Inzaghi
06-16-2012, 12:29 AM
g:gun, m:melee, a: armor v: vehicle, c:in-game cash, r: rp
So there are 6^6=46656 possibilities. Then we count the # in each case, and #/46656 is the actual chance.
1 token at most
One token in each type: gmavcr (an example)
P(6,6)=720
2 tokens at most
(a) five kinds of tokens: ggmavc
C(6,1)*C(5,4)*P(6,6)/P(2,2)=10800
(b) four kinds of tokens: ggmmav
C(6,2)*C(4,2)*P(6,6)/P(2,2)/P(2,2)=16200
(a) three kinds of tokens: ggmmaa
C(6,3)*P(6,6)/P(2,2)/P(2,2)/P(2,2)=1800
Total = 28800
3 tokens at most
(a) four kinds of tokens: gggmav
C(6,1)*C(5,3)*P(6,6)/P(3,3)=7200
(b) three kinds of tokens: gggmma
C(6,1)*C(5,1)*C(4,1)*P(6,6)/P(3,3)/P(2,2)=7200
(c) two kinds of tokens: gggmmm
C(6,2)*P(6,6)/P(3,3)/P(3,3)=300
Total = 14700
4 tokens at most
(a) three kinds of tokens: ggggma
C(6,1)*C(5,2)*P(6,6)/P(4,4)=1800
(b) two kinds of tokens: ggggmm
C(6,1)*C(5,1)*P(6,6)/P(4,4)/P(2,2)=450
Total = 2250
5 tokens at most
two kinds of tokens: gggggm
C(6,1)*C(5,1)*P(6,6)/P(5,5)=180
6 tokens at most
one kind of tokens: gggggg
C(6,1)*P(6,6)/P(6,6)=6
The conclusions:
1) To receive any reward in one level
Level 1: 1.54% chance to receive Lowride Plus (9/9), $1000, Spike Hammer (13/8), 50 RP, Irish Shooter (11/10) or Irish Courage (6/11). 1296 gold is average cost to receive the reward
Level 2: 61.73% chance to receive Getaway Runner Plus (21/37), $10,000, Viking Blade(16/20), 250 RP, Siege Rocket Launcher(28/12) or Ballistic Vest(12/28). 32.4 gold is average cost to receive the reward
Level 3: 31.51% chance to receive Black Bandit Plus (48/42), $100,000, Scorpion Knife(39/30), 1,000 RP, Man-Saw Chaingun(30/39) or Flex Armor(15/55). 63.5 gold is average cost to receive the reward
Level 4: 4.82% chance to receive Fluid Transfer Plus (140/85), $1,000,000, Tiger Blade(83/67), 5,000 RP, Scorpion Elite(72/78) or Despoiler(68/82). 1036.8 gold is average cost to receive the reward
Level 5: 0.386% chance to receive Power Racer Plus (477/318), $10,000,000, Dragon Star(337/193), 15,000 RP, Riot Sniper Rifle(293/237) or Mechanized Guard(140/390). 5184 gold is average cost to receive the reward
Level 6: 0.0129% chance to receive Blazing Monster (1400/850), $100,000,000, Axe of Reaping(823/677), 100,000 RP, Punisher Platform(688/812) or Powered Exosuit(386/1114). 155,520 gold is average cost to receive the reward
2) We only consider five kinds of rewards as "real" ones. (B/c in-game cash is trash)
Lv 1: 600/46656=1.29% chance; 1,555 gold
Lv 2: (9000+(4/2+10)/15*16200+(10+10*2/3)/20*1800)/46656=50.3% chance; 39.7 gold
Lv 3: (6000+6000+(4/2+10)/15*300)/46656=26.2% chance; 76.2 gold
Lv 4: 1875/46656=4.02% chance; 498 gold
Lv 5: 150/46656=0.0321% chance; 6,221 gold
Lv 6: 5/46656=0.01072% chance; 186,624 gold
3) We only consider four kinds of rewards. (RP is not important for HL players)
Lv 1: 480/46656=1.03% chance; 1,944 gold
Lv 2: (7200+(8/2+6)/15*16200+(4+12*2/3+4/3)/20*1800)/46656=41.2% chance; 48.6 gold
Lv 3: (4800+4800+(8/2+6)/15*300)/46656=21.0% chance; 95.2 gold
Lv 4: 1500/46656=3.22% chance; 622 gold
Lv 5: 120/46656=0.257% chance; 7,776 gold
Lv 6: 4/46656=0.00857% chance; 233,280 gold
4) We only consider three kinds of rewards. (No more guns, please!!)
