User talk:Misacek01 - Revision history

Misacek01: /* Affordability */

2018-09-03T03:27:22Z

Affordability

← Older revision		Revision as of 03:27, 3 September 2018
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	**''Note that the expressions above have been simplified to reflect the fact that this particular topic has F = 0. Since it is the only topic with this equation type, the loss of generality does not matter.''		**''Note that the expressions above have been simplified to reflect the fact that this particular topic has F = 0. Since it is the only topic with this equation type, the loss of generality does not matter.''
	*In all calculations above, the constant <code>C</code> (see equations) is ignored; for the topics where <code>C ≠ 0</code>, results must be adjusted by adding <code>C × (N - F)</code>. This only applies to '''follower robot count''' and '''artillery shooting speed'''.		*In all calculations above, the constant <code>C</code> (see equations) is ignored; for the topics where <code>C ≠ 0</code>, results must be adjusted by adding <code>C × (N - F)</code>. This only applies to '''follower robot count''' and '''artillery shooting speed'''.
			In all cases, the player can calculate the research price of their target level using the general equations (1), (2), (3) (see preceding sections), look up the price of the first "infinite" level in the table above, then use the summation properties described herein to arrive at a total science pack budget.
			*Note that these prices reflect '''research units''', which will not be equal to science packs if [[productivity module\|productivity modules]] are used in labs. (In that case, the science pack requirement will be lower.)

	=== Throughput ===		=== Throughput ===

Misacek01: /* Affordability */

2018-09-03T03:22:50Z

Affordability

← Older revision		Revision as of 03:22, 3 September 2018
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	**''Note that the expressions above have been simplified to reflect the fact that this particular topic has F = 0. Since it is the only topic with this equation type, the loss of generality does not matter.''		**''Note that the expressions above have been simplified to reflect the fact that this particular topic has F = 0. Since it is the only topic with this equation type, the loss of generality does not matter.''
	*In all calculations above, the constant <code>C</code> (see equations) is ignored; for the topics where <code>C ≠ 0</code>, results must be adjusted by adding <code>C × (N - F)</code>. This only applies to '''follower robot count''' and '''artillery shooting speed'''.		*In all calculations above, the constant <code>C</code> (see equations) is ignored; for the topics where <code>C ≠ 0</code>, results must be adjusted by adding <code>C × (N - F)</code>. This only applies to '''follower robot count''' and '''artillery shooting speed'''.


	~~<code></code>~~

	=== Throughput ===		=== Throughput ===

Misacek01: /* Affordability */

2018-09-03T03:21:53Z

Affordability

← Older revision		Revision as of 03:21, 3 September 2018
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	*The cumulative price of the first <code>N - F</code> levels of infinite research topics whose underlying equation is an arithmetic series (equation type (3)) is <code>(N - F) × (P[N] + P[F + 1]) ÷ 2</code>; i.e, <code>N - F</code> times the mean of the prices of the first and last "infinite" level.		*The cumulative price of the first <code>N - F</code> levels of infinite research topics whose underlying equation is an arithmetic series (equation type (3)) is <code>(N - F) × (P[N] + P[F + 1]) ÷ 2</code>; i.e, <code>N - F</code> times the mean of the prices of the first and last "infinite" level.
	**Expanding production capacity by a factor of ''X'', as above, will in this case allow an additional <code>N × (X - 1)</code> levels to be researched before the benefit of the expansion is wiped out (i.e., research progress speed drops to or below what it was pre-expansion).		**Expanding production capacity by a factor of ''X'', as above, will in this case allow an additional <code>N × (X - 1)</code> levels to be researched before the benefit of the expansion is wiped out (i.e., research progress speed drops to or below what it was pre-expansion).
	*The cumulative price of the first '''''N''''' levels of '''artillery shell shooting speed''', the sole infinite research topic whose underlying equation is a powers-of-three geometric series (equation type (2)) is <code>1.5 × P[N] - 0.5 × P[1]</code>; i.e., 1.5 times the price of the final researched level, less half the price of the first level. ''(Note that the expressions above have been simplified to reflect the fact that this particular topic has F = 0. Since it is the only topic with this equation type, the loss of generality does not matter.)''		*The cumulative price of the first '''''N''''' levels of '''artillery shell shooting speed''', the sole infinite research topic whose underlying equation is a powers-of-three geometric series (equation type (2)) is <code>1.5 × P[N] - 0.5 × P[1]</code>; i.e., 1.5 times the price of the final researched level, less half the price of the first level.
	*In all		**''Note that the expressions above have been simplified to reflect the fact that this particular topic has F = 0. Since it is the only topic with this equation type, the loss of generality does not matter.''
			*In all calculations above, the constant <code>C</code> (see equations) is ignored; for the topics where <code>C ≠ 0</code>, results must be adjusted by adding <code>C × (N - F)</code>. This only applies to '''follower robot count''' and '''artillery shooting speed'''.

