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Subject: Burning Power- Clarification rss

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Jacob Schacht
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I am just posting this to clarify something that I still occasionally see people mistakenly say that burning power early makes the power cycle faster.

The simplest way I can explain why that's incorrect is with a simple formula, Spendable Power=.5*Power Gained. If you start with all of your power in bowl I, then your spendable power will always equal half of the power you gain, rounded down, e.g. If you start with twelve power in bowl I and gain eight power your spendable power is four. If you start with four power in bowl I and gain eight power, your spendable power is four.

So the only benefit to burning power is to gain a one time speed boost, no long term benefits.
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Chris Johnson
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That's not really true.

Since you have to move all power tokens out of Bowl 1 before you can move any from Bowl 2 (aside from burning, of course), having fewer power tokens does speed up the rate at which one gets *usable* power.
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Dan Green
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Spoiler (click to reveal)
While your power is in bowl 1, a lower max decreases the time it takes to have usable power again.

If I have 12 power in bowl one and I want to buy a priest, I have to gain 15 power before I can do this.

If I have 7 power in bowl one and I want to buy a priest, I have to gain 10 power before I can do this.


However, while your power is in bowl 2, the amount remains the same.

Bowl 1 has 3, Bowl 2 has 9. If I want to buy a priest, I have to gain 6 power.

Bowl 1 has 3, Bowl 2 has 4. If I want to buy a priest, I have to gain 6 power.

The only drawback to burning power is reducing the number of actions you can take before cycling power fully. It will reduce your "burst" action potential. However, this is already often limited by the other players, so burning power will allow you recover faster from taking multiple power actions (or buying multiple resources). The key is always in finding the right number to hit based on the game.


Edit: After reading the post below, I understand that we are looking at it differently. I believe the OP to be correct. In short, my argument assumed they argued against burning power, but their argument assumes you will burn power (i.e. spendable power is the sum of burn-to-use and usable power).
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Jacob Schacht
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Your answer is precisely why I posted this. Here are three examples that show why you are incorrect.


12 power in bowl I.
Gain 8 power.
Results in 4 power in bowl I, 8 power in bowl II, 0 power in bowl III and 4 spendable power.



8 power in bowl I
Gain 8 power.
Results in 0 power in bowl I, 8 power in bowl II, 0 power in bowl III and 4 spendable power.



4 power in bowl I
Gain 8 power.
Results in 0 power in bowl I, 0 power in bowl II, 4 power in bowl III and 4 spendable power.


Edit: originally posted after seeing Fnord23's reply but before seeing Day2dan's. However, my reply corrects both of you. The thing you are missing is that half the power in bowl II is also spendable. The purpose of this is to show that the speeds do not change, not that it's incorrect to burn power.
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James Mathias
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Jakebeleren wrote:
Your answer is precisely why I posted this. Here are three examples that show why you are incorrect.


12 power in bowl I.
Gain 8 power.
Results in 4 power in bowl I, 8 power in bowl II, 0 power in bowl III and 4 spendable power.



8 power in bowl I
Gain 8 power.
Results in 0 power in bowl I, 8 power in bowl II, 0 power in bowl III and 4 spendable power.



4 power in bowl I
Gain 8 power.
Results in 0 power in bowl I, 0 power in bowl II, 4 power in bowl III and 4 spendable power.


Edit: originally posted after seeing Fnord23's reply but before seeing Day2dan's. However, my reply corrects both of you. The thing you are missing is that half the power in bowl II is also spendable. The purpose of this is to show that the speeds do not change, not that it's incorrect to burn power.


You cannot spend power unless it's in bowl 3, so your first two examples actually have a spendable power of 2, as you'd need to burn 2 of the 4 in bowl two to move two into bowl three, that you can then spend. Nevermind, I misread your post.
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Dan Green
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Ninja edits put us both into agreement. Thanks, this is definitely interesting to ponder.
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Dan Green
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jmathias wrote:


You cannot spend power unless it's in bowl 3, so your first two examples actually have a spendable power of 2, as you'd need to burn 2 of the 4 in bowl two to move two into bowl three, that you can then spend.


