Note and greeting

This article is the consideration to say readability is a little bit. There, leap of logic because of that, mess assumptions, various of prejudice, contains a misleading representation. But the excuse for still readability is done in Hoko,Please forgive me!

Hello everyone! System Scepter start from excuse suddenly, My name is Fumihiko. You are Would you Have a nice day enjoying the cardo. I have confidence to return To course with a big smile as usual on this question. I, we have various delusion on my own for my daily life further enjoy. This is the guy that'll keep writing the memorial because such delusion is accumulated to some extent. Contents of the accident should not be book on average, it is something like the discussion of the turn lean book. Please bear with me by all means those who you free.

For book to use for example

I would like to go what will become optimized for the title while adjusting actually a book in this article. Book to adjust this time is the previous book that I made that Berukutsu. Assumed map junction (normal), assumed the number is four, the goal is 8000G.

"Berukutsu"

It wins muscle this book is aim is quite simple. 1, 2 Cactus wall in round, Mommy, seeded rose the land Urchin, level 5 chain, including Tasker and Dutchess until later 6 rounds, to achieve the 12 round the 6 chain while increasing the hand-held magical power to up to 10 rounds 4 transformer. The goal to make the other one level 5 to about 20 round to create a level 5 in the capital. Is good if Ubaitore the 6 chain eyes (5 chain after transformer) in a glove or armed paladin of power when incurred by color or late chance. Baimisu let us also put scary because the shelter, I want to put to level 5 which was made in the transformer. Was that.
If this plan is strong or weak, realistic whether or not, also, but I think it is the chosen card in order to achieve this there are various opinions, such as appropriate whether or not, please understand the time being.

The meaning of the title

Etc. if the difference in quality, perhaps you think that is assumed, even most of the book is made on the basis of the win muscle, such as the "×× to ○○ round (up to)" as above, or unconsciously. In other words, it is not considered an ideal Playing on the basis of the round. This is the title had said, "round-based Playing". On the other hand book will not. For when describing the book it is only "△△ is × sheets" a reference it is often like a number, and what to draw in any round rather than is random, to "○○ round when we talk about book △ △ say the draw "is familiar what the assumptions and excuse, is unsuitable as a plan. This is the title had said, "the number base of the book".
However, we will consider in depth the inappropriate that here dare "draw a △△ to ○○ round". I just said that unsuitable as planned, but in fact does not mean there is not at all means. That is the average. That is the expected value "average probability of catching △△ to ○○ round" Speaking more small difficulty is that supposed to be calculated.

The round to draw the number

In first calculation is required under preparation. Seeks this time is "expected value of the number of sheets to draw △△ to ○○ round," but can not be in the calculation this state. For example, the number of cards drawn 20R eyes would not be 20 sheets. We first to There are five initial hand (with one draw), you may make additional draw in the draw source said that the gifts and Hope. Such "expected value of the number of sheets to draw △△ until the draw ○○ sheets" from the gap "expected value of the number of sheets to draw △△ to ○○ round," but is likely to Motomari is not Motomari likely directly. Then determine the "expected value of the number of catching up to ○○ round", it converted into a number of cards to draw a round to it, and to determine the expected value to draw a particular card by using the result. It is likely to be calculated If this.

As do fine calculation in the Hoko, we used only here in the result. Frankly, the number of cards givin up to that round
(Several rounds +5) × (1+ (the sum of the number of cards that can be subtracted in Doroso) ÷ 50)
is. For example, the expected value of the number of Hope until the 10R is four entered the book is closed likely card and (10 + 5) × (1+ (2 × 4) ÷ 50) = 17.4 sheets (2 × 4) is givin two Hope is that four. Additional example, the expected value of the number of cards can be subtracted in book two and three Hope Debiriti enters the up 20R (20 + 5) × (1+ (1 × 2 + 2 × 3) ÷ 50) = It is 29 sheets.

Then, is the "expected value of the number of sheets to draw △△ until the draw ○○ sheets", but this is simple. this is
(This card of the number of sheets drawn up) × (number of sheets were placed in the card) ÷ 50
It can be calculated by. For example, when the draw 10 sheets from the book that contains the four drain magic, will be 10 × 4 ÷ 50 = 0.8 sheets givin it. People of that givin than to not trace of what not closed the one on average, there are many, it is that it becomes much.

In it decides to seek the "expected value of the number of sheets to draw △△ to ○○ round" of the main subject. But this is Motomari is "or draw what sheets to ○○ round" in the paragraph on the two (the expected value of the sum of the card, which can be subtracted before the round), before the draw "○○ copies in one on top of the paragraph △ since △ was Motomari the expected value of the number of sheets "to draw, you can see that which is obtained immediately the combination of these. That is,
(Expected value of the sum of the card, which can be subtracted before the round) × (number of sheets were placed in the card) ÷ 50 = (expected value of the card which can be subtracted before the round)
is. And this little deformation
(The number was placed in the card) = (expected value of the card which can be subtracted before the round) × 50 ÷ (expected value of the sum of the card, which can be subtracted before the round)
is. Here, let's change the words. It seems that it remains now (the number you put the card) is to determine the (expected value of the card which can be subtracted before the round), but this point of view in reverse. (The expected value of the card which can be subtracted before the round) is the well-considered and have already decided. This is nothing but the number of cards you want to pull up to that round that you are current reference rather than. Looking so is the (number of sheets you put the card) will be required number of which is determined by the number of cards you want to pull up to that round. In other words
(Required insertion number) = (the number of arguments you want the card until the round) × 50 ÷ (expected value of the sum of the card, which can be subtracted before the round)
So, now we are to be able to calculate the "(stochastically) required insertion number" from the "number of sheets up to that round or want to draw it!" If full use of it to the average, I feel that accident found no book can make.