Misacek01: /* Affordability */

2018-09-03T03:18:15Z

Affordability

← Older revision		Revision as of 03:18, 3 September 2018
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	As the price of most infinite research topics (specifically, those based on geometric progressions) increases very steeply, it may be a good idea for players to set realistic target levels for each of the infinite research topics they wish to pursue, and make their factory plans accordingly. To that end, the following properties of cumulative infinite research prices may be useful:		As the price of most infinite research topics (specifically, those based on geometric progressions) increases very steeply, it may be a good idea for players to set realistic target levels for each of the infinite research topics they wish to pursue, and make their factory plans accordingly. To that end, the following properties of cumulative infinite research prices may be useful:

	*The cumulative price of the first (N - F) levels (notation as in previous sections; i.e., here counting "infinite" levels only) of infinite research topics whose underlying equation is a powers-of-two geometric series (see equation type (1) in preceding sections) is 2 × P[N] - P[F+1]; i.e., twice the price of the final researched level, less the price of the first "infinite" level.		*The cumulative price of the first <code>N - F</code> levels (notation as in previous sections; i.e., here counting "infinite" levels only) of infinite research topics whose underlying equation is a powers-of-two geometric series (see equation type (1) in preceding sections) is <code>2 × P[N] - P[F+1]</code>; i.e., twice the price of the final researched level, less the price of the first "infinite" level.
	**This tends toward 2 × P[N] as N goes to infinity.		**This tends toward <code>2 × P[N]</code> as ''N'' goes to infinity.
	**The above also shows that, assuming constant research speed (usually, this is the same as science pack production capacity), each subsequent level of an infinite research topic of this type will take about as long as ''all'' preceding infinite levels took combined (or, twice as long as the previous level).		**The above also shows that, assuming constant research speed (usually, this is the same as science pack production capacity), each subsequent level of an infinite research topic of this type will take about as long as ''all'' preceding infinite levels took combined (or, twice as long as the previous level).
	**Further, assuming one has reached a level M they consider the "highest feasible" with their current science pack production capacity, expanding said capacity by a factor of X will allow at least floor(log[2](X)) and at most ceiling(log[2](X)) (i.e., the next lower / higher integer from the base-2 logarithm of X) additional levels to be researched before the next level takes longer to research with the expanded capacity than level M + 1 would have taken with the pre-expansion production capacity.		**Further, assuming one has reached a level M they consider the "highest feasible" with their current science pack production capacity, expanding said capacity by a factor of '''''X''''' will allow at least <code>floor(log[2](X))</code> and at most <code>ceiling(log[2](X))</code> (i.e., the next lower / higher integer from the base-2 logarithm of ''X'') additional levels to be researched before the next level takes longer to research with the expanded capacity than level <code>M + 1</code> would have taken with the pre-expansion production capacity.
	***For example, if one expands production capacity by a factor of 10, they will be able to research at least floor(log[2](10)) = 3 and at most ceiling(log[2](10)) = 4 additional levels in a given technology before the exponential increase in price wipes out the benefits of their ~~x10~~ capacity expansion.		***For example, if one expands production capacity by a factor of 10, they will be able to research at least <code>floor(log[2](10)) = 3</code> and at most <code>ceiling(log[2](10)) = 4</code> additional levels in a given technology before the exponential increase in price wipes out the benefits of their ×10 capacity expansion.
	*The cumulative price of the first (N - F) levels of infinite research topics whose underlying equation is an arithmetic series (equation type (3)) is (N - F) × (P[N] + P[F + 1]) / 2; i.e, (N - F) times the mean of the prices of the first and last "infinite" level.		*The cumulative price of the first <code>N - F</code> levels of infinite research topics whose underlying equation is an arithmetic series (equation type (3)) is <code>(N - F) × (P[N] + P[F + 1]) ÷ 2</code>; i.e, <code>N - F</code> times the mean of the prices of the first and last "infinite" level.
	**Expanding production capacity by a factor of X, as above, will in this case allow an additional N × (X - 1) levels to be researched before the benefit of the expansion is wiped out (i.e., research progress speed drops to or below what it was pre-expansion).		**Expanding production capacity by a factor of ''X'', as above, will in this case allow an additional <code>N × (X - 1)</code> levels to be researched before the benefit of the expansion is wiped out (i.e., research progress speed drops to or below what it was pre-expansion).
	*The cumulative price of the first '''''N''''' levels of '''artillery shell shooting speed''', the sole infinite research topic whose underlying equation is a powers-of-three geometric series (equation type (2)) is 1.5 × P[N] - 0.5 × P[1]; i.e., 1.5 times the price of the final researched level, less half the price of the first level. ''(Note that the expressions above have been simplified to reflect the fact that this particular topic has F = 0. Since it is the only topic with this equation type, the loss of generality does not matter.)''		*The cumulative price of the first '''''N''''' levels of '''artillery shell shooting speed''', the sole infinite research topic whose underlying equation is a powers-of-three geometric series (equation type (2)) is <code>1.5 × P[N] - 0.5 × P[1]</code>; i.e., 1.5 times the price of the final researched level, less half the price of the first level. ''(Note that the expressions above have been simplified to reflect the fact that this particular topic has F = 0. Since it is the only topic with this equation type, the loss of generality does not matter.)''
			*In all

