8 Ball Pool Information NasuSamaruk01,5 , kunal9082,3 , Player X3 , Sims5334 and TDoGWarrior4 1

Author of this article 8 Ball Pool Information thread starter 3 Credit for Tier Information 4 Credit for All Cue Informations 5 Credit for Of Weekly Competitions and Winnings 2

Abstract This article contains all information coming from the official 8 Ball Pool forum. Each and every section covers different topics for the game. Since this article contains more than 10 pages, I included the hyperlink for you to navigate through section. Other than that, I would like to thank kunal908, Player X, Sims533, TDoGWarrior and others for gathering the information. Hope they help!

Contents 1 Levels and Experience Points 1.1 Simple XP Goal Approximation . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Advanced XP Goal Approximation . . . . . . . . . . . . . . . . . . . . . . .

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2 Behind Stats Mathematics 2.1 Of Streaks & Percentages . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 How many wins do we need to obtain certain percentage? . . . . . . .

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3 Cues & Powers

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I 1

Levels and Experience Points

n 8 Ball Pool Multiplayer game, Miniclip included some types of games called tiers. In addition, players can choose whether to play 1-on-1 or tournament for a certain tier. Each and every tier costs an entry fee and a prize. Regardless of the level and skills of opponent, the higher the prize, the more XP you gain from either loss or win. Here is the current following XP system from the thread. Make note that in case of any upcoming tier, I will keep up to date with the chart.

Table 1.1 Tier Information Tiers Downtown London Pub Sydney Marina Bar Moscow Winter Club Tokyo Warrior Hall Las Vegas Full House Jakarta Volcano Toronto Maple Suite Cairo Kasbah Dubai Golden Challenge Shanghai Oriental Pearl Paris Chˆ ateau Rome Colosseum

1 on 1 Loss Win +14 XP +68 XP +35 XP +177 XP +72 XP +360 XP +177 XP +884 XP +309 XP +1,547 XP +707 XP +1,768 XP +884 XP +2,210 XP +999 XP 3,127 XP +1,114 XP 4,044 XP +1,114 XP 4,044 XP +1,114 XP 4,044 XP +1,114 XP 4,044 XP

Tournament Loss Win +17 XP +82 XP +44 XP +212 XP +90 XP +432 XP +221 XP 1,061 XP +387 XP 1,856 XP +442 XP +2,122 XP

Before we cover rank and levels information, let’s keep in mind about the weekly competitions and leagues since there are some users who are interested in knowing their places. Firstly, we have 10 following league competitions: 1. Brass: Level 1 - 9 2. Bronze: Level 10 - 14 3. Silver: Level 15 - 19 4. Gold: Level 20 - 24 5. Platinum: Level 25 - 34 6. Amethyst: Level 35 - 44 7. Sapphire: Level 45 - 54 8. Emerald: Level 55 - 74 9. Ruby: Level 75 - 99

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10. Diamond: Level +100 In addition, you can only be promoted at the end of the competition, even if you reach past the specific level limit of the same tier. For instance, if you are in Brass League, and you made to Level 20 before the end of the competition, you stay in that league. Secondly, we have the country, friend and world competitions. Level-promoting does not have any effect on such competitions. Unlike country and world competitions, in friend competitions, adding friends to your list includes their total weekly earnings for the current competition. I would then like to include some info about rewards for those who are not familiar with the current system. Since the recent XP update, you earn a pool cash on level up to 150. In other words, a pool cash is rewarded for each new level you reach. Using what we know about the level limits for each league, we finally combine that with Ranks & Levels Information to obtain the following tables.

Table 1.2a - Ranks & Levels For Brass League Ranks Trainee Beginner

From 1 2 3 4 5

To 2 3 4 5 6

XP needed 25 127 231 472 720

Ranks Student

From 6 7 8 9

To 7 8 9 10

XP needed 976 1,239 1,772 2,322

Table 1.2b - Levels For Amateurs In Bronze League From 10 11 12 13 14

To 11 12 13 14 15

XP needed 2,887 2,887 3,470 4,070 6,693

Table 1.2c - Levels For Skilled In Silver League From 15 16 17 18 19

To 16 17 18 19 20

XP needed 8,064 9,476 10,930 12,428 12,757

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Table 1.2d - Ranks & Levels For Gold League Ranks Skilled Semi-Pro

