Three killed Technical Posts

Three types of assortment
license to kill,
3 killed a total of 108, including 30 killed (kill 21 black, 9 ZHANG killed, 70% black), 15 Flash (all red), 8 Peach (all red), 6 burning bridges, 5 pilfering, 4 out of nothing, 3 southern barbarian invasion, 3, fight, 3, indulgence, and 3 perfect, 2 Lightning, 2 bumper harvest, 2, Collateral, 10,000 arrows shot, 1 Peach Garden; equipped with a total of 20 ( 60% black), and +1 / -1 Ma of the 3, 11 weapon (Zhuge Liannu 2, other 1), 3 Armor (2 Bagua Zhen, 1 Inwang shield)

number determine the probability of the basic situation:

1. Inwang shield and the shield gossip, choose which is better? This problem is caused by human elements fashion characteristic. Under normal circumstances, 70% of the black death, and gossip to determine probability of 50% (54 of each red and black cards), so Inwang ward shield shield a little higher than the gossip, but there are several cases to special management.

a) If you choose the character is Guo Jia, then elect the gossip shield it, those who determine the attribute of all your cards, that is when you have the shield gossip, others kick you just to bring you card. This is a location when there ambition be more amusing, equipped Liannu your teammates, and then let him bombard you,Womens Lacoste Arin Trainers, when you determine the failure and blood Mopai deduction, you can kill to give his teammates, huh, huh, a tiny sick ... ...

b) if the presence of Sima Yi, to consider if you are below his teammates, and if so, to consider the use of gossip, and if not, gossip becomes garbage.

c) If the birds there, and not the words of his teammates, to pay consideration. Guan Yu with 54 red cards as a kill, and kill 21 black, for the number two, he had to kill 72% of the red, your shield is still considered Inwang into gossip.

d) If the presence of Zhao Yun, and not his teammates, they should pay attention. Zhao has killed 45 (24 ZHANG killed, including 15 ZHANG flash), Red 53.3% probability of kill, Inwang shield is not handy.

e) Finally, memorandum that there is no accident that Inwang shield, when Zhao Yun Guan Yu to kill you, will basically kill the red, so from a practical point of view, the two men met, Inwang Shield is a elaboration.

2. Pizhong by lightning What is the probability? Oh, run into the presence of Sima Yi, or the top of your pate to the equivalent of a speedy rod, or the equivalent of you are the lightning rod, basically there is no probability. In general, the spades between 2 and 9 of spades card, a total of 17 (including five killed, four weapons, one armor, a +1 horses, six tips), the probability is 15.74 %, from the outlook of mathematical expectation, that is, touch 6 cards, including one that is, in other words, basically six to determine which will be a lightning rod. The actual game, taking into account the weapons, armor, Markey will be equipped out of this and not arise in the card heap, so the probability will be beyond reduced to 10.2%.

3. What is the probability of being reluctant to leave? A total of 108 27 of centers card, in which a weapon, a + 1 nag, 1 -1 horse centers, reluctant to leave to escape the probability is 25%, but in the actual game, weapons, nag equipment will be out, so will reduce the chance of escape to 22.2%.

4. When the hands have to kill a flash, it ought not afford to quit any brand of blood easier? This is also depends on the court circumstance may be,

a) If a shield equipped, then choose to kill, blah ... ... ^ - ^, Oh, many people will forget their gear.

b) if to validate Kyi, to choose the black death, black death for killing both, yet also for the flash. Similarly, if Guan Yu to leave flash, all the flash is red, can be used as killing.

c) for other general people, we have to consider the position of the field, and your role. If you are a god, reside Shanba, we will fight you. If you are the enemy side, then left Shanba. In increase to these two circumstances, the tribunal must also consider whether there is Cao Cao, this children Intuit horrible, 3 southern barbarian aggression and a thousand pointers shot, he will be scatter into the 6 southern barbarian invasion and two thousand signals shot , while the southern barbarian aggression probability is 75%, if the hand is not perfect, it would kill it to take into account, so be AOE decease.