Misacek01: /* Affordability */

2018-09-03T03:14:13Z

Affordability

← Older revision		Revision as of 03:14, 3 September 2018
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	As the price of most infinite research topics (specifically, those based on geometric progressions) increases very steeply, it may be a good idea for players to set realistic target levels for each of the infinite research topics they wish to pursue, and make their factory plans accordingly. To that end, the following properties of cumulative infinite research prices may be useful:		As the price of most infinite research topics (specifically, those based on geometric progressions) increases very steeply, it may be a good idea for players to set realistic target levels for each of the infinite research topics they wish to pursue, and make their factory plans accordingly. To that end, the following properties of cumulative infinite research prices may be useful:

	The cumulative price of the first (N - F) levels (notation as in previous sections; i.e., here counting "infinite" levels only) of infinite research topics whose underlying equation is a powers-of-two geometric series (see equation type (1) in preceding sections) is 2 P[N] - P[F+1]; i.e., twice the price of the final researched level, less the price of the first "infinite" level.		*The cumulative price of the first (N - F) levels (notation as in previous sections; i.e., here counting "infinite" levels only) of infinite research topics whose underlying equation is a powers-of-two geometric series (see equation type (1) in preceding sections) is 2 × P[N] - P[F+1]; i.e., twice the price of the final researched level, less the price of the first "infinite" level.
	*This tends toward 2 P[N] as N goes to infinity.		**This tends toward 2 × P[N] as N goes to infinity.
	**The above also shows that, assuming constant research speed (usually, this is the same as science pack production capacity), each subsequent level of an infinite research topic of this type will take about as long as ''all'' preceding infinite levels took combined (or, twice as long as the previous level).		**The above also shows that, assuming constant research speed (usually, this is the same as science pack production capacity), each subsequent level of an infinite research topic of this type will take about as long as ''all'' preceding infinite levels took combined (or, twice as long as the previous level).
	**Further, assuming one has reached a level M they consider the "highest feasible" with their current science pack production capacity, expanding said capacity by a factor of X will allow at least floor(log[2](X)) and at most ceiling(log[2](X)) (i.e., the next lower / higher integer from the base-2 logarithm of X) additional levels to be researched before the next level takes longer to research with the expanded capacity than level M + 1 would have taken with the pre-expansion production capacity.		**Further, assuming one has reached a level M they consider the "highest feasible" with their current science pack production capacity, expanding said capacity by a factor of X will allow at least floor(log[2](X)) and at most ceiling(log[2](X)) (i.e., the next lower / higher integer from the base-2 logarithm of X) additional levels to be researched before the next level takes longer to research with the expanded capacity than level M + 1 would have taken with the pre-expansion production capacity.
	***For example, if one expands production capacity by a factor of 10, they will be able to research at least floor(log[2](10)) = 3 and at most ceiling(log[2](10)) = 4 additional levels in a given technology before the exponential increase in price wipes out the benefits of their x10 capacity expansion.		***For example, if one expands production capacity by a factor of 10, they will be able to research at least floor(log[2](10)) = 3 and at most ceiling(log[2](10)) = 4 additional levels in a given technology before the exponential increase in price wipes out the benefits of their x10 capacity expansion.
	The cumulative price of the first (N - F) levels of infinite research topics whose underlying equation is an arithmetic series (equation type (3)) is (N - F) (P[N] + P[F + 1]) / 2; i.e, (N - F) times the mean of the prices of the first and last "infinite" level.		*The cumulative price of the first (N - F) levels of infinite research topics whose underlying equation is an arithmetic series (equation type (3)) is (N - F) × (P[N] + P[F + 1]) / 2; i.e, (N - F) times the mean of the prices of the first and last "infinite" level.
	*Expanding production capacity by a factor of X, as above, will in this case allow an additional N (X - 1) levels to be researched before the benefit of the expansion is wiped out (i.e., research progress speed drops to or below what it was pre-expansion).		**Expanding production capacity by a factor of X, as above, will in this case allow an additional N × (X - 1) levels to be researched before the benefit of the expansion is wiped out (i.e., research progress speed drops to or below what it was pre-expansion).
	The cumulative price of the first N levels of '''artillery shell shooting speed''', the sole infinite research topic whose underlying equation is a powers-of-three geometric series (equation type (2)) is 2 P[N] - P[1]; i.e., ~~twice~~ the price of the final researched level, less the price of the first ~~"infinite"~~ level.		*The cumulative price of the first '''''N''''' levels of '''artillery shell shooting speed''', the sole infinite research topic whose underlying equation is a powers-of-three geometric series (equation type (2)) is 1.5 × P[N] - 0.5 × P[1]; i.e., 1.5 times the price of the final researched level, less half the price of the first level. ''(Note that the expressions above have been simplified to reflect the fact that this particular topic has F = 0. Since it is the only topic with this equation type, the loss of generality does not matter.)''