From 20 21 22 23 24

To 21 22 23 24 25

XP needed 13,096 13,443 13,799 14,164 14,540

Table 1.2e - Ranks & Levels For Platinum League Ranks Semi-Pro

From 25 26 27

To 26 27 28

XP needed 14,925 15,321 15,727

Ranks

Professional

From 28 29 30 31 32 33 34

To 29 30 31 32 33 34 35

XP needed 16,143 16,571 17,010 17,461 17,924 18,399 18,886

Table 1.2f - Ranks & Levels For Amethyst League Ranks Professional

Virtuoso

From 35 36 37 38 39 40 41 42 43 44

To 36 37 38 39 40 41 42 43 44 45

XP needed 19,387 19,901 20,428 20,969 21,525 22,095 22,681 23,282 23,899 24,532

Table 1.2g - Levels For Expert In Sapphire League From 45 46 47 48 49

To 46 47 48 49 50

XP needed 25,182 25,850 26,535 27,238 27,960

From 50 51 52 53 54

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To 51 52 53 54 55

XP needed 28,701 29,461 30,242 31,043 31,866

Table 1.2h - Ranks & Levels For Emerald League Ranks

Veteran

From 55 56 57 58 59 60 61 62 63 64 65

To 56 57 58 59 60 61 62 63 64 65 66

XP needed 32,710 33,577 34,467 35,380 36,618 37,280 38,268 39,282 40,323 41,392 42,489

Ranks

Master

From 66 67 68 69 70 71 72 73 74

To 67 68 69 70 71 72 73 74 75

XP needed 43,615 44,771 45,957 47,175 48,425 49,708 51,026 52,378 53,766

Table 1.2i - Ranks & Levels For Ruby League Ranks Master

Grand Master

From 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90

To 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91

XP needed 55,191 56,653 58,155 59,696 61,278 62,901 64,568 66,279 68,036 69,839 71,689 73,589 75,739 77,541 79,596 81,705

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Ranks

VIP

From 91 92 93 94 95 96 97 98 99

To 92 93 94 95 96 97 98 99 100

XP needed 83,870 86,093 88,375 90,716 93,120 95,588 98,121 100,721 103,391

Table 1.2j - Ranks & Levels For Diamond League Ranks

VIP

Superstar

From 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119

To 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

XP needed 106,130 108,943 111,830 114,793 117,835 120,958 124,163 127,454 130,831 134,298 137,857 141,510 145,260 149,110 153,061 157,117 161,281 165,555 169,942 174,446

Ranks

King

Pool Emperor

From 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149

To 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150

XP needed 179,068 183,814 188,685 193,685 198,818 204,086 209,494 215,046 220,745 226,595 232,599 238,763 245,090 251,585 258,252 265,096 272,121 279,332 286,735 294,333 302,133 310,139 318,358 326,794 335,455 344,344 353,469 362,836 372,451 382,321

Fact 1. There are currently 150 levels in the game. Though in mobile version there exists an XP upper bound for Level 150, no matter the number of matches you played, you stay in the same level.

T 1.1

Simple XP Goal Approximation hough Table 1.1 illustrates specific amounts of XP earned for either loss or win, the certain numbers of played matches, wins and losses do not apply to all players. In other words, they do not win at the same rate. According to Ranks & Levels Information, Player X derived the approximate the amount of specific tier matches

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to exceed certain amount of XP as followed:   XP needed expected # of specific matches = XP win × (win %) + XP loss × (1 − (win %))

(†)

Clearly, by Table 1.1, you earn more XP from winning and less XP from losing. If the win percentage is very high, then the value of the bottom equation is greater than XP needed. This decreases the expected number of matches to play. Otherwise, low win percentage increases the number of matches to reach certain XP. Thus, Fact 2. The higher your win percentage, the less played matches needed. The lower your win percentage, the more played matches needed. Example. Let us observe the following image carefully:

Figure 1.1: Player X’s profile Player X’s win percentage is 72.4%, which is equivalent to 0.724. If he were to play 1-on-1 matches in Moscow Winter Club to reach 59,696 XP, and his current amount of XP is 23,596 XP, the difference is 36,100 XP to reach level 79. Therefore,   36100 expected # of specific matches = 360 × 0.724 + 72 × (1 − 0.724) = d128.69 · · · e = 129 which leads to the following general method: 7

Step 1: Check your personal win percentage. Step 2: Take the XP won and XP loss for the specific tier type from Table 1.1. Step 3: Find the amount of XP you need to reach the goal. Step 4: Calculate, using Equation (†). Remark. If we were to determine the number of specific matches for reaching higher level that is not adjacent to ours, then we need to combine more than an amount of XP needed. For instance, if Player X were to reach Level 100 from the current XP and level, he needs to sum up all XP values from Level 79 (adjacent level) to Level 100 (using Table 1.2i) before substituting all the values together for Equation (†).

