sacrifice an average of 15 points to block our play

We will get 30 if the setup is blocked or if we don’t make the setup play

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Math from slide 6

If we go for the setup our EV is 20+(50*0)+((30+15)*1)=65

If we don’t go for the setup our EV is 34+30=64

Even though our setup will always get blocked, it is still best to make it!

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Opponent’s Perspective

You might be wondering why the opponent would be willing to block if it requires a sacrifice

Let’s look at the math from the opponent’s perspective

From the opponent’s perspective, we have to consider how likely it is for the play in question to be a setup

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Math Example

We see our opponent make a play. There is a 40% chance it is a setup

We can make a 35 point play that doesn’t block or a 20 point play that blocks

If we make the 35 point play our opponent will average 75 points if it’s a setup and 35 if it’s not.

If we make the 20 point play our opponent will average 35 points

If we don’t block our EV is 35-(75*.4+35*.6) or -16

If we block our EV is 20-35 or -15

Even if we don’t think it’s very likely for our opponent’s play to be a setup, we still choose to block

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Side Example: Why do we bluff in poker?

Let’s say we bet 100 chips into a 100 chip pot. We always have a good hand when we do this. 20% of the time we have a good hand that will always beat our opponent

20% of the time we win 100 chips because we bet and our opponent folds (they will always fold in the long run if we play this way). 80% of the time we reach showdown

Now let’s say we bet 100 chips into a 100 chip pot. ⅔ of the time we have a good hand, and ⅓ of the time we’re bluffing.

If our opponent calls, we win 200 chips ⅔ of the time and lose 100 chips ⅓ of the time. This averages out to winning 100 chips.

If we’re willing to bluff, we will do something that averages winning 100 chips with the 20% of good hands we have in our range and 10% of hands that become bluffs. Now we average a 100 chip victory 30% of the time instead of 20, and we are able to bring our weakest non showdownable hands out of showdown

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Fake Setups Explained

Setup plays generally look suspicious. They are not particularly high scoring, and often they use a specific set of tiles that could be used to score better elsewhere

For those reasons, it is generally very transparent if you are making a setup unless you also make fake setups

Let’s say that whenever we make a play, and we could’ve scored more with the tiles we had, it is a setup. Generally these setups are 100% transparent, because you could’ve scored more elsewhere and your opponent knows that, because they see the tiles you’ve put down

Our opponent will always block unless they have a really nice play, which they should do (see the math in above slides; it’s almost always worth it)

The only value we get out of our setup is provoking our opponent into making a sacrifice

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Fake Setups part 2

Now let’s introduce some fake setups into our range. If we sacrifice 2 points to make a fake setup without any hope of hitting it, and our opponent blocks 70% of the time for an average 10 point sacrifice, we have sacrificed 2 points for an average 7 point sacrifice from our opponent, netting us 5 points of EV

Also, if we are willing to make fake setups, our opponent will sometimes not block when we are making a setup, because they know we can make a fake setup. We get some of our EV from there

We will eventually hit an equilibrium point where we do not care whether or not our opponent blocks or not, because we get the same amount of EV with our range

A fishing play is a good candidate for making a fake setup, because fishing is one of the few situations where we are comfortable making a low scoring play other than setups

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Setting up a tile you do not have

This is not the same as a fake setup. This is a desperation tactic generally used in the preendgame

You set up an unblockable spot even though you do not have the letter in question.

If you draw it you get to use it. If your opponent already has it they use the spot and they win by more.

Generally wins are so important that you go for the small chance of victory over the massive spread sacrifice if your opponent hits it. Sometimes in specific spread situations this play is ill advised