Misacek01: /* Affordability */

2018-09-03T03:07:01Z

Affordability

← Older revision		Revision as of 03:07, 3 September 2018
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	The cumulative price of the first (N - F) levels (notation as in previous sections; i.e., here counting "infinite" levels only) of infinite research topics whose underlying equation is a powers-of-two geometric series (see equation type (1) in preceding sections) is 2 P[N] - P[F+1]; i.e., twice the price of the final researched level, less the price of the first "infinite" level.		The cumulative price of the first (N - F) levels (notation as in previous sections; i.e., here counting "infinite" levels only) of infinite research topics whose underlying equation is a powers-of-two geometric series (see equation type (1) in preceding sections) is 2 P[N] - P[F+1]; i.e., twice the price of the final researched level, less the price of the first "infinite" level.
	*This tends toward 2 P[N] as N goes to infinity.		*This tends toward 2 P[N] as N goes to infinity.
	**The above also shows that, assuming constant research speed (usually, this is the same as science pack production capacity), each subsequent level of an infinite research topic of this type will take about as long ~~to complete~~ as ''all'' preceding infinite levels took ~~cumulatively~~.		**The above also shows that, assuming constant research speed (usually, this is the same as science pack production capacity), each subsequent level of an infinite research topic of this type will take about as long as ''all'' preceding infinite levels took combined (or, twice as long as the previous level).
	**Further, assuming one has reached a level M they consider the "highest feasible" with their current science pack production capacity, expanding said capacity by a factor of X will allow at least floor(log[2](X)) and at most ceiling(log[2](X)) (i.e., the next lower / higher integer from the base-2 logarithm of X) additional levels to be researched before the next level takes longer to research with the expanded capacity than level M would have taken with the pre-expansion production capacity. For example, if one expands production capacity by a factor of 10, they will be able to research at least floor(log[2](10)) = 3 and at most ceiling(log[2](10)) = 4 additional levels in a given technology before the exponential increase in price wipes out the benefits of their x10 capacity expansion.		**Further, assuming one has reached a level M they consider the "highest feasible" with their current science pack production capacity, expanding said capacity by a factor of X will allow at least floor(log[2](X)) and at most ceiling(log[2](X)) (i.e., the next lower / higher integer from the base-2 logarithm of X) additional levels to be researched before the next level takes longer to research with the expanded capacity than level M + 1 would have taken with the pre-expansion production capacity.
	*The cumulative price of the first (N - F) levels of infinite research topics whose underlying equation is an arithmetic series (equation type (3)) is		***For example, if one expands production capacity by a factor of 10, they will be able to research at least floor(log[2](10)) = 3 and at most ceiling(log[2](10)) = 4 additional levels in a given technology before the exponential increase in price wipes out the benefits of their x10 capacity expansion.
			The cumulative price of the first (N - F) levels of infinite research topics whose underlying equation is an arithmetic series (equation type (3)) is (N - F) (P[N] + P[F + 1]) / 2; i.e, (N - F) times the mean of the prices of the first and last "infinite" level.