Lv 1: 360/46656=0.772% chance; 2,592 gold
Lv 2: (5400+(9/2+3)/15*16200+(1+9*2/3+9/3)/20*1800)/46656=30.8% chance; 64.8 gold
Lv 3: (3600+3600+(9/2+3)/15*300)/46656=15.8% chance; 127 gold
Lv 4: 1125/46656=2.411% chance; 829 gold
Lv 5: 90/46656=0.193% chance; 10,368 gold
Lv 6: 3/46656=0.00643% chance; 311,040 gold
5) We only consider two kinds of rewards. (I only want cars and armors!!)
Lv 1: 240/46656=0.514% chance; 3,888 gold
Lv 2: (3600+(8/2+1)/15*16200+(4*2/3+12/3)/20*1800)/46656=20.6% chance; 97.2 gold
Lv 3: (2400+2400+(8/2+1)/15*300)/46656=10.5% chance; 190 gold
Lv 4: 750/46656=1.608% chance; 1,244 gold
Lv 5: 60/46656=0.1286% chance; 15,552 gold
Lv 6: 2/46656=0.00428% chance; 466,560 gold
6) We only consider one kind of rewards (The cars are way too powerful!!!)
Lv 1: 120/46656=0.257% chance; 7,776 gold
Lv 2: (1800+5/2/15*16200+10/3/20*1800)/46656=10.3% chance; 194 gold
Lv 3: (1200+1200+5/2/15*300)/46656=5.25% chance; 380 gold
Lv 4: 375/46656=0.804% chance; 2,488 gold
Lv 5: 30/46656=0.0643% chance; 31,104 gold
Lv 6: 1/46656=0.00214% chance; 933,120 gold (=49,760 US dollar in the 20% off sale!!!)
So there are 6^6=46656 possibilities. Then we count the # in each case, and #/46656 is the actual chance.
1 token at most
One token in each type: gmavcr (an example)
P(6,6)=720
2 tokens at most
(a) five kinds of tokens: ggmavc
C(6,1)*C(5,4)*P(6,6)/P(2,2)=10800
(b) four kinds of tokens: ggmmav
C(6,2)*C(4,2)*P(6,6)/P(2,2)/P(2,2)=16200
(a) three kinds of tokens: ggmmaa
C(6,3)*P(6,6)/P(2,2)/P(2,2)/P(2,2)=1800
Total = 28800
3 tokens at most
(a) four kinds of tokens: gggmav
C(6,1)*C(5,3)*P(6,6)/P(3,3)=7200
(b) three kinds of tokens: gggmma
C(6,1)*C(5,1)*C(4,1)*P(6,6)/P(3,3)/P(2,2)=7200
(c) two kinds of tokens: gggmmm
C(6,2)*P(6,6)/P(3,3)/P(3,3)=300
Total = 14700
4 tokens at most
(a) three kinds of tokens: ggggma
C(6,1)*C(5,2)*P(6,6)/P(4,4)=1800
(b) two kinds of tokens: ggggmm
C(6,1)*C(5,1)*P(6,6)/P(4,4)/P(2,2)=450
Total = 2250
5 tokens at most
two kinds of tokens: gggggm
C(6,1)*C(5,1)*P(6,6)/P(5,5)=180
6 tokens at most
one kind of tokens: gggggg
C(6,1)*P(6,6)/P(6,6)=6
The conclusions:
1) To receive any reward in one level
Level 1: 1.54% chance to receive Lowride Plus (9/9), $1000, Spike Hammer (13/8), 50 RP, Irish Shooter (11/10) or Irish Courage (6/11). 1296 gold is average cost to receive the reward
Level 2: 61.73% chance to receive Getaway Runner Plus (21/37), $10,000, Viking Blade(16/20), 250 RP, Siege Rocket Launcher(28/12) or Ballistic Vest(12/28). 32.4 gold is average cost to receive the reward
Level 3: 31.51% chance to receive Black Bandit Plus (48/42), $100,000, Scorpion Knife(39/30), 1,000 RP, Man-Saw Chaingun(30/39) or Flex Armor(15/55). 63.5 gold is average cost to receive the reward