specifics of each of the roles,
role explosive articles,

1. Huangyue Ying, explosive extraordinary players. Before discussing the explosive, where first a state, here are the prologue explosive power, explosive personally meditation the latter chapter of little significance, and the situation is complex, can not do anything to make a conclusion. Huang Yueying explosive is the largest private sensibility, or along mathematics, a total of 35 tips, of which three may not be used (1, Taoyuan, 2 by knife), where assumptions can be used. 35 tips in this, there are four out of nothing (you can alteration 3),Lacoste Swerve Trainers, 5 pilfering, 2 bumper grain harvest (which can alteration two), the repose of the kit can change one. For Huang Yueying for a license to equivalent Tips 4 / 35 * 3 +7 / 35 * 2 +24 / 35 * 1 = 1.43 card. Huang Yueying after the corner of the start time, there will be six cards in hand, with the permutations and fusions to calculate the retinue conclusion,
a) 0 张 Tips probability of 8.9%
b) 1 张 probability Tips was 27.5%
c) 2 张 Tips probability 33.8%
d) 3 张 Tips probability of 21.3%
e) 4 张 Tips probability of 7.2%
f) 5 Tips for a probability of 1.2%
g) 6 张 Tips probability of 0.85%
Jiang Zi, we can obtain the actual hand Huang Yueying increase in the number of numerical expectation,
1 * 0.275 +2 * 0.338 +3 * 0.213 +4 * 0.072 +5 * 0.012 +6 * 0.0085 = 1.913
Tips for taking into account equivalent to 1.43 per card, so Huang Yueying the number of cards in hand should be 1.913 * 1.43 = 2.74, nearly 3 card. Here we can define the explosive Huang Yueying 2.74 + +, where + + contains the two meanings,

1) the maximum instantaneous explosive force would be great, if you look the hands of nearly 20 Huang Yueying card It is also not shocked, that is entirely possible.

2) the explosion in the licensing process will be used out of the ruinous forces of kit can not be ignored, in the Huang Yueying just have used up all the tips, the often harmed lord will see only little hand, and was laughed ... ...

incidentally encountered Huang Yueying under the lord's play, where I met a lot of weaponry to lord slit up yellow on several times, to waste Huang Yueying's hand, or at least given a advising, in fact, this is the bad play. At least the first round do not equip weapons, it should not hit anyone, Jiang Zi Huang Yueying turn shot, they can disallow the Collateral and the Peach Garden Kit to further inhibit the chances of the outbreak Huang Yueying.

2. Zhen Ji, the whole explosive players. This relatively cozy to calculate, 108 red and black cards there are the half that time to determine the probability of success is 50%, here to do a mathematical expectation,
1 * 0.5 +1 * 0.52 +1 * 0.53 + 1 * 0.54 +1 * 0.55 ... + ... ..., can be similar to 1, the same explosive power as defined Zhen Ji 1 +, where + implies a averaging, is the possibility of outbreak of hand will get a lot of RP may also be Sima Yi changed after the decision to get more.
PS: 81 F Crosis added: If the licensing model is not unlimited, but 108 to calculate expectation is 0.98112 ~

3. Pseudopleuronectes, pre-explosive players. This is more accessible calculated, and get started hand 4, touch 2, since the loss of blood touched 6 3:00, a total of 12 cards can be, relatively low chance out of nothing, here ignored. Chance of explosion is 7.4% of peach, peach explosion equivalent to more than a card, then, so bust the mathematical expectation is 2 * 0.926 +3 * 0.074 = 2.074, a total of 3 of the blood, so a total of 6.22. Because Huang Gai is a basic set of cards, a total of 12 also, the basic no more, and 12 card can do is more limited, and it did not make the accident, the afterward round then basically perished. According to a conviction of blood for 2 brand, where you can define Pseudopleuronectes explosive is 0.22, but because the explosive is relatively settled, you can use 12 cards to rupture Liannu, it is also loved by the role players. There is also touched by the path lord Huang Gai's play, of way, and treatment is the inverse of Huangyue Ying,Buy Lacoste, Huang Gai to try to deduct the amount of blood, making Pseudopleuronectes lost outbreaks.

4. Lu Xun, the late gunpowder players. Lu Xun is the eruption of the late-type players, these figures are more appropriate when the Trojan Horse. With affair skills that made him singled out in the late throne. Even the outbreak of the probability of the largest camps for always the tips,Womens Lacoste Shua Trainers, killing, and peach can be used here simply the most, minimum probability defined,

1) Maximum probability: to kill (with Liannu), peach ( their wastage of blood), pilfering, Peach Garden, Lightning (will ache yourself), Collateral, duel (will hurt yourself), southern barbarian invasion (injury to teammate), thousand arrows shot (injury to teammate), and the remaining kit and equipment, only the flash and the perfect can not be used, the outbreak probability of 83.3%

2) minimal risk: 37 kit and equipment will be able to use a probability of 34.4%
see Lu Xun's late burst is not threaten to stable, depending on the form field. Since the outbreak of player he is late, and the outbreak of the probability of instability, where do Comparative explosive.

generals articles

5. Guan Yu, anti-type players. 108 cards, half red for the kill, kill 21 black plus the total number killed up to 75 to kill, not to say that basically did not kill the hands.

6. Zhao, either aggressive and defensive players. 45 killed / flash, basically anything that can do the job.

7. Zhang, deadly terrorist-type players, and then spears with Zhangba basically invincible.

8. Riboud, injury type players, basically a shot that is DOT.

other articles
9. Big Joe, cover-type players. 27 boxes, permutations and combinations showed that only 17% of the probability of a carton are not at hand, the probability of at least 83% of the sealing of an individual. Together with Sima Yi is simply a nightmare for the competitors ... ...

