## Combining hull options

Discuss the Traveller RPG and its many settings
Hakkonen
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### Combining hull options

If I want to design a ship with a light (-25% cost), streamlined (+20% cost) hull, what's the order of operations? Do I just add the modifiers for a net -5% cost?
baithammer
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### Re: Combining hull options

The use of the +/- indicates additive, so yes -5%.
AnotherDilbert
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### Re: Combining hull options

As per the example of the Heavy Fighter on p102:

50 Dt hull, streamlined(+20%), reinforced(+50%)

Hull cost = 50 × 0.05 × 120% × 150% = MCr 4.5

So, for a streamlined(+20%), light hull(-25%)

Hull cost = 50 × 0.05 × 120% × 75% = MCr 2.25
baithammer
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### Re: Combining hull options

Which is incorrect with the modifiers notation, +20% = 0.2 and -25% = - 0.25, not 1.2 and 0.75

The long form of the difference.

50,000 + 20% - 25%

50,000 + 10,000 - 12,500 = 47,500

47,000 * 50 = 2,375,000

2,375,000 / 1,000,000 = 2.375

vs

50,000 * 1.2 * 0.75

50,000 * 0.9 = 45,000

45,000 * 50 = 2,250,000

2,250,000 / 1,000,000 = 2.25
Condottiere
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### Re: Combining hull options

I don't think there's a canonical ship that goes both up and down, only up.
baithammer
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### Re: Combining hull options

MGT 1st Ed HG Light Carrier, 30kdt Closed hull (-10% cost) = 2,700 Mcr

30,000t x 0.1 Mcr = 3,000 Mcr

3,000 x 0.9 = 2,700 Mcr
Condottiere
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### Re: Combining hull options

In theory, Second supersedes First.
baithammer
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### Re: Combining hull options

I just find it funny that notation is correct in 1st edition and incorrect in 2nd, where its indicated as additive modifiers (+ / -) yet the values used are multiplicative.
AnotherDilbert
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### Re: Combining hull options

I don't think we can read the rules to literally, e.g.:
Light Hull: By decreasing the cost of a hull by -25%, a ship will have its Hull points decreased by -10%.
Resolving the double negation this would mean increasing the cost by 25% for an additional 10% Hull points.

baithammer wrote: I just find it funny that notation is correct in 1st edition and incorrect in 2nd, where its indicated as additive modifiers (+ / -) yet the values used are multiplicative.
Are you saying that "increase the cost 25%" would mean anything different from "increase the cost +25%"? That is not a notation I have ever seen.
baithammer
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### Re: Combining hull options

Are you saying that "increase the cost 25%" would mean anything different from "increase the cost +25%"? That is not a notation I have ever seen.
The proper structure is increase cost by 25% which is an additive statement versus 125% of the cost which is multiplicative.

With the original example you get the following equations.

x + 0.20x -0.25x = x-0.05x = 0.95x

Compared to

1.2x * 0.75x = 0.9x
AnotherDilbert
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### Re: Combining hull options

baithammer wrote: The proper structure is increase cost by 25% which is an additive statement versus 125% of the cost which is multiplicative.
I have never heard of that convention, rather the opposite.

A simple example would be:
An apple costs \$1.00. You get a 10% discount. You add 10% sales tax. What do you pay?
Answer: \$1.00 × 90% × 110% = \$0.99.

Or:
An apple costs \$1.00. The price is increased 10%. The price is then increased 10% again. What is the price?
Answer: \$1.00 × 110% × 110% = \$1.21.
baithammer
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### Re: Combining hull options

First example is a set of sub-totals which can be generalized as multiplicative.

\$1.00 - \$0.10 ( 10% discount) = \$0.90
\$0.90 + \$0.09 (10% Sales Tax) = \$0.99

Second one is a bit different.

Since both % are applied to the same base they add together, so 10% + 10% = 20%

\$1.00 + \$0.10 + \$0.10 = \$1.20
Sigtrygg
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### Re: Combining hull options

You apply the discount to the base cost and you calculate the tax on the base cost, you then work out the total
apple £1
10% discount 10p
10% tax 10p.

You pay £1 and the government gets its extra 1p in tax

Course if you do tax first the government couldn't care less about the discount.

Personally I would sum all the discounts and additional costs to come up with a final multiplier, otherwise you are going to fudging the order in which you apply them to get the best deal.
AnotherDilbert
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### Re: Combining hull options

Sigtrygg wrote: You apply the discount to the base cost and you calculate the tax on the base cost, you then work out the total
apple £1
10% discount 10p
10% tax 10p.
No. [ https://blog.taxjar.com/sales-tax-disco ... romotions/ ]
Sales tax, or more complicated VAT (since £), is calculated on actual price payed, defined depending on jurisdiction.

