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# Tell me more about the Final Score Bonus ("FSB")

Let's discuss the Final Score Bonus (henceforth, "FSB") because it impacts many aspects of scoring.

## What is FSB?

FSB is a property of a bear. E.g., your Fore Bear might have an FSB of 18% and your Twilight Bear might have an FSB of 936%. (Please remember these values as we will use them in other examples on this page.)  As you play an event, the FSB will add bonus points on top of each point you earn (more details below). Higher numbers are better!

## Can I increase a bear's FSB?

A bear's FSB will increase as the bear increases in level.

## How do I take advantage of a bear's FSB?

Choose that bear at the start of the event.

## What if I choose more than one bear at the start of the event?

We add up the FSBs from all the chosen bears, and apply that sum as the FSB during that event.

## What if I choose zero bears at the start of the event?

Then the FSB for that event is 0. I.e., you'll get regular points but you won't get any bonus points.

## My bear's FSB seems to be slightly off from what is displayed in the game

We don't show fractional parts of the FSB onscreen, even though we do use them in the calculations. For example, let's say that your bear has an FSB of 1827.6%. We'll display 1828% to you, but we'll use 1827.6% in our calculations. (The display will round to the nearest integer. If the value to be rounded is ".5" (halfway between) then we'll round to the number that is even--this is called "banker's rounding.")

## How does FSB help me as I take actions (play letters and words) during an event?

During an event, the FSBs of the bears you've chosen give bonus points on top of every point you earned in the game. E.g., let's say that you took an action that, not considering FSB, earned 20 points.

• If you chose no bears when beginning the event, then there is no FSB and you simply get the 20 points you earned. • If you chose only Fore Bear (with its 18% FSB) at the beginning of the event, then the FSB would contribute 3 bonus points (18% of 20, rounded down), so you'd get a total of 23 points for taking that action. • If you chose only Twilight Bear (with its 936% FSB) at the beginning of the event, then the FSB would contribute 187 bonus points (936% of 20, rounded down), so you'd get a total of 207 points for taking that action.
• If you chose both Fore Bear (with its 18% FSB) and Twilight Bear (with its 936% FSB) at the beginning of the event, then their FSBs add together. 18% + 936% = 954%. Thus the FSBs of your bears contribute 190 bonus points (954% of 20, rounded down). So you'd get a total of 210 points for taking that action.
• Likewise, if you took more than two bears, their FSBs add together. This affects the number of extra points you get for taking the action, and thus the total points you get for taking the action.

## How does FSB help me at the end of the event when the bears on the board get counted up?

At the end of the game, you earn points for each bear on the board. The number of points each bear gives you is determined by the area occupied by the bear (e.g., a 2x3 bear has an area of 6) and the combined FSBs of the bears you chose at the the beginning of the event (remember that we add up the FSBs of the bears that you choose). It is given by this formula:

Points for one bear of a particular Area = ( ( Area ^ 1.85 ) * ( 1 + FSB ) ), rounded down.

• Note that the FSB in the above formula is identical for all bears in the event; it does not matter that a bear has a particular graphic.

Also, note that we first determine how much many points a particular bear of area X is worth, then give you that number of points for each such bear on the screen. This is important because the rounding takes place before the number of bears is considered. If you try to multiply by the number of bears before doing your rounding, you may get the wrong number.

• For example, prior to any rounding a bear of Area 1 with FSB 80% is worth 1.8 points. If you have five bears of Area 1, you might think that you'll get 9 points for the five together (1.8 x 5 = 9.0 exactly, right?). Actually, you'll get only 5 points for the five together, because we first round 1.8 down to 1, and then 1 x 5  = 5.

A few other reasons your numbers might be off if you're trying to do the math on your own:

• As mentioned above, we don't show fractional parts of the FSB onscreen, even though we do use them in the calculations. For example, let's say that your bear has an FSB of 1827.6%. We'll display 1828% to you, but we'll use 1827.6% in our calculations. (The display will round to the nearest integer. If the value to be rounded is ".5" (halfway between) then we'll round to the number that is even--this is called "banker's rounding.")
• The order of operations means that, even if you know the point value of a bear of size X at 0% FSB, you cannot simply multiply that point value by your FSB and assume that you will get the correct result.
• E.g., a bear of area 4 is worth 12 points at 0% FSB. You might think it would therefore be worth 24 points at 100% FSB (100% more points, right?), but it is actually worth 25 points at 100% FSB. You can see this if you try Area=4 and FSB=100% in the formula.
• You might not be turning the FSB percentage into a non-percentage number. E.g., an FSB of 1234% means that you should plug 12.34 into the formula, not 1234.

### Example

A player played an event with with bears of the following FSBs:

• 1827.6% (the game displays 1828% but I know the calculation for the full number)
• 1610% (this number is exact)
• 1265% (this number is exact)

The combined FSB from all these bears is 1827.6% + 1610% + 1265% = 4702.6%

The player got the biggest possible bear on a 5x8 board, for an Area of 40.

The formula is (I'll display some numbers rounded, but no rounding occurs until the last step):

Points for one bear of a particular Area = ( ( Area ^ 1.85 ) * ( 1 + FSB ) ), rounded down.
= ( ( 40 ^ 1.85 ) * ( 1 + 4702.6% ) ), rounded down.
= ( ( 40 ^ 1.85 ) * ( 1 + 47.026 ) ), rounded down.
= ( ( 920.05 ) * ( 48.026 ) ), rounded down.
= ( 44186.28 ), rounded down.
= 44186.

This is indeed what the player saw reported in the Big Bears line of the Your Score screen.

## Why do you call it a "Final Score Bonus" if the effects are applied throughout the game rather than afterward?

I think it's because once a long time ago the FSB wasn't applied until you got to the Your Score screen. But that caused some sort of confusion, so we now apply it throughout the game instead (which admittedly leads to other types of confusion). I don't have a good explanation for why we didn't change the name at the same time.