Book optimization

So ready to optimize the book. Here, the optimization say it refers to the work to adjust the number of cards in the book to was determined earlier (required insertion number) the last minute. In addition, although the actual book you should adjust the number of draw source, if necessary, draw source in the gift 4 Prophecy 3 to make it easier to compare the results in the convenience and before and after optimization of the explanation is fixed.
The fact that several sheets can be subtracted at the gift I think there is an opinion to the average of 2.5 sheets of 1, 2, 3, 4 sheets this time. In addition, Prophecy is assumed to draw basically the creature, which changes at random (in detail later commentary), when determining the number of the item spell in accordance with the proportion of the creature has entered when determining the number of creature a mere 1 treats as a draw. So first, let's continue to optimize the spell.

The minimum required spell optimization

Spelling will determine the number of sheets to focus directly on whether you want to use before any round. As described in the book to use for example, spell cards involved in this winning muscle (use you want to round) the land transformer (12 rounds), the magic shelter (13 rounds).

(Required insertion number) = (the number of arguments you want the card until the round) × 50 ÷ (expected value of the sum of the card, which can be subtracted before the round)

So, is the insertion number = 1 × 50 ÷ 20.4 = 2.33 pieces of transformer (20.4 and say is the number of cards that can be subtracted to up to 12 rounds). Magic shelter will find that a 1 × 50 ÷ 22.7 = 2.21 sheets required as well. This time, put one by two by simply rounding Although the increase may not sink subtle.

Item optimization

Items Unlike the spell will suffer a role to play to some extent. This time you want or calculated use until just the same what round is divided into three "base defense for the item," "item for the chain maintenance," "item for cutting chain" as an item required by the win muscle, it individual items and assign it to. "Base defense for the item" is I want one to up to 11 round is a round to create a level 4 for the transformer. In addition, I want to draw also the second piece to up to 16 round which is the middle much of the round because there is quite a time to make the other one level 5 after transfection. In order former satisfy requires 1 × 50 ÷ 20.16 = 2.48 sheets. The latter is to satisfy the condition requires 2 × 50 ÷ 26.46 = 3.78 sheets ((where the number of cards you want to pull up to that round) is two is different as ever). It employs more many people, four turned rounded to the nearest 3.78 sheets (disk 2, sphere shield 1, adopted REACT Armor 1) you. We will continue to determine the number of similarly "item for the chain maintenance". Here also it will split the opinion I want to draw one up to 7 round that would have a lot of Scepter finish established a chain. This number is 3.3 sheets required for this, but three was rounded off by way of example (Specter lobes 1, gelatin Armagh 1, spike shield 1) Turn on. It becomes a little less, but is determined that there is no also not balanced because there are some many items for base defense. The end of the plan to use in conjunction with the Armed Paladin and the glove is "item for cutting chain". This is necessary 1.89 sheet because it is time to stop the one pulling the other party about 16 rounds if to and use. Two to the nearest (gremlin eye 2) Turn on.

Creature optimization

In fact, we do finally a creature optimization wanted to do most in this article! This is where you perform optimization by focusing on the value of each time the creature (function rate). Creature Sylvain Dutchess plan to this time on, the Great Tasker, living glove, land Urchin, cactus wall, Mommy, Knight errant, and is Prophecy. Only the maximum value determine the number of sheets required for each round in the same way as earlier adopted, it is suitably likely can also be allocated to each type there is, but the problem is in this. For example as a result 20 sheets of creature of the calculation was found to be necessary. But it will not be able to adopt 20 a creature of the territory cost retention. On the other hand it does not have the territory cost is so shall not in very strong book also be hardened with 20 sheets average about creatures power. Then decide whether to count the number of sheets in the round for each creature (0 to 1), so that you aim the number barely necessary so that the many possible strong creature in each round. Between 1 to 10 rounds since the beginning of not turn creatures other than the invasion 6 chain in the 10-round might do in the finished later 16 round is scheduled Consider this. We must first decide so good at relatively the strength of the creature in order to do this. Sylvan Dutchess subjective 100% This time, Great Tasker, land Urchin, cactus wall, Mommy, living glove, (as the land territory ensure the role of) the order of the Knight errant and strong. Territory is one in the first round, two in the second round, three in the third round, four in the 5 round, five in 6 round, six in 10 round, I think ideal. Sylvain Dutchess, you must have two territory to summon. In the plans of the above it is to want become card after the third round at a minimum, but it does not necessarily mean that in a two-chain even take two. Here, suppose you use from 5 round a further 1 round passed me three and the territory is. Therefore, Sylvain Dutchess 0 sheets value of up to 4 rounds, 5 rounds and later as having a value of one sheet. Great Tasker 3 round onward, land Urchin, cactus wall, Mommy is always available from the first round to 10 rounds. Want to use to aggression is living Globe and Knight errant, is on the same level with other creatures be said to be definitive if no other to stay creature came early on is tricky. Again, to determine the value by subjective, Knight errant worth of about 0.2 sheets of up to 10 rounds, living glove Earlier 0 sheet value of about 0.2 sheets that will try 5 round later begin to exceed 60/60 we have a minute of value. The value was determined by far in the value of each one, the product of the insertion number is the value of each round of the final creature. Finally this time is Foresight that have been determined to be adopted three but this is
(Its value of Foresight in the round time) = (has (not every creature to be introduced in that round) Total Value) ÷ (the number of all the creatures) × 3
is. It will be the value that was determined to here as below and in the table (except for the Foresight).

