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I'm having a little trouble reaching a conclusion I'm happy with. The following is an "ability" for a game, which has a damage output and a "cooldown". The cooldown is how long I must wait before I can use the ability again after it has been used, measured in seconds.

Q deals 300 damage and has a cooldown of 3 seconds. The dps (damage-per-second) of Q is 100.

I have a total of 4 abilities, including Q; with varied cooldowns. Using each of these abilities will reduce the cooldowns of the other abilities by 1 second. Eith this is mind, how do I calculate the dps of Q?

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As stated, it doesn't really make sense for me. How do you define the DPS of one ability in context of the other ones? Unless you ignore them completely, in which case it is again $100$. It would make more sense to calculate the total DPS of all the four abilities, though I imagine it won't be a very simple calculation. –  tomasz Nov 2 '12 at 23:59

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You need to find the repeatable pattern that uses Q most often. Say you have one other ability R that cools down in 5 seconds. You use Q and then immediately R (or do you have to wait a second?). You can use Q then at second $2$ (right?). R is now available at second 4, and you can use it to make Q available also at second 4, so you fire again. Now you have to wait until 7 for the next Q, 8 for the next R, 9 for the next Q and you are ready to start over at 12 with both recharged. Five shots of Q in 12 seconds means 125 dps.

I'm not sure I have the rules right, but you may be able to see how to work on it. With three other abilities, you need to think about what order to do them in, and maybe wait for one until it recharges all the others. I don't think there is an easy rule, but often the right pattern is obvious.

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you're understanding is correct.. and by creating a simulation i could calculate the dps over a specified duration, like you have. however, i was looking for the more difficult rule to calculating the dps regardless of time taken. though i can't help but think it may be somewhat of a paradox, and that a simulation may be required. –  john smith Nov 3 '12 at 0:01
    
@johnsmith: Here you use Q at 0,2,4,7,9 seconds in a repeat of 12. So you do 1500 per 12 seconds, then need to count up where you are in the cycle. If your battle lasted 32 seconds, that is $2\cdot 12 +8$ so you do $2 \cdot 1500 + 1200$ –  Ross Millikan Nov 3 '12 at 0:04
    
thanks for the help, ross –  john smith Nov 3 '12 at 0:14

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