That is his point. Given that you will burn power, the speeds do not change. The three examples are actually flowing into one another to form a course of power gain in a game. (start with 12, gain 8, burn 4 to spend 4, start with 8, gain 8, burn 4 to spend 4...)
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Chris Johnson
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*Sigh*

Re-read my post.

Burning power absolutely increases the rate at which you get *usable* power (not only in the moment, as your examples propose, but just as significantly, over the course of the game).

Yes, you will ultimately end up with (roughly) the same amount of power in Bowl 3 over the course of the game. But the difference between *when* you get it with 12, 9, 8, or 6 tokens can make a significant difference. (Not to mention the effect on the maximum power you can have available to spend.)

If you can't see the meaningful difference between burning power and the "normal" rate of flow of power tokens to Bowl 3, perhaps you might want to adopt a somewhat less know-it-all tone...
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Jacob Schacht
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I believe your definition of *usable* power ignores the very rule that we are discussing.

From the english rule book:

If you do not have enough Power in Bowl III to take a specific
Power or Conversion action, on top of your Action, you may move
Power tokens from Bowl II to Bowl III and then immediately take
the desired Action. However, for each Power token moved in this
fashion, you need to remove 1 Power token from Bowl II from the
game. From now on, you will irrevocably have to deal with fewer
Power tokens in your cycle. (You may not sacrifice Power if you
only have 1 Power token in Bowl II.)


So the spendable or *usable* power at anytime =Bowl III power +.5(Bowl II power)
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Andrew E
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Counting power in bowl 2 as "spendable" is technically true, but it's not the right way to think about the game.

You only get to spend so much power out of bowl 2 per game unless you're willing to face very serious drawbacks. Around 4-6 (until the very end). This is a non-renewable resource. Therefore, spending 1 out of bowl 3 is very much preferable to spending 2 out of bowl 2, even though both result in 1 power.

That said, burning off your power is in fact a strict detriment to your power flow, so long as you understand what's going on. You only get the long recharge time everybody notices with 12 power if you go on a shopping spree when you build it up. If you spend it more evenly like you would after having burned 4-6 off, then you'll get it back just as evenly, but with a larger reserve.

And *that* said, I think it's still usually best to burn some power early because the doing the above means you're holding onto usable power in bowl 3, when in fact you usually want to be spending your power resources to get more stuff on the board sooner rather than later. Usually.
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Grant
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I can't believe this is still being debated. Jacob (the OP) is absolutely correct. This has been shown in multiple threads, mathematically and through examples, every time someone brings up the question or suggests there is some benefit to burning power beyond getting the immediate use of it.

It does NOT make your power cycle faster.

It does NOT make power in bowl three available sooner.

Moving 1 power token from bowl 1 to bowl 3 gives you EXACTLY the same amount of power as moving 2 tokens from bowl 1 to bowl 2. In the former example it means you burned power earlier in the game. In the latter example it means you're going to burn power now.

And that is the point that I think AndrewE is missing when he says "spending 1 out of bowl 3 is very much preferable to spending 2 out of bowl 2". Of course that statement is true, but the resulting conclusion, that you should burn a few power to get to use power in bowl 1 faster, is flawed. If the PROBLEM is that you have too much power in bowl 1 (so the power isn't making it into bowl 3 fast enough), then that means you haven't burned power yet, so now you have the option to do so.

Whether you burn power early, mid, or late, the total power available to you never changes. What you LOSE by burning is the ability to stockpile a ton of power. Whether or not that is important to your strategy is another story.
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Bryan Thunkd
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grant5 wrote:
Moving 1 power token from bowl 1 to bowl 3 gives you EXACTLY the same amount of power as moving 2 tokens from bowl 1 to bowl 2. In the former example it means you burned power earlier in the game. In the latter example it means you're going to burn power now.
This is the key idea.