10. Hua Tuo, support-type players. This character is not diagnosed, no authorize, 50% of peach, the cards, 100% of peach, simply obstinacy ah.

11. Canning, cleared the sign-type athletes. 54 dark color for burning bridges, and a red scalding bridges, scalding bridges is basically 50%, does not absence to split also said than done.

then some other characters basically Han probability, not discussed here
very powerful ~ ~ ~
there are even more powerful ~ ~
Abstract:
Three killed in this paper calculated the probability of some interesting results, including: expectations of Zhen Ji Luo 1, and Zhou Yu created an equal, if I were you the Luo and the heroic compare the two skills, the former is dominant. Huang Yueying expectations are not as high as imagined, is only 0.798. Pseudopleuronectes initial average of about 15 hand, Zhou Tai is the most likely time of death the 5th determine, calculate the average worth, Zhou Tai, the average death time was 5.43.

Profile:
probability theory today, level, teacher talked about geometric distribution could not find a good sample of when, standing on the podium stunned, and I was submerged in a time of good in the moment. Mountain at the foot of the month, it was dark and stormy night, as Zhen Ji Dudou my lord, to have been lost in the graph, full of blood, my lord, I saw at red blood Fuzhang to laugh when I started the Luo, then Board appears on the following sequence: black, black, black, black, black ... ... lord have heard in a loud exclaimed in swallowed their anger and eventually died. With respect and admiration for Chen Ji, I try to calculate what the expectations of Chen Ji Luo found that even with the anticipated results are different, so I was a hero to other RP type were analyzed, then there this hydrology.

1. Zhen Zhou Ji and Ji Zhen comparison

heartless beauty
Luo: Round the initial stage, can be active magistrate, determine if the outcome is a black suit, as resolute successful, the license reverted to hand the decision and can proceed to determine; if the result is a red color, as determined failure, skills aborted. can continue until the loath decision to continue or to determine the results into the red so far.

heroic
viceroy, Zhou Yu: Mopai touch three-stage

Gongjin card skills at a peep, and more elect up a card, and Zhen Ji will wordy and more, can be summed up in addition to already have those two, it can also until the touch has been touched until the red. We have seen a red card has been choked for Chen Ji, have seen the black card as fabulous as the Yan Ji rain. Zhen Ji to find out how much worth the skills in the end, we calculate the number of Zhen Ji additional Mopai expectations.
knowledge of the probability theory can know the number of X Zhang Zhen Ji Mo Pai is a geometric distribution of discrete random variables, where the parameters p 1 / 2. Said Yan Ji with a number of additional Mopai expectations, there





the amount of this catena is very uncomplicated

;



This shows that the expectations of Zhen Ji Luo 1, with one equal set of Zhou Yu (Chen Ji ahead I think the expectations will be smaller), one from the expectations of view, there is no feud between the two. But given the peerless nature of the three killed, particularly devices such as Zhuge Liannu the subsistence of the power of licensing and more time increases very quickly, there is a risk that the pursuit of the player's psychology, so there

; Nature 1. In general, utility feature u hand the number of sheets on hand x is a monotonically increasing convex function.

properties of convex function is not laborious to certify, Zhen Ji's hand deserving to the effectiveness of skills than Zhou Yu's effectiveness, that is, under regular circumstances, if Luo and heroic simply compare the two skills, the former is dominant.

2. more strokes on the British dislike Seclusion sister

Huang Yueying
Touch of Zen ; set Chile: a kit using the card when she quickly after the touch from the top of a card deck to add hand.

I deem we all fell resting seeing Huang Yueying see the experience of playing stand-alone, with the above results, we can also attempt to calculate the Huang Yueying expectations. As fabricated sleeves are magnetic, we will separate out the publish for discussion. First, in array to simplify the calculation, we make the emulating assumptions:

Assumption 1. Mopai the process model without replacement vote. That is, anybody time, from the deck upon the palpable potentiality of a particular brand * p * is the number of sheets of this card in the aggregate number of canvases in proportion. This is not merely for their own Mopai namely stage, also ignored the other hand your card to be feasible. Zhen Ji in the dispute, we have accustomed this speculation. This speculation caused the error is small. In fact, the enumerated expectancy is generally small, approximately 1, so touch a lot of the same mark Zhang probability is very small, persistent with our assumptions.

we first discuss the impact of out of nothing for the mean player.
said a appointment with the p * the probability of Mopai touch something out of nothing, there are p *= a * / s, a * is the number of sheets out of nothing, s is the total number of sheets, in a activities out of nothing touched the two cards in at least one out of nothing is the probability of 1 - (1-p *) × (1-p *), since p * is small, do seem to take for the 2p *. The actual situation of a *= 4, s = 109, p *= 0.037. The elucidation of n times there is something out of nothing from nothing in the case of licensing for the n +1 order something out of nothing, so from the above causing we get:

Property 2. order out of nothing can be ignored.