Sigtrygg wrote: Personally I would sum all the discounts and additional costs to come up with a final multiplier, otherwise you are going to fudging the order in which you apply them to get the best deal.
Multiplication is commutative; order of operations does not matter to the result.
Price payed = \$1.00 × 90% × 110% = 110% × 90% × \$1.00 = \$0.99
AnotherDilbert
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### Re: Combining hull options

baithammer wrote: Second one is a bit different.
Since both % are applied to the same base they add together, so 10% + 10% = 20%
\$1.00 + \$0.10 + \$0.10 = \$1.20
They are not calculated on the same base:

"An apple costs \$1.00." . . . . . . . . . . . . . . . CurrentPrice = \$1.00
"The price is increased 10%." . . . . . . . . . . . CurrentPrice = CurrentPrice × 110% = \$1.00 × 110% = \$1.10
"The price is then increased 10% again." . . .CurrentPrice = CurrentPrice × 110% = \$1.10 × 110% = \$1.21
"What is the price?" . . . . . . . . . . . . . . . . . . .CurrentPrice is \$1.21

If you want to define a base price from which percentages are calculated you have to say so, normally something like: "The base price is \$1.00. Increase by 10% of base price, increase by 10% of base price again".
Sigtrygg
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### Re: Combining hull options

I apply the cheap option a 10% discount to a drive say. I take it three times.

The drive has a base cost of MCr10.

How much do I pay?

Is it 0.9 x 0.9x 0.9 x 10 = MCr7.29

or is it 0.7 x 10 = MCr7?
baithammer
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### Re: Combining hull options

I apply the cheap option a 10% discount to a drive say. I take it three times.
10 x 1.3 = 13 Mcr as its an actual multiplicative arrangement. ( Notice its not +10% but just 10% )
Sales tax, or more complicated VAT (since £), is calculated on actual price payed, defined depending on jurisdiction.
Which is contradicted by the article you linked, not to mention VAT is often baked in to the price rather than a separate line item.
In layman’s terms, that means if the original price of something you sell was \$100, but you offer a 50% discount, then the taxable price is \$50.
^ The article further points this out in the above.
AnotherDilbert
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### Re: Combining hull options

Sigtrygg wrote:
Tue Oct 24, 2017 8:37 am
I apply the cheap option a 10% discount to a drive say. I take it three times.
Unfortunately undefined in the rules.

The example of the Fleet Courier on p132 says apply them to the base price (additive):

M-Drive Thrust 2 (Reduced Size × 3)
Size: 400 Dt × 2% × (1 - 10% - 10% - 10% ) = 400 × 2 × 70% = 5.6 Dt
Cost: 5.6 Dt × 2 × 150% = MCr 16.8
AnotherDilbert
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### Re: Combining hull options

baithammer wrote:
Sales tax, or more complicated VAT (since £), is calculated on actual price payed, defined depending on jurisdiction.
Which is contradicted by the article you linked, not to mention VAT is often baked in to the price rather than a separate line item.
Sales tax is calculated on actual price payed (including partly payed by someone through a coupon) [except in Texas] {further exceptions...}
The simple case is (quote from the linked article):
Because discounts are generally offered directly by the retailer and reduce the amount of the sales price and the cash received by the retailer, the sales tax applies to the price after the discount is applied. For example, your normal selling price is \$30 but you are offering a 5 percent discount for first time customers. The tax base is \$28.50.
With 10% sales tax you pay: \$30 × 95% × 110% = \$31.35

VAT is always included in the price, it is defined as a part of the actual price payed, not as an added tax.

baithammer wrote:
In layman’s terms, that means if the original price of something you sell was \$100, but you offer a 50% discount, then the taxable price is \$50.
^ The article further points this out in the above.
Yes, so with 10% sales tax you would pay \$100 × 50% × 110% = \$55

Discounted price = \$100 × 50% = \$50
Payed including tax = \$100 × 50% × 110% = \$55
baithammer
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### Re: Combining hull options

Going to give another stab at the difference between the two formulations.

One positive modifier 20% and a negative modifier -25%.

50,000 + 20% -25%

x + 0.2x - 0.25x

x - 0.05x

- 5%

vs

50,000 * 1.2 * 0.75

x * 1.2 * 0.75

x * 0.9

- 10%

Note the additives each modify x and then are totaled where as each modifier under the second case are modifying each other regardless of x.

The next example is what you get with two positive modifiers.

50,000 + 20% + 25%

x + 0.2x + 0.25x

x + 0.45x

45%

vs

50,000 * 1.2 * 1.25

x * 1.2 * 1.25

x * 1.5

50%

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