Imagine a scenario where both players have 12 power discs in bowl 2. Player A burns off 6 discs to get 6 power now, which he uses. If player B wants he could do the same. But if he doesn't need the power right now he can wait and he won't fall behind (assuming both player are getting power at the same rate).

So let's fast forward a little... Both players get 6 additional power bumps, player A moves his six discs to bowl 2. Player B, who still has 12 discs in bowl 2 moves 6 to bowl 3 and uses them. Both players got, and spent 6 power so far.

Now both players get another 6 power bumps, player A moves his 6 discs to bowl 3 and uses them. Player B moves 6 discs from bowl 2 to bowl 3 and uses them. Both players have gotten and spent 12 power now.

It will take player A 12 power bumps to get his 6 discs from bowl 1 to bowl 3, where he will have another 6 spendable power. With the same 12 power bumps, player B can get 12 discs to bowl 2... Where he can burn 6 to get 6 spendable power. From that point on both players have the same number of discs in the same bowls. Both got and spent 18 power.

Player A was no faster than player B.
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Jan B.
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It clearly doesn't matter if one individual power token cycles faster. Power as an overall resource is available at the same speed, regardless of the amount of power tokens remaining in the bowls.
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Dan Green
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sthrjo wrote:
Compare two extremes: Player A has sacrificed all but one token in bowl I. After 2 power+ it is in bowl III and can be used, and then after the 4:th, 6:th power+ and so on. The individual token itself cycles 0.5 laps per power+.
Player B has 12 tokens in bowl I. After 13 power+ the first one can be used from bowl III. Then after 14, 15 and so on up to 24. Each individual token cycles slower in average: After 24 power+ each token has finished one lap. That is 1/24 laps per power+ per token. But since B has 12 of them, this does not matter for the average cycle speed compared to A. Only the startup phase length is different, and the buffering capacity.
See [article=11636564][/article]. Noone seems to come up with the perfect description of the power cycle that everone can agree on.


But in Player B's case, they have the same effective usable power after 2 power+, because they can burn one and place one in III. Your power becomes effectively usable at exactly the same rate, in any situation.
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Robert Stewart
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As a thought experiment, consider what happens if you start with 1,000,000 power rather than just 12, but aren't allowed to burn power.

If you start with the 1,000,000 power in Bowl I, then you will never be able to spend power.

If you start with the 1,000,000 power in Bowl II, then the game is very much like the standard game.

If you start with the 1,000,000 power in Bowl III, then you effectively have unlimited resources (compared to the standard game).

What's my point? If you don't burn power, power in Bowl II is (almost) completely irrelevant - so long as you have enough to cover your power gains, it doesn't matter whether that leaves you with none in Bowl II or you have a million spare power in Bowl II.


Burning N power does 3 things:
A) It gives you an immediate one-time gain of N power
B) It reduces the amount of power you can potentially burn during the rest of the game by N
C) It reduces your maximum power spend by N for the rest of the game.

If Bowl I is empty and you have 6 power in Bowl III that you use for the double-shovel action, then 6 power gain will empty Bowl I and another 6 power gain will leave you back where you started, whether you have 6 power left in Bowl II the whole time, or you burned 6 power earlier in the game.


If two players - Alice and Bob - both start with 12 power in Bowl II, Alice burns 6 power while Bob is given 6 power+, they both play the game identically, gaining and spending the same amounts of power at the same time, and ending with all their power left in Bowl II, where Bob burns 6 while Alice is given 6 power+, then the only way it would have broken down is if they ever got more power+ than Alice could use - throughout the game, Bob would have had 6 more power in Bowl II than Alice, and that would have been the only difference between them.

The power would not have moved any faster for Alice than for Bob.
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Dan Green
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rmsgrey wrote:
...so long as you have enough to cover your power gains, it doesn't matter whether that leaves you with none in Bowl II or you have a million spare power in Bowl II.


I think this sums up what you should be thinking about when burning power in game. The thought experiment is helpful for getting to this point - your speed of cycling does not change from burning power assuming that more power can be burned.