1.2

Advanced XP Goal Approximation

Note: The information in this subsection contains a lot of mathematics. Proceed at your own risk.

P

layer X found the approximation of accumulating to certain XP. However, his equation only applies to the specific match. We should ask ourselves: is it possible to formulate the approximation for any type of match or more? We work this question out carefully from scratch.

Let’s observe Equation (†). Notice that the variables XP won and XP loss came from Table 1.1. With all known variables, we determine the number of specific matches to be played. The approximation works for any XP you need to reach and any type of matches you play. For this case, we can sum up more than an equation to obtain the summation of similar equations. Therefore, the general equation is expected # of matches = +

12  X i=1 4  X j=1

XP goal(αi ) XP win(αi ) × win % + XP loss(αi ) × (1 − win %)



XP goal(βj ) XP win(βj ) × win % + XP loss(βj ) × (1 − win %)

 (‡)

For Equation (‡) 1. α1 , α2 , · · · , α12 are 12 variables that represent known, distinct 1-on-1 tier matches. You can see the list of available 1-on-1 tier matches in Table 1.1. 2. β1 , β2 , β3 , β4 are four variables that represent known, distinct tier tournaments. Consult Table 1.1 for more information about available tournaments. 3. XP goal(αi ) is the function that represents XP goal for the certain type of 1-on-1 match. 8

4. XP goal(βj ) is the function that represents XP goal for the certain type of tournament. 5. XP win(αi ), XP loss(αi ), XP win(βj ) and XP loss(βj ) are functions that represent certain amount of XP for wins and losses, respectively, for specific tier. The conditions are 1. XP goal(αi ), XP goal(βj ) ≥ 0 for any 1 ≤ i ≤ 12 and 1 ≤ j ≤ 4. 2. total XP needed =

12 X

XP goal(αi ) +

i=1

4 X

XP goal(βj ) ≥ 0.

j=1

3. total XP needed ≥ current XP, which is equivalent to total XP needed − current XP ≥ 0. These conditions imply that the number of matches to be played must be nonnegative integer since XP goals are nonnegative integers. Firstly, because the sum of nonnegative values is nonnegative, the expected number of matches must be nonnegative. Secondly, the value of ceiling equation must be an integer. Since the sum of integers is an integer, the sum of ceiling equations is an integer. These verify that the calculation must be correct. Similar steps follow for this complex computation, but there exists extra info to keep in mind: Step 1 Check your personal win percentage. Step 2 Take the XP won and XP loss for your tier choices from Table 1.1. Step 3 Find the amount of XP you need to reach the goal. If you have more than a tier choice, you decide how many XPs you want to accumulate for a certain tier. Otherwise, continue to the next step. Step 4 Calculate, using Equation (‡). Example. Let’s revisit Figure 1.1. Suppose that Player X plays 1-on-1 Jakarta matches and London tourneys. Assume that his initial win percentage is 72.4, and that he wants to earn 20,000 XP from Jakarta and 16,100 XP (altogether 36,100 XP) from London. By Table 1.1, 1. 1-on-1 Jakarta Volcano matches: XP win (+1,768 XP) and XP loss (+707 XP) 2. Downtown London Pub tournaments: XP win (+82 XP) and XP loss (+17 XP) Therefore, 

20000 expected # of matches = 1768 × 0.724 + 707 × (1 − 0.724)   16100 + 82 × 0.724 + 17 × (1 − 0.724) = d13.55 · · · e + d251.32 · · · e = 14 + 252 = 266 9



Remark. Though the approximations we discovered do not verify with the possible future outcomes all the time, they are the most efficient formulas to calculate the number of matches to be played. For accuracy, you may play a match by match and count the played matches to exceed certain XP, but this seems very tedious for players to use.