			*Expanding production capacity by a factor of X, as above, will in this case allow an additional N (X - 1) levels to be researched before the benefit of the expansion is wiped out (i.e., research progress speed drops to or below what it was pre-expansion).
			The cumulative price of the first N levels of '''artillery shell shooting speed''', the sole infinite research topic whose underlying equation is a powers-of-three geometric series (equation type (2)) is 2 P[N] - P[1]; i.e., twice the price of the final researched level, less the price of the first "infinite" level.

Misacek01: /* Affordability */

2018-09-03T02:38:56Z

Affordability

← Older revision		Revision as of 02:38, 3 September 2018
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	As the price of most infinite research topics (specifically, those based on geometric progressions) increases very steeply, it may be a good idea for players to set realistic target levels for each of the infinite research topics they wish to pursue, and make their factory plans accordingly. To that end, the following properties of cumulative infinite research prices may be useful:		As the price of most infinite research topics (specifically, those based on geometric progressions) increases very steeply, it may be a good idea for players to set realistic target levels for each of the infinite research topics they wish to pursue, and make their factory plans accordingly. To that end, the following properties of cumulative infinite research prices may be useful:

	The cumulative price of the first N levels of infinite research topics whose underlying equation is a powers-of-two geometric series (see equation type (1) in preceding sections) is 2 P[N] - P[F+1]; i.e., twice the price of the final researched level, less the price of the first "infinite" level. This tends toward 2 * P[N] as N goes to infinity.		The cumulative price of the first (N - F) levels (notation as in previous sections; i.e., here counting "infinite" levels only) of infinite research topics whose underlying equation is a powers-of-two geometric series (see equation type (1) in preceding sections) is 2 P[N] - P[F+1]; i.e., twice the price of the final researched level, less the price of the first "infinite" level.
	*		*This tends toward 2 P[N] as N goes to infinity.
			**The above also shows that, assuming constant research speed (usually, this is the same as science pack production capacity), each subsequent level of an infinite research topic of this type will take about as long to complete as ''all'' preceding infinite levels took cumulatively.
			**Further, assuming one has reached a level M they consider the "highest feasible" with their current science pack production capacity, expanding said capacity by a factor of X will allow at least floor(log[2](X)) and at most ceiling(log[2](X)) (i.e., the next lower / higher integer from the base-2 logarithm of X) additional levels to be researched before the next level takes longer to research with the expanded capacity than level M would have taken with the pre-expansion production capacity. For example, if one expands production capacity by a factor of 10, they will be able to research at least floor(log[2](10)) = 3 and at most ceiling(log[2](10)) = 4 additional levels in a given technology before the exponential increase in price wipes out the benefits of their x10 capacity expansion.
			*The cumulative price of the first (N - F) levels of infinite research topics whose underlying equation is an arithmetic series (equation type (3)) is