The only limit you need to make for yourself is the number at which power burning should be stalled, which will be based on your assumed power gain rate and plan for spending power (i.e. the amount you need to take 2 desired actions in a short frame of time).
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Bryan Thunkd
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Okay, here it is... a visual representation. Please note... I show how much power both players have taken, as well as how much potential power they have at any given moment... which is a combination of the power in bowl 3 AND the power they could get by burning the discs in bowl 2.




It's no faster to burn power earlier. Both players always have the same sum of power spent and potential power. Alice sacrificed power earlier to get her 6 earlier, but Bob always had the opportunity to match her and catch up on power whenever he was ready to sacrifice his.
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Dan Green
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Wonderful. Love it. Thanks!
 
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Jens Kunst
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Wow, this is an awesome thread. Almost philosophical.
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LudoH LudoH
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perfect illustration!

It also illustrates very well the only 3 drawbacks to burning early:
- you have less powers so if you burn more than 6 there are some actions you cannot do anymore (i.e. double shovel)
- you can store less power: in the example Bob can reach a potential of 12, not alice
- you cannot earn too many powers at a time: at round 7, alice can only earn 6 more bumps while bob can gain 18 (and they both have the same potential)

Of course the big advantage of burning early is that you can benefit early from the power ... which makes a big difference, no need to illustrate this
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Mike Thompson
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It is obviously - but trivially! - true that burning power results in your power discs cycling faster for the remainder of the game. This DOES NOT mean that you get more usable power. 6 tokens cycling at twice the speed as twelve tokens results in the same amount of usable power. But they DO cycle faster and it is wrong to say they do not.
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Mike Thompson
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I should slightly alter my position to state that this isn't actually trivial from a gameplay perspective, only from a mathematical one. Having (for example) 6 usable power every turn is probably better than 12 power every other turn because of the rate at which power actions are used. Yes, you can spend six this turn and keep six for next turn, but you're an entire turn behind before you can synch up that cycle - in addition to the six half-power bumps you forwent to keep the 12 tokens to begin with.
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Bryan Thunkd
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CyanideNow wrote:
Having (for example) 6 usable power every turn is probably better than 12 power every other turn because of the rate at which power actions are used.
It takes 12 power to get 6 discs from bowl 1 to bowl 3. Those same 12 power would move 12 discs from bowl 1 to bowl 2... Where 6 of them can be sacrificed to get 6 power. So there is never a point where the guy with only 6 discs has more available power than the guy with 12. He's not getting it every other turn, at least he doesn't have to if he doesn't want to.

CyanideNow wrote:
Yes, you can spend six this turn and keep six for next turn, but you're an entire turn behind before you can synch up that cycle - in addition to the six half-power bumps you forwent to keep the 12 tokens to begin with.
You are never a turn behind. You can always sacrifice power to catch up.

Go back and look at my illustration to understand what I'm saying.
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Grant
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CyanideNow wrote:
I should slightly alter my position to state that this isn't actually trivial from a gameplay perspective, only from a mathematical one. Having (for example) 6 usable power every turn is probably better than 12 power every other turn because of the rate at which power actions are used. Yes, you can spend six this turn and keep six for next turn, but you're an entire turn behind before you can synch up that cycle - in addition to the six half-power bumps you forwent to keep the 12 tokens to begin with.

No. For all the reasons that have already been explained in painstaking detail, no. This is just wrong.
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Robert Stewart
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CyanideNow wrote:
It is obviously - but trivially! - true that burning power results in your power discs cycling faster for the remainder of the game. This DOES NOT mean that you get more usable power. 6 tokens cycling at twice the speed as twelve tokens results in the same amount of usable power. But they DO cycle faster and it is wrong to say they do not.


Only if you wait for them all to cycle and then spend them all - someone with a power income of 12 can always spend an average of 6 power every turn, whether they have 6 discs or 12 - with more discs, they can spend less than 6 one turn and more the next.

If you leave 6 tokens sitting in Bowl II the whole time, then the remaining 6 tokens cycle at the same rate they would if the stationary ones weren't there.
 
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