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3. what is the best combination of skills?

#### User Info: thecooltodd

thecooltodd
11 years ago#21
Colin's COP is irrelevant because it's a straight multiplication of effective purchasing power: you can buy 1.5 times as much stuff regardless of whether you have more income or a bigger discount. It factors out of the comparison. (OTOH, your COP meter does charge faster if you're using Gold Rush, since your units are more expensive.).

Wrong. I was trying to calculate the ideal spending rate. Look at it this way: If Colin has Gold Rush but does not buy units and he uses his COP, he will have more money than if he has Fire Sale and does not buy units. In fact, when using Gold Rush he gains 50 gold per every extra hundred funds or 1000 gold, whereas using Fire Sale only allows you to save ONLY about 14 gold per every 1000 gold. That save in 14 gold will amount to 7 gold more when Colin uses his COP, which is 43 gold less than Gold Rush. NOT IRRELEVANT.

But upon trying to calculate his ideal spending rate where the balance between money saved is equal to money gained based on factoring in Colin's Gold Rush. I realized even if I did factor in his COP, it would only factor it in once and I would have to recalculate it depending on the number of times he uses his COP. And that would be an oversimplified version where I do not take into account the fact that Gold Rush allows Colin's meter to charge faster than when he's equipped with Fire Sale.

Ideally where the amount of money he has is irrelevant, Fire Sale is clearly better. Gold Rush is better because if he spends less money than a Colin with a Fire Sale, his COP will be much more effective and frequent. ?Comprende? I was unable to find the ideal rate but I can post what I did get to if anyone cares.

Colin's SCOP, on the other hand, would tilt the calculation toward Gold Rush. "Effective Purchasing Power" doesn't matter; all that matters is the raw credits you have accumulated, and thus Gold Rush would give you 1.1 times as much of at attack boost. However, I don't think anyone uses Power of Money until they're cleaning up anyway, so I don't think that should form the basis of your Force selection.

Exactly. You forget though that Colin's COP is also dependent on raw credits he has. And I wouldn't even factor in Colin's SCOP because through proper uses of his COP, money issues shouldnt be a problem.
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#### User Info: darkfire9430

darkfire9430
11 years ago#22
Wrong. I was trying to calculate the ideal spending rate. Look at it this way: If Colin has Gold Rush but does not buy units and he uses his COP, he will have more money than if he has Fire Sale and does not buy units.

You really should run the math before disagreeing with someone who did. You've completely wrong. You can't just look at money; you have to look at what the money buys you. Failing to do that means you're only considering the effects of Gold Rush, not the effects of Fire Sale.

Let's go back to our 10-city Colin. What is his effective purchasing power after using his COP?

10 cities * 1000 * 1.5 (from COP) * 5/4 = 18,750.

Now what's the purchasing power of a 10-city Colin with Gold Rush after a COP?

10 cities * 1100 * 1.5 (from COP) * 5/4 = 20,625

How about the purchase power of a 10-city Colin with Fire Sale after a COP?

10 cities * 1000 * 1.5 (from COP) * 100/72 = 20,833

So again, Fire Sale is better. Of course, there's nothing magical about 10 cities; I'm just using that because it makes the numbers easier. More generally

Colin's economic advantage = 5/4 -> effectively 125% funds.
GR Colin's economic advantage = 5/4 * 1.1 -> effectively 137.5% funds
FS Colin's economic advantage = 100/72 -> effectively 138.9% funds

Using his COP just multiplies all those amounts by 1.5. While that (obviously) gives Colin an even bigger advantage over his opponents, it doesn't change the ordering.

It's not about how much money he has (unless you're looking at his SCOP). It's about what he can buy with that money. A Gold Rush-using Colin has his 10% boost magnified by the COP. But a Fire Sale-using Colin also has his greater discount magnified by the COP. If you aren't accounting for the latter, then you aren't setting up the problem correctly.

#### User Info: darkfire9430

darkfire9430
11 years ago#23
Also... don't confuse Gold Rush the force (+100/property) with Gold Rush the COP (50% more funds). Both Gold Rush (the force) Colin and Fire Sale Colin can use Gold Rush (the COP).

I realized during my morning run that the comparison can be made even easier and more intuitive (I swear... I feel like I'm back in my teaching days).

Let's say Colin wants to buy a Fighter (base cost: 20,000):

Regular Colin only needs to save 16,000 credits to make the purchase. Yay, him.

