Introduce a new mechanism
In addition to 12. 17 "limited arrival" announced by Pamirs in the Japanese War, it will enter the standard up pool in Yangon in turn and open a new "Fate Arrival" up card pool.
"Fate arrival" card pool rules
Firstly, a guaranteed number t of 80- 100 is randomly generated, and the probability of extracting S under non-guaranteed conditions is 1.5%. If there is no S in the previous continuous (T- 1) engine, the T engine will definitely extract S; Whenever S is drawn out, the guaranteed number is cleared, and the guaranteed number T is re-randomly within 80- 100.
For example, when the new pool is opened, the initial guarantee number t of the gray crow randomly reaches 92. If the grey crow fails to make an S in the first 9 1 round, then it will definitely make an S in the 92nd round ... But if the grey crow seldom hits once, for example, an S is sent on the 85th, then the guarantee count of the grey crow becomes 0 again, and then a new T is randomly selected, for example, T=87. At this point, if the next 86 rounds fail to issue an S, the next round must issue an S, and so on.
Note: Since the government has not specified the random rules when T=80- 100, the following discussion will discuss the equal probability of presupposing that t is random to any number in 80- 100.
Mathematical model analysis of old and new mechanisms
This part analyzes the probability p(n) that the first S is issued for the nth time after the new pool is opened.
In the old mechanism, the guarantee number was fixed at 60 and the basic probability was 0.5%, so:
When 0
When n=60, p(n)= the probability of not sending S before (n- 1) * the probability of sending S at the nth time = (1-0.5%) 59 *100%;
Obviously, the first output of S must be within 60, so when n 60, p(n)=0.
Draw a p(n) image (the line is about to drop):
About 75% of the cases are shipped at the 60th walk, which is an equal pool for all beings, putting an end to seals and non-chiefs, and at the same time losing the excitement of normal card drawing.
In the new mechanism, it is assumed that the probability that the preserving number T takes any number in 80- 100 is equal, then the final p(n) should be obtained by the formula.
For p(n, t), by analogy with the old mechanism, we can quickly draw the following conclusions:
When 0
When n=T, p (n, t) = (1-kloc-0/.5%) (t-1) *100%;
When nT, p(n, T)=0.
Synthesize the above formulas, calculate and draw the p(n) image under the new mechanism:
It can be seen that the peak of shipment is concentrated before 20 rounds and after 80 rounds, which makes the card drawing feel more, but there are also hidden dangers of breeding seals.
If you compare two pictures together, it will be more intuitive:
In addition, with the help of the calculation formula of mathematical expectation
It can be calculated that the mathematical expectations of the first S under the old mechanism and the new mechanism are 565,438+0.9 and 49.5 respectively. If the mathematical expectation is reciprocal, the comprehensive probabilities of the old mechanism and the new mechanism are 1.925% and 2.02 1% respectively, which is slightly different from the official 1.9% (the possible reason is in the article).
Program card drawing simulation of old and new mechanisms
The probability distribution of the first S is discussed earlier, but for moderate and severe Kryptonian players, obviously one S can't satisfy them, so here we continue to simulate 1000000 players to extract two Yangon up pools under the old and new mechanisms respectively, and count the probability distribution of the first 1000, and the results are as follows:
Put them together for comparison:
It can be clearly seen that the pool probability distribution under the new mechanism is more uniform, more random and the card drawing experience is more exciting; The old mechanism focuses on the integer multiple of 60 when shipping, which is basically equivalent to clearly marking 60 and drawing an S.
Card drawing suggestion
Krypton-free players (counting the original cumulative guarantee, less than 60 rounds can be drawn): draw the first 20~30 rounds in the upward pool of the new mechanism, and fight with high probability.
Micro-krypton player (60~80 rounds can be drawn for cumulative guarantee): draw 60 rounds in the up pool of the old mechanism, and buy the next S steadily, because in case the first 20 or 30 rounds fail to be shipped in the pool of the new mechanism, more than 80 rounds must be drawn before transshipment. If you can't save more than 80 rounds before the end of the activity, you can only lose your blood.
Kryptonian players (/kloc-more than 0/00 rounds): priority is given to the new mechanism, because the comprehensive probability under the new mechanism is slightly higher after calculation. After a shipment, you can continue to draw less than 100 rounds, and then continue to draw according to the strategy of krypton-free players or micro-krypton players.
Heavy Krypton players (experience card drawing and life experience, money is not a problem): both pools draw, and experience and feel the different experiences brought by the two card drawing mechanisms.
Error analysis caused by comprehensive probability
If the comprehensive probability of 1.90% is taken as the standard to deduce the basic probability of the old and new mechanisms, it can be inferred that the basic probability of the old mechanism should be 0.4536% and that of the new mechanism should be 1.3274%, so the official basic probability of the old mechanism is 0.5%, which can be considered as rounding off by 0.4536%, and the situation under the new mechanism is even more serious.
Our previous discussions all assumed that the probability of T=80- 100 in the new mechanism is uniform, but if the probability of t approaching 100 is greater than the probability of approaching 80, it will definitely lead to the decline of the comprehensive probability. If extreme cases are considered, T will only randomly reach 100, then the basic probability of 1.90% under the new mechanism can be deduced to 1.5347%. Therefore, when the value of t is between the above-mentioned complete average and extreme cases, that is, it tends to 100 to some extent, the basic probability under the new mechanism should be between 1.3274% and 1.5347% under the complete average and extreme cases. When the value of t is properly constrained, the basic probability under the new mechanism will be officially announced after rounding.
So there are two ways to understand the official data:
The basic probability of 1. 0.5% and 1.5% are both accurate values, so when T=80- 100 is completely random, the actual comprehensive probability of the old mechanism is 1.925%, and that of the new mechanism is 2.02/kloc-. The analysis of the previous parts is based on this.
2. The comprehensive probability of1.9% is an accurate value, so the accurate basic probability under the old mechanism is 0.4536%, rounded to 0.5%; In the new mechanism, the value of t tends to 100, and the basic probability of its accuracy after rounding is 1.5%. In this case, the analysis error of the previous parts is not big, and it can still be applied.