MarioParty5_RNG

Digging into how Mario Party 5 handles RNG.

RNG Function

I've found two random functions in the game's code so far. They are similar to the HSD_Rand and HSD_Randi functions provided by sysdolphin. I've named them rand and randi respectively.

rand returns a random integer. Source

randi returns a random integer between 0 (inclusive) and max_value (non-inclusive) where max_value is the provided parameter. Source

Both are definitely Linear congruential generators. They also appear to be Lehmer Random Number Generators.

Capsule IDs

When getting an capsule from the capsule machine, capsules have the following internal IDs:

00 = Mushroom
01 = Super Mushroom
02 = Cursed Mushroom
03 = Warp Pipe
04 = Klepto
05 = Bubble
06 = Wiggler
07 = ERROR CAPSULE
08 = ERROR CAPSULE
09 = ERROR CAPSULE
0A = Hammer Bro
0B = Coin Block
0C = Spiny
0D = Paratroopa
0E = Bullet Bill
0F = Goomba
10 = Bomb-omb
11 = Koopa Bank
12 = ERROR CAPSULE
13 = ERROR CAPSULE
14 = Kamek
15 = Mr. Blizzard
16 = Piranha Plant
17 = Magikoopa
18 = Ukiki
19 = Lakitu
1A = ERROR CAPSULE
1B = ERROR CAPSULE
1C = ERROR CAPSULE
1D = ERROR CAPSULE
1E = Tweester
1F = Duel
20 = Chain Chomp
21 = Bone
22 = Bowser
23 = Chance
24 = Miracle
25 = Donkey Kong
26 = VS
27 = ERROR CAPSULE
28 = ERROR CAPSULE (DEBUG)
29 = ERROR CAPSULE (DEBUG)
2A = ERROR CAPSULE

Obtaining an capsule with a capsule ID over 2A results in a soft lock.

Any capsule labeled ERROR CAPSULE looks like this when obtained:

When you attempt to use it, the model for it is apparently some level geometry:

If you use it on yourself it crashes the game. If you throw it though...

The capsules labeled ERROR CAPSULE (DEBUG) are capsules used for debugging the game. They have actual models but don't appear to do anything.

Capsule Randomness

When you go to a capsule machine in-game you can get a random capsule. The capsule ID you get is returned from the the result of calling the function FUN_800c8fa0 at 0x800c0cb0.

I've documented the function here: random_capsule.c

Capsules in the game are grouped by what I will refer to as buckets. Before the game picks which capsule you'll get, it first picks which bucket it will choose from. I've mapped each capsule to each bucket here, but have included a summary of the buckets below:

Bucket A (0x41)

Mushroom
Cursed Mushroom
Warp Pipe
Hammer Bro
Coin Block
Koopa Bank

Bucket B (0x42)

Super Mushroom
Klepto
Spiny
Bomb-omb
Kamek
Piranha Plant
Lakitu

Bucket C (0x43)

Bubble
Goomba
Mr. Blizzard
Magikoopa
Ukiki
Bone
Bowser

Bucket D (0x44)

Paratroopa
Tweester
Duel
Chain Chomp

Bucket E (0x45)

Wiggler
Bullet Bill
Chance
Miracle

Gecko Codes

To prove the existence of these buckets, you can use the following Gecko codes for a specific bucket to always be used:

Always use Bucket A (0x41)

C20C9280 00000001
3A600041 00000000

Always use Bucket B (0x42)

C20C9280 00000001
3A600042 00000000

Always use Bucket C (0x43)

C20C9280 00000001
3A600043 00000000

Always use Bucket D (0x44)

C20C9280 00000001
3A600044 00000000

Always use Bucket E (0x45)

C20C9280 00000001
3A600045 00000000

The Actual Algorithm

So what happens is that first the game determines what bucket you'll be using. The bucket you'll be using depends on two factors.

The first I call turn_param. This factor is a number between 0 (inclusive) and 2 (inclusive), calculated as a proportion of the number of turns left compared to the total number of turns. The beginning of the game this value will be 0, and near the end of the game it will be 2. A python script has been included that will return the turn_param given the current turn number and total number of turns. You can find it in this repository under turns.py
The second factor is your current place in the game. First place results in a current_place of 0. Second place results in a current_place of 1, and so on.

The below image shows what your chances of getting a particular bucket selected are given your current_place and turn_param. I calculated these values using a script I've included in this repository under bucket.py

Once your set of bucket percentages have been chosen, the game then uses these percentages to randomly select a bucket between them. So for example, at the beginning of the game (turn_param = 0) you cannot get any capsules from bucket E no matter what place you're in. By the end of the game (turn_param = 2), all players but the player in first place can get a capsule from bucket E.

Once your bucket is chosen, the game iterates through the list of capsules in that bucket 5 times and swaps the current capsule in the iteration with a random other capsule in the list. It will not swap if the random other capsule happens to match the current capsule. Therefore, anywhere between 0 and number_of_capsules_in_the_list * 5 swaps will occur.

Once the swaps are complete, a random capsule is selected from the list. Each capsule in the list at this point has an equal chance of being grabbed.

NicholasMoser / MarioParty5_RNG