Day at the Races

What is Day at the Races?

Day at the Races is a seemingly random Mario Party 2 coin battle minigame where players bet on racers.

Sample Video of mini-game: https://www.youtube.com/watch?v=R6aG__AkaNE

Playing this enough times you will quickly learn that Thwomp is terrible.  But why?

1: There are 4 signs along the course.  Each character will do one of three things at a sign.  Speed up, trip, or continue as they were.  When a character trips, they will speed up afterwards.
2: Each character has different movement speeds and movement mechanics.
3: When using savestates, the entire race progression is determined when the start button is pressed.  Therefore who picks which racer has nothing to do with which racer wins.
4: Each racer has three starting animations you can see prior to choosing them.  You can choose the racer after seeing which animation they have.

Fast Boo: Flashing twice a second.
Normal Boo: Flashing once per two seconds.
Slow Boo: Not flashing, looking down.

Fast Whomp: Wobbling side to side.
Normal Whomp: Standing straight up.
Slow Whomp: Hunched over slightly.

Fast Bob-Omb: Bright fuse lit.
Normal Bob-Omb: Average fuse lit.
Slow Bob-Omb: No fuse lit.

Fast Thwomp: Rising and pounding quickly.
Normal Thwomp: Rising and pounding slowly.
Slow Thwomp: Sitting on the ground.

Note: "Fast" and "Normal" Thwomp often get caught on the starting gate based on what point they are in their animation.  It might be possible to manipulate this.

Poking around in memory, my perception was that the racer placings are seemingly not determined until they cross the finish line.  This would mean that the game only knows the actions each racer takes at each sign.

The RNG did not loop within 130,000 iterations, and the high word and the low word both affect the result of the race, so I could not do the complete sample size since it seemed higher than 65536.

Given this, I wrote a script to continually delay starting the minigame by one input frame, record animations, and run 12,557 races at about 2000 frames each.  (We had more, but I messed up recording an animation value, thanks for the help Zim and Trooble ^_^.  Zim was running 4 instances of BizHawk at 200 fps taking up 75% CPU on an i7. Thanks also to Bizhawk devs for the HUD disabling. )

The raw data of brute forcing is probably more accurate than a theoretical approach of movement modeling and probability of each individual event at each sign due to possible slight biases in RNG patterns.

Results:

First places:

Fast Boo: 46.4%
Normal Boo: 35.9%
Fast Whomp: 33.5%
Fast Bob-Omb: 28.9%
Slow Boo: 27.3%
Normal Whomp: 25.9%
Slow Whomp: 24.6%
Normal Bob-Omb: 22.7%
Slow Bob-Omb: 19.8%
Slow Thwomp: 14.3%
Fast Thwomp: 13.0%
Normal Thwomp: 11.7%

Second or First:

Fast Boo: 66.9%
Fast Whomp: 62.7%
Fast Bob-Omb: 60.1%
Normal Boo: 58.2%
Normal Whomp: 55.7%
Normal Bob-Omb: 52.0%
Slow Boo: 51.1%
Slow Whomp: 51.0%
Slow Bob-Omb: 47.4%
Fast Thwomp: 34.5%
Slow Thwomp: 33.2%
Normal Thwomp: 30.4%

Fourth Place:

Thwomp: 43.6%

--

Cross-comparisons on the data such as "Does Slow Whomp happen to beat Slow Boo more when they are both in the race?" might be possible.

Sum of all animations:

Bob	Who	Boo	Thw		AvBob	AvWho	AvBoo	AvThw

2956	3585	4440	1576		0.235406546	0.285498129	0.35358764	0.125507685
3687	3656	2818	2396		0.293621088	0.291152345	0.22441666	0.190809907
3423	3165	2857	3112		0.272596958	0.252050649	0.227522497	0.247829896
2491	2151	2442	5473		0.198375408	0.171298877	0.194473202	0.435852513
12557	12557	12557	12557

Fast Animations:

FastBob	FastWho	FastBoo	FastThw		FastBob	FastWho	FastBoo	FastThw
928	1540	1450	196		0.289096573	0.335219852	0.464148528	0.130146082
1001	1341	641	324		0.311838006	0.291902481	0.205185659	0.215139442
747	1066	542	417		0.23271028	0.232041794	0.173495519	0.27689243
534	647	491	569		0.16635514	0.140835873	0.157170294	0.377822045
3210	4594	3124	1506
0.255634308	0.365851716	0.248785538	0.119933105

Normal Animations:

NormBob	NormWho	NormBoo	NormThw		NormBob	NormWho	NormBoo	NormThw
1390	1639	1725	916		0.226716686	0.259458604	0.359001041	0.117210493
1799	1882	1072	1459		0.293426847	0.297926231	0.223100937	0.186692258
1726	1630	1060	1897		0.281520144	0.258033877	0.220603538	0.242738324
1216	1166	948	3543		0.198336324	0.184581289	0.197294485	0.453358925
6131	6317	4805	7815
0.488253564	0.503066019	0.382655093	0.622362029

Slow Animations:

SlowBob	SlowWho	SlowBoo	SlowThw		SlowBob	SlowWho	SlowBoo	SlowThw
638	406	1265	464		0.198383085	0.246658566	0.273336214	0.143386897
887	433	1105	613		0.275808458	0.263061968	0.238764045	0.189431397
950	469	1255	798		0.29539801	0.284933171	0.271175454	0.246600742
741	338	1003	1361		0.230410448	0.205346294	0.216724287	0.420580964
3216	1646	4628	3236
0.256112129	0.131082265	0.368559369	0.257704866