Misacek01: /* Affordability */

2018-09-03T02:22:35Z

Affordability

← Older revision		Revision as of 02:22, 3 September 2018
Line 11:		Line 11:

	As the price of most infinite research topics (specifically, those based on geometric progressions) increases very steeply, it may be a good idea for players to set realistic target levels for each of the infinite research topics they wish to pursue, and make their factory plans accordingly. To that end, the following properties of cumulative infinite research prices may be useful:		As the price of most infinite research topics (specifically, those based on geometric progressions) increases very steeply, it may be a good idea for players to set realistic target levels for each of the infinite research topics they wish to pursue, and make their factory plans accordingly. To that end, the following properties of cumulative infinite research prices may be useful:

			The cumulative price of the first N levels of infinite research topics whose underlying equation is a powers-of-two geometric series (see equation type (1) in preceding sections) is 2 P[N] - P[F+1]; i.e., twice the price of the final researched level, less the price of the first "infinite" level. This tends toward 2 * P[N] as N goes to infinity.
			*



			<code></code>

	=== Throughput ===		=== Throughput ===

Misacek01: /* Infinite Research */

2018-09-03T02:17:32Z

Infinite Research

← Older revision		Revision as of 02:17, 3 September 2018
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	== Page Edits Under Construction (Please Don't Edit) ==		== Page Edits Under Construction (Please Don't Edit) ==

	=== ~~Infinite Research~~ ===		=== Affordability ===
			Infinite research is essentially an inexhaustible resource sink for players who build very large bases. While the bonuses it provides can significantly improve the player's capabilities (particularly as regards combat), they are subject to diminishing returns; thus, the per-level contributions from very high levels of infinite research will eventually provide only marginal improvements.

			As the price of most infinite research topics (specifically, those based on geometric progressions) increases very steeply, it may be a good idea for players to set realistic target levels for each of the infinite research topics they wish to pursue, and make their factory plans accordingly. To that end, the following properties of cumulative infinite research prices may be useful:

	=== Throughput ===		=== Throughput ===

Misacek01 at 01:58, 3 September 2018

2018-09-03T01:58:53Z

← Older revision		Revision as of 01:58, 3 September 2018
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	== Page Edits Under Construction (Please Don't Edit) ==		== Page Edits Under Construction (Please Don't Edit) ==

			=== Infinite Research ===


	=== Throughput ===		=== Throughput ===
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	**Where exactly you set your cutoff is up to you, but if your trains spend, say, 1/3 of total circuit time waiting, your network is probably nearing its limits and you might do well to consider expanding it. (Although before that, it may be a good idea to check that the source of excessive delays is not deadlocks, trains out of fuel, biter damage, poor or incorrect signalling, and other "preventable" problems.)		**Where exactly you set your cutoff is up to you, but if your trains spend, say, 1/3 of total circuit time waiting, your network is probably nearing its limits and you might do well to consider expanding it. (Although before that, it may be a good idea to check that the source of excessive delays is not deadlocks, trains out of fuel, biter damage, poor or incorrect signalling, and other "preventable" problems.)
	**''As a side note, this also implies there is a ''maximum'' throughput that a network with a given topology can have such that adding further trains past the number corresponding to the maximum actually ''lowers'' the throughput. An intuitive way to visualize this is a road which obviously moves more cars from start to end when not quite full than when completely jammed. While there are certainly more individual cars per unit length on the solid-jam road than on the half-full one, none of them are getting anywhere, while on the half-full road at least ''some'' cars are getting somewhere. Unfortunately, again the optimum capacity is hard to calculate unless the network is trivially simple.''		**''As a side note, this also implies there is a ''maximum'' throughput that a network with a given topology can have such that adding further trains past the number corresponding to the maximum actually ''lowers'' the throughput. An intuitive way to visualize this is a road which obviously moves more cars from start to end when not quite full than when completely jammed. While there are certainly more individual cars per unit length on the solid-jam road than on the half-full one, none of them are getting anywhere, while on the half-full road at least ''some'' cars are getting somewhere. Unfortunately, again the optimum capacity is hard to calculate unless the network is trivially simple.''


	~~== Infinite Research ==~~