round	1	2	3	4	5	6	7	8	9	10
Dutchess	0	0	0	0	1	1	1	1	1	1
Glove	0	0	0	0.1	0.1	0.1	0.1	0.1	0.1	0.1
Errant	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2
Tasker	0	0	1	1	1	1	1	1	1	1
Urchin	1	1	1	1	1	1	1	1	1	1
Cactus	1	1	1	1	1	1	1	1	1	1
Mommy	1	1	1	1	1	1	1	1	1	1

It is a way to aim the number barely necessary so that the many possible strong creature in each round of the main subject, but to do it me up to this point does not change the item or spell, to calculate the number of sheets required for each round, one of the to determine the number of sheets so as not to fall below it in the round. Determination of the number is reduced one by one from the bottom first, all four put, cease to reduce After less than the required number in one of the round. We will continue to adjust to the degree that he said.By the way, this can be calculated exactly the best efficiency is called the integer optimization problem, but not in the calculation amount to human beings do.

However this time before you do this you should determine whether the put many pieces the Globe and errant from the balance of Foresight. This is 2.3 sheets required number because one needed to up to 16 rounds together. First, all reduced one by one from the bottom put four, two gloves by the method cease to reduce After less than the required number in any of the rounds, errant will be fixed at 0 sheets.

The will continue to adjust again the number. Here is only briefly result.

	round	1.0	2.0	3.0	4.0	5.0	6.0	7.0	8.0	9.0	10.0
Number of sheets	Required number of	8.1	13.2	16.7	14.4	16.9	18.9	17.4	16.0	14.9	16.7
2	Dutchess	0.0	0.0	0.0	0.0	2.0	2.0	2.0	2.0	2.0	2.0
2	Glove	0.0	0.0	0.0	0.2	0.2	0.2	0.2	0.2	0.2	0.2
0	Errant	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
3	Tasker	0.0	0.0	3.0	3.0	3.0	3.0	3.0	3.0	3.0	3.0
4	Urchin	4.0	4.0	4.0	4.0	4.0	4.0	4.0	4.0	4.0	4.0
4	Cactus	4.0	4.0	4.0	4.0	4.0	4.0	4.0	4.0	4.0	4.0
4	Mommy	4.0	4.0	4.0	4.0	4.0	4.0	4.0	4.0	4.0	4.0
3	Foresight	1.9	1.9	2.2	2.2	2.7	2.7	2.7	2.7	2.7	2.7
19	total	13.9	13.9	17.3	17.6	19.9	19.9	19.9	19.9	19.9	19.9

Spelling optimization

I decided the number of essential spell item creatures to win muscle up here. Fixed card at this stage is 39 sheets. We will decide the remaining 11 sheets. In all spell should But this time decide to order the subsequent fill the win muscle and reality hole of the ideal set, in fact arbitrarily assumed not stepped chain, can be of convenience had been enemy territory, conveniently enough magical power we aim to bridge the gap (as described in Hoko). First is a chain, but I think to make a foot spelling and disasters spell. The time especially suspicious is the part 2 chain is made in up to five rounds. This time, thinking that draw the earth shift or magical leap to up to four round, by 0.5 sheets of allocated to the equality of each of number 1, further ground shifted to about 17 round of the front of the goal is I want one. Thus 0.5 sheets ground shift in the 4 round, you expect that the givin 1.5 sheets in 17 rounds. This time, three Turn rounded off since the 2.7 piece of it is often necessary for the latter. Similarly drain magic is like to be givin the second sheet 1 sheet in the eighth round to begin earn magical power of the transformer, to 20 round that magical power is insufficient. Here is the three rounded to the nearest 3.1 sheets of larger latter. One to escape and 13 round the combined HW8 for similarly high avoided, 18 two of the 3.45 sheets of the latter in order to be subtracted the second sheet to escape round, which assigns a one to HW8 in is the book completed. This article is the end put the last again after adjustment of the book. Thank you for your reading.

"Celestial globe"