Scratch odds

[Inzaghi]

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!!!)

[PawnXIIX]

I love the overload of statistics but there was already a thread on this...

Ohh...having a nerdgasm over here :P

I assume that the gold values you estimate at the bottom assumes that you mutliply the cost of gold based on the number of attempts it would take on average to receive one of those rewards?

[Inzaghi]

I love the overload of statistics but there was already a thread on this...

Ohh...having a nerdgasm over here :P

I assume that the gold values you estimate at the bottom assumes that you mutliply the cost of gold based on the number of attempts it would take on average to receive one of those rewards?
Yes. But here I added more info. If you don't need some rewards out of the 6 kinds, you can remove those and refer to the adjusted probability. Also, if you target at one specific weapon, the expected spent RM can also be found here.

[Feng1234]

Impressive.