Level 4: 4.82% chance to receive Fluid Transfer Plus (140/85), $1,000,000, Tiger Blade(83/67), 5,000 RP, Scorpion Elite(72/78) or Despoiler(68/82). 1036.8 gold is average cost to receive the reward
Level 5: 0.386% chance to receive Power Racer Plus (477/318), $10,000,000, Dragon Star(337/193), 15,000 RP, Riot Sniper Rifle(293/237) or Mechanized Guard(140/390). 5184 gold is average cost to receive the reward
Level 6: 0.0129% chance to receive Blazing Monster (1400/850), $100,000,000, Axe of Reaping(823/677), 100,000 RP, Punisher Platform(688/812) or Powered Exosuit(386/1114). 155,520 gold is average cost to receive the reward
2) We only consider five kinds of rewards as "real" ones. (B/c in-game cash is trash)
Lv 1: 600/46656=1.29% chance; 1,555 gold
Lv 2: (9000+(4/2+10)/15*16200+(10+10*2/3)/20*1800)/46656=50.3% chance; 39.7 gold
Lv 3: (6000+6000+(4/2+10)/15*300)/46656=26.2% chance; 76.2 gold
Lv 4: 1875/46656=4.02% chance; 498 gold
Lv 5: 150/46656=0.0321% chance; 6,221 gold
Lv 6: 5/46656=0.01072% chance; 186,624 gold
3) We only consider four kinds of rewards. (RP is not important for HL players)
Lv 1: 480/46656=1.03% chance; 1,944 gold
Lv 2: (7200+(8/2+6)/15*16200+(4+12*2/3+4/3)/20*1800)/46656=41.2% chance; 48.6 gold
Lv 3: (4800+4800+(8/2+6)/15*300)/46656=21.0% chance; 95.2 gold
Lv 4: 1500/46656=3.22% chance; 622 gold
Lv 5: 120/46656=0.257% chance; 7,776 gold
Lv 6: 4/46656=0.00857% chance; 233,280 gold
4) We only consider three kinds of rewards. (No more guns, please!!)
Lv 1: 360/46656=0.772% chance; 2,592 gold
Lv 2: (5400+(9/2+3)/15*16200+(1+9*2/3+9/3)/20*1800)/46656=30.8% chance; 64.8 gold
Lv 3: (3600+3600+(9/2+3)/15*300)/46656=15.8% chance; 127 gold
Lv 4: 1125/46656=2.411% chance; 829 gold
Lv 5: 90/46656=0.193% chance; 10,368 gold
Lv 6: 3/46656=0.00643% chance; 311,040 gold
5) We only consider two kinds of rewards. (I only want cars and armors!!)
Lv 1: 240/46656=0.514% chance; 3,888 gold
Lv 2: (3600+(8/2+1)/15*16200+(4*2/3+12/3)/20*1800)/46656=20.6% chance; 97.2 gold
Lv 3: (2400+2400+(8/2+1)/15*300)/46656=10.5% chance; 190 gold
Lv 4: 750/46656=1.608% chance; 1,244 gold
Lv 5: 60/46656=0.1286% chance; 15,552 gold
Lv 6: 2/46656=0.00428% chance; 466,560 gold
6) We only consider one kind of rewards (The cars are way too powerful!!!)
Lv 1: 120/46656=0.257% chance; 7,776 gold
Lv 2: (1800+5/2/15*16200+10/3/20*1800)/46656=10.3% chance; 194 gold
Lv 3: (1200+1200+5/2/15*300)/46656=5.25% chance; 380 gold
Lv 4: 375/46656=0.804% chance; 2,488 gold
Lv 5: 30/46656=0.0643% chance; 31,104 gold
Lv 6: 1/46656=0.00214% chance; 933,120 gold (=49,760 US dollar in the 20% off sale!!!)