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 Actual Costs of Geysers

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Geordi



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Join date : 2011-10-03

PostSubject: Actual Costs of Geysers   Mon Oct 03, 2011 7:49 am

So I decided to do some math today...

Part 1: Split Costs
how much each geyser costs if you wait until you break even before you get the next one.
Break time is how much time it takes to break even with not buying the geyser.
Normalized cost is what the geyser would cost if you didn't have to wait after buying it, given that you would break even at the same time anyway. Trust me when I say that it is a kindness on the developer's part that you get to wait instead of paying full price.

formulas:
cost of geyser = 100
mineral loss:
cost_of_geyser + recovery_time * (income_before/20)
break time:
mineral_loss / ((income_after - income_before)/20)
normalized cost:
break_time * ((income_after - income_before)/20)

1st Geyser: (100 before, 110 after, 25 seconds recovery)
Mineral Loss: 225.0
Break Time: 475.0 ~ 7:54
Normalized Cost: 237.5

2nd geyser: (110 before, 125 after, 50 seconds recovery)
Mineral Loss: 375.0
Break Time: 550.0 ~ 9:10
Normalized Cost: 412.5

3rd Geyser: (125 before, 145 after, 75 seconds recovery)
Mineral Loss: 568.75
Break Time: 643.75 ~ 10:43
Normalized Cost: 643.75

4th Geyser: (145 before, 170 after, 100 seconds recovery)
Mineral Loss: 825.0
Break Time: 760.0 ~ 12:40
Normalized Cost: 950.0

5th Geyser: (170 before, 200 after, 125 seconds recovery)
Mineral Loss: 1162.5
Break Time: 900.0 ~ 15 minutes
Normalized Cost: 1350.0

Before I go on to the next part I want to do a quick demonstration:
If you do the above computations as if you buy the first three geysers at once, you get the following:
Mineral Loss: 1050
Break Time: 466.6
Normalized Cost: 1387.5

Notice that Break Time is SHORTER than for the first geyser alone! What this should tell you is that if you plan on getting multiple geysers, you must get the subsequent geysers ASAP.

With that in mind, we go on to...

Part 2: Interleaved Costs
In order to compute these, we have to know what our remaining 'debt' is two minutes after we bought the previous geyser. Luckily, math will take care of it.

Here are two players playing simultaneously.
A: At time 0, I have 100 minerals. I buy my first geyser.
B: At time 0, I have 100 minerals. I sit on it.

A: At time 120, I have (120-25)*110/20 = 522.5 minerals, I buy my second geyser, leaving 422.5.
B: At time 120, I have 100 + 120*100/20 = 700 minerals. I sit on it.

A: At time 240, I have 422.5 + (120-50)*125/20 = 860 minerals, I buy my third geyser, leaving 760 minerals.
B: At time 240, I have 700 + 120*100/20 = 1300. I sit on it.

A: At time 360, I have 760 + (120-75)*145/20 = 1086.25 minerals.
B: At time 360, I have 1300 + 120*100/20 = 1900.

Now we look at our two players, we are six minutes into the game;
A has 1086.25 and B has 1900, so B is ahead 813.75 minerals.
A's income is 145/20, and B's is 100/20, so A will reach B in 813.75/((145-100)/20) = 361.6 seconds, or 721.6 seconds into the game, OR roughly 12 minutes into the game.

For comparison, suppose you were to wait until you broke even on each geyser before you bought a new one, you would end up breaking even on the third geyser in 1293.75 seconds, or roughly 21:33!!!

Part 3: Conclusions
Zee has an excellent post in the Income 2.0 thread about eco strategy. I agree with most of what he says, with the following adjustments:
Losing middle time to recovery is preferable to your opponent getting +15%, if you can pull off the trick of having the middle AND having just finished your recovery, that is the best. But don't think you shouldn't get a geyser just because your team just took the middle.
I have never seen a game end before the 12 minute mark, so I think it's safe to say that getting all three geysers as fast as you can is sensible strategy.
Two Geysers is probably very workable, from 12 minutes to 15 minutes you will still be ahead of the 3 geyser players, and after that you won't be far behind (I didn't show this math, but I did do it).
The absolute worst thing you can do is wait between geysers when you intend to get more. Don't do that. If you're going to get another geyser, do it ASAP, if you're not, don't change your mind later.

As far as geyser 4 is concerned, note that at the 20 minute mark, you will be behind for 12 minutes if you get geyser 4, and I have literally never seen a game go beyond 32 minutes (checked my history).
That said, if your team is consistently dominating the middle at that point, I would get it because you're ahead anyway, and it guarantees that your lead will be even stronger if they take the middle back.

Don't get geyser 5, just don't.
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Zee
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PostSubject: Re: Actual Costs of Geysers   Sun Oct 09, 2011 4:33 am

Nice wrap up, i'll add my comments to it:

Quote :
But don't think you shouldn't get a geyser just because your team just took the middle.

Absolutely agreed, the one thing to keep in mind is that if you notice a pattern in waves (sometimes you hold the middle, sometimes them), it is preferable to time your gas when you don't hold, so you lose less income from it. When you push them deep (fighting at cannon, cannon destoryed), by all means take the geyser if you want.

Quote :
I have never seen a game end before the 12 minute mark, so I think it's safe to say that getting all three geysers as fast as you can is sensible strategy.

Well i have seen 10-11 minute games from both ends of the stick. OK maybe i have not lost in 11 mins, but i have won for sure. IIRC my record is 9 mins with an AT reaper rush versus a very badly reacting team.
I'd say you should be on the lookout for enemy all-ins or very hard pushes. Zealot - Immo on 1 gas is rather deadly to cannons and fortresses, as is Hydra - Roach or MM - Reaper. 1 gas all in is very powerful TBH, and may even snipe your HQ under air units if you go air to hardcounter them. Rmember 1 gas means they'll have a lot more money than you do early on if you take 2 or 3 gas (not to mention they'll be holding the middle all the time, granting them almost equal income to 2 geysers). I'd say 2 gas is safe to take, but the third should only be taken if the enemy is not pushing so hard that you cannot retake the middle in a reasonable amount of time. Losing the middle may actually lead into a snowball you cannot recover from
(example: 2 players do some 1 gas or 0 gas allin, 1 player does moderate force and does eco/geyser: if all-in succeeds, they win, if not, that 1 player will have a monster eco and the others will not be far behind, you still have to build a larger army than them to even move out)

Quote :
The absolute worst thing you can do is wait between geysers when you intend to get more. Don't do that. If you're going to get another geyser, do it ASAP, if you're not, don't change your mind later.

This is the part i do not agree with. The way i see is that gas is a trade of early game power for late game power. IMO the key to win the eco battle is to trade between these powers right. If you go 3 gas as soon as cooldowns finish, you risk losing the middle and not be able to push back for a very long time (3 gas loses vs 2 gas lowtech or 1 gas allin). Also it is senseless to contineu an all-in if it is clear they'll hold it and soon push you back to the middle. You better take your time to even out the eco difference. With middle being held for a while you may end up gaining on them.

I usually follow my principles and they seem to be working well. Even if i lose i usually outscore even the enemy, or at least end up in 2nd place, unless they do something that makes me totally powerless (like mass BL + roachqueen vs Toss from a better eco / with bad allies)
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