I S 2

Behind Stats Mathematics

n the official forum, there are users in the official forum who post threads about certain stats other than XP and levels. Most recently, I had seen and posted in threads that focus on stats-mathematics. Since no one has suggested any such formula to kunal908’s 8 Ball Pool Information thread, I believe that including this section would guide those and others to understand some applications of mathematics to the game.

2.1

Of Streaks & Percentages ince the old game release and updates, there are tons of players who obtain some stats. The most common stat that players like to look at is percentage since this catches their attention. Before you read this subsection, consider the following questions:

1. How many won games do we need to accumulate to certain win percentage? 2. What if we were to do the same for tournament percentage? 3. How much does a percentage fluctuate if you play a lot of games?

Remark. Though it is less likely that players will use mathematics, The streaks-andpercentages information will be handy for those who want or like to know how many wins to increase.

I 2.1.1

How many wins do we need to obtain certain percentage?

n 8 Ball Pool game, we see players with different levels and stats when we choose the tier. Not surprisingly, there are long-time high-level players who choose lowtier to improve their stats (as well as avoiding much pressures to lose against tough opponents!). If you play with them more than once at some different times in the tier, you should notice that they make an amount of progress. That says: from a set of stats you start with, you need to make certain amount of wins to reach your goal. Before we answer the first question, let’s take some steps first by understanding the connection between streaks and percentages. Recall that the formula of the win percentage is win percentage =

total number of wins × 100 total number of played games

Calculating percentages for all streaks - both loss and win streaks - shows that 10

0 out of any non negative integer - 0% .. . 1 1 1 2 3 4

out out out out out out

of of of of of of

4 3 2 3 4 5

games games games games games games .. .

-

25% 33 1 /3 % 50 66 2 /3 % 75% 80%

all played games won - 100% which illustrates the infinite series of increasing percentages. If we were to combine at least two streaks from above, then we take the average to determine the percentage for the overall wins over played games. Another way to look at this is to take the numbers of wins and game played and combine them correspondingly. Example. If you make a 2-win streak (2 out of 3 games) and then, 2-loss streak (equivalent to 1 out of 3 games), win percentage =

2+1 × 100 = 50% 3+3

For any combination of streaks, we calculate in this manner. If we want to know whether the current percentage increases or not due to the streak made, we need to compare both our percentage and the streak percentage. As in the example, if we start with the 2-win streak and then, end up with the 2-loss streak, then 2-win streak worth more than 2-loss streak since 66 2 /3 % is greater than 33 1 /3 %. For this case, the percentage decreases. In fact, Fact 3. If the streak worth strictly more percentage than your win percentage, then your win percentage increases. Otherwise, your win percentage either decreases or remains the same. We can easily make note that Fact 4. Without the mix of wins and losses, any percentage is either 0% or 100%, but not both. With any number of losses only, the percentage is 0%. With any number of wins only, the percentage is 100%. Mathematically, new win percentage =

x+z × 100 (x + z) + (y + w)

(ℵ)

where 1. x, y, z, w ∈ N, where N denotes the set of natural numbers1 1

If you have taken any set-related science course, you should notice that some professors/teachers do not include 0 from the natural numbers because they believe that there is no way to count zero. However, there is no standard convention of the natural numbers. Let’s agree that N contains zero.

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2. x denotes the current number of wins 3. y denotes the current number of losses 4. z 2 denotes the wins you will make 5. w3 denotes the losses you will make 6. x + z represents the total wins you will make 7. y + w represents the total losses you will make

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Cues & Powers

iniclip included cues with powers for 8 Ball Pool Multiplayer on August 24, 2014. Firstly, each and every cue consists of four attributes: Force, Aim, Spin and Time aka F.A.S.T. (as TDoGWarrior abbreviated). The minimum attribute point/bar is 0, whereas the maximum attribute point/bar is 10. Here is the simple illustration of how each attribute works:

Figure 2.1: Each and every attribute behaves differently in the game. 2 3

Keep in mind that this does not represent the win streak Likewise, this does not represent the loss streak

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As well as attributes, most cues have 50 energy units; each energy unit costs any type of shot you make. Once the cue runs out of energy, it will lose all its powers except when it’s automatically or manually charged.

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