Huang Yueying Now we start to the expectations of the number of sheets accompanied Mopai a. Have to do a hypothetical here, Huang Yueying can out of the outfit will be all used up, while ignoring all the nice harvest of (too collapsed.) After the first set of calculations using a outfit with the increased number of sheets of Chi b. P said Huang Yueying with a touch lower the probability of non-delay kit (not including out of nothing.) Geometric delivery based on similar properties, we can get relations:
; b = 1 + p × b + p * × (3 +3 b)
b was solved:
b = (1 +3 p *) / (1-p-3p *)
game , p = 18/109 = 0.165. along to the calculator was b = 1.53. Thus, we can start to a. (This is a comprehensive consideration of the general tips and fabricated the colossal project ...)

; a = p × p × 2b +2 p × b + p * × p * × 2 (2 + b) +2 p * × (2 + b)-2p × p * (2 +2 b)
= 0.798

; calculation results are startling, Huang Yueying expectations are not as lofty as dreamed,Womens Lacoste Observe Trainers, is only 0.798! In compare, not as good as the decision of Zhou Yu and Diao Chan 1, Chen Ji, the average one. On this issue, we can explain the nature of a given. From b> 1 can be base, Huang Yueying once touched a kit, the potential is very ample, and Huang Yueying in the first round of six when hand is exceedingly horrifying. Huang Yueying a lower average risk in commute for a higher, that is explosive.

3. Gongjin, please, move me!

to kill the game in the three countries, there are always some people for the wrong taste of a hero has a special love of violence.

Pseudopleuronectes Qingshenjianfei
bitter mutton for the country: the licensing stage, can be a little less physically athletic, two cards from the deck. Can be used multiple times in his circular of the skills.

with before analysis, the calculation of Huang Gai is many simpler. Do first the hypothesis:
assumptions 2. (Violent Pseudopleuronectes assumptions) will be considered by Huang Gai will be in any possible state of their own into a drop of blood. Then there are inferences

Corollary 1. violence Pseudopleuronectes all peaches and Peach Garden is equivalent to nothing.

then touch something out of nothing + (4-1) × 2 +12 p * × (1-p *) ^ 11 × 2 + (12 choose 2) p * ^ 2 × (1-p *) ^ 10 × 4
= 12 +1.766

calculation found that many of the hands of the initial number of sheets, p * is not small, Order Imagine such a person sitting under the lord's house shouting, (After that we will not disdain violence Pseudopleuronectes the ...)

4. Letter Chun

consequently everlasting life to those who do not mention.

Zhou Tai Battle of the body of
unyielding calendar: Any time you depress the physical restrained 0 alternatively fewer, reduced 1 o'clock every physical: from the deck at the top showed the character of a card on your embark, if the licensing board on the role of points and you have a card are any another, you will not die, this only as a near-death state.

in the history of the maximum disgusting little strong, I have nearly as Huang Gai Zhang Liannu hand toward the lord to kill, was stopped halfway under the house patriotic Zhou Tai, Yingkang All kill and survive, the final being the knife Kanfan. Since then, the Zhou Tai in the end will all long to live both into creeks and lakes on the mystery ... secret ...
likened with the premier two answers, narrated to the calculation of Zhou Tai is not quite complex, lemma does not involve anything at all times the basic wisdom of probability methodology are used to it. The total number of that card with s (here catching s = 52 × 2 = 104), beginning from the dying, An said in the first n second determination is still standing afterward the incident, Dn, said Zhou Tai died in the 1st n times to resolve the incident. We have:

;



the relationship between the An and Dn was:




calculated values ​​into the data list:




and image:




Conclusion: Zhou Tai is not so hard object. Zhou Tai is the most promising time of death was determined 5 times, calculation of the average value,Lacoste Protect Laser Trainers, Zhou Tai, the average death time was 5.43 (formerly a statement that is 7 times). Zhou Tai was able to finally understand long to live either.



discussion:
this periodical, a hero aboard several RP-type probability of instructive results, in which Chen and Zhou Ji Thailand is basically the exact calculation, meantime the discussion is about something out of nought alike, are not thought the shock of bumper harvest for the calculation of Huang Gai there is a excellent degree of uncertainty. Cattle were capable to give wish to have more reasonable Pseudopleuronectes results.



References:
[1] Introduction to Probability Theory, Wang Renguan, Peking University Press, April 1994 first Edition
[2] to kill the improvement version of the Three Kingdoms manual, YOKA GAMES