When GR Colin saves those 16,000 credits, he gains an additional 1,600 credits. So after he bought the Fighter, he has 1,600 additional credits to spend as he pleases.

When FS Colin saves those 16,000 credits, he doesn't gain anything more. However, Fighters only cost FS Colin 14,400 credits. (The fact that he gets 8% off the original price of 20,000 instead of 8% off the modified price of 16,000 is why Fire Sale is better for Colin.) So after he bought the Fighter, he has... an additional 1,600 credits to spend as he pleases. Huh, it's the same.

But wait. When GR Colin spends the 1,600 credits (say on a pair of infantry), he doesn't get any additional benefit. When FS Colin spends the 1,600 credits, he still gets his additional 8% discount. Each infantry costs him 720, so he has 160 credits left over. There's FS Colin's economic advantage. Of course, he'll get the discount again when he spends the 160 credits. [No, this doesn't result in infinite money. The sum of an infinite geometric series where the rate is less than one is a finite number equal to (initial amount)/(1 - rate)].

If you still disagree with me, then hurry up and post your math so I can show you where you're wrong.

#### User Info: thecooltodd

thecooltodd
11 years ago#24
I can post what I started if you like, but it's inconclusive.

I was trying to factor in ideally when a player uses Colin's COP (or at least when I do), which would be at right before buying units after a turn where I don't spend any money (or very little on maybe just Infantry). So that's two turns worth of funds that Colin has, and I tend to join units to add additional funds on. But joining units is too complicated to factor in because than you'd have to account for how much is joined (which would be in favor of a Gold Rush Colin because he gets more funds for units joined over 10 than a Fire Sale Colin).
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#### User Info: darkfire9430

darkfire9430
11 years ago#25
Sure, post it.

Joining units doesn't matter, because the additional money GR Colin gets is exactly offset by FS Colin's discount.

Suppose it were possible to join two 10HP units. Let's use Fighters again because I already did the math on that. GR Colin would get 16,000 from joining his Fighters, whereas FS Colin only gets 14,400. However, those two numbers have exactly the same purchasing power-- that is, they'll both buy a new Fighter, or an Md. Tank and a Recon, or two tanks and two mechs, etc. for their respective Colins.

Colin's COP doesn't change that-- instead of buying a Fighter with the join, you can now buy 1.5 Fighters, or three tanks and three mechs, etc.

The key to all of this analysis is to think in terms of purchasing power, not in terms of credits. If you only consider credits, then you aren't accounting for Fire Sale. If it helps, convert all credits into the number of infantry Colin can buy with those credits. The ratios between the costs of each unit are constant, so a Tank is always worth 7 infantry (credit-wise, not strategy-wise), regardless of discount.

#### User Info: thecooltodd

thecooltodd
11 years ago#26
Well, looks like I'm running out of options to try to prove something. How do you calculate how fast the power meter charges up?
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Rubik's Cube (3x3x3) solved in 20.87 seconds by me. ^_^

#### User Info: metroid composite

metroid composite
11 years ago#27
Well, yeah. It makes sense.

The increase in buying power provided by gold rush is linear.
The increase in buying power provided by both the -5/8% cost skills is exponential.

Actually it's harmonic rather than exponential. i.e. 1/x rather than e^x. In other words, -80% cost would give Colin infinite buying power (limited by the number of Factories, to be fair).

Say a player can only spend money he's raised through cities (which is true for any CO not named Sasha).

It's still effectively true for Sasha--for the most part nobody uses her SCOP. The weird one is actually Sensei, since he can generate income by merging units after he spawns them, but now the type of his buildings matter (can't generate free stuff from these lame "bases" and "HQs").

I was trying to factor in ideally when a player uses Colin's COP (or at least when I do), which would be at right before buying units after a turn where I don't spend any money (or very little on maybe just Infantry).

This only actually makes a difference when you're using two COs. I.e. with skills off when using Colin/Sasha, if you plan to spend very little during a turn (only building Infantry, say) you'll actually save more money by running the turn as Sasha. Her infantry cost more, but this is offset by the fact that you're only spending a fraction of her income this turn. I.e. if your income is 8000 and you build three infantry, with Colin you're left with (8000-2400) = 5600, but with Sasha you're left with (8800-3000)=5800. (And you can also accumulate yet more money by merging Sasha's units and benefiting from her higher prices before switching back to Colin).

However, this is only relevant when you can switch COs to take advantage of the leftover. When you're only using one CO, the formula is always...

Number_Of_Cities * Income_Per_City / Cost_Percentage
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