FM AI notes

(on DarkNite and high mages)
If I let him have control then he's rolling the RNG to see if he lays a trap or plays Mountain.
Whereas if I have control then they always play the field spell, no RNG roll.

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Random fun fact: the AI will not activate a face-down Raigeki if you have less monsters than them.

Also, there's an order the AI looks over spells.
HFD, Sparks, Hinotama, Final Flame, Ookazi, Tremendous Fire, Mooyan Curry, Red Medicine, Goblin's Secret Remedy, Soul of the Pure, Dian Keto, equips, rituals, DPL, SoRL, Stop Defense, DCJ, Warrior Elimination, Eternal Rest, Stain Storm, Eradicating Aerosol, Breath of Light, Eternal Drought, Spellbinding, Shadow Spell, Crush Card, Raigeki, Forest, Wasteland, Mountain, Sogen, Umi, Yami, Dark Hole
Equips are looked over in the order they're on the field, as are rituals.

HFD, equips, rituals, SoRL, Spellbinding, Shadow Spell, Crush Card, Raigeki, field spells, Dark Hole
HFD, Shadow Spell, Raigeki
SoRL, Spellbinding

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From GenericMadScientist:
So far all I've looked at is determining what monster the AI plays if they can't play a magic or fusion. It seems to be as straightforward as looking at the top x cards (x changes per duelist) and playing the one with the highest max, picking the first one in case of a tie.

So, to give the value of x for each opponent (and so how much they cheat):

Heishin 1		20

Rex				8
Weevil			8
Mai				10
Bandit Keith	12

Shadi			12
Bakura			14
Pegasus			16
Isis			16

Kaiba			16
Mage Soldier	12

Mountain Mage	14
Atenza			16

Ocean Mage		14
Secmeton		16

Desert Mage		14
Martis			16

Labyrinth Mage	16
Seto 2			18

Forest Mage		14
Anubisius		16

Meadow Mage		14
Kepura			16

Sebek			20
Neku			20
Heishin 2		20
Seto 3			20
DarkNite		20
Nitemare		20

Deck composition (again from GMS):
If you ignore rerolling (although I don't think that's a good idea) and just want a very rough estimate, then the obvious formula would be 1 - (1 - x/2048)^40. But it doesn't work well. Like for example if you do that then it says the odds of Seto 3 having a BEUD in his deck is just under 80%, but when I simulated it I think I got an answer of 87%.

Frequency	Odds in deck (rough)
1			1.9
2			3.8
3			5.7
4			7.5
...
8			14.5
10			17.8
12			20.9
...
20			32.5
30			44.6
40			54.6
48			61.3
50			62.8
60			69.6
64			71.9
70			75.1
80			79.7 (actual is ~87.0)
90			83.4
100			86.5
110			89.0
120			91.1
130			92.7
140			94.1
150			95.2
160			96.1

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My theory:
ok, so correct me if I'm wrong, @GenericMadScientist, but this formula should be close to accurate for determining % of an opponent playing their best turn 1 card (assuming it does not tie anything):

1 - (1 - F/2048)^H

where F = the frequency as listed in TEA, and H = the size of their starting "hand"

Duelist		Monster			Odds of playing turn 1 (if monster is played)
Rex			1350+			9.3
Rex			1000+			16.7
Rex 		900+			60.5
Weevil 		Jirai			17.1
Keith 		Zoa				6.8
Bakura 		Shield/Wall		36.3
Peggy 		MBD				6.6
Isis		BSD				8.0
Isis		BSD/THTD		16.8
Isis		2250+ 			57.3
Isis		2100+			88.4
Isis		2000+			98.3
Kaiba		BEWD			26.8
Kaiba		3000			46.0
Lab. Mage	GG				32.1
Lab. Mage	3000+			62.4
Seto 2		GG				44.8
Seto 2		3000+			89.0
Meadow 		Shield			20.4
Meadow 		2100+			49.9
Kepura		GG				40.5
Kepura		GG/BSD			65.2
Kepura		3000+			82.8
Anubisius	PUGM			31.8
Anubisius	PUGM/GM/JB		69.2
Sebek		Metalzoa		44.4
Sebek		3000 or Zoa		88.0
Neku		Skull Knight	48.0
Neku		2900+			92.5
Heishin 2	GG				49.1
Heishin 2	GG/MBD			64.1
Heishin 2	3000+ or Zera	93.5
Seto 3		BEUD			56.8
Seto 3		BEUD/GG/MBD		87.6
Seto 3		3000+			99.4
DarkNite	MBD				28.5
DarkNite	3000+			63.9
Nitemare	BEUD			28.5
Nitemare	3500+			74.3
Nitemare	3000+ or Tri-H	95.4

*haven't updated with simulation data

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OTHER:
- if he has magic and trap, can't set magic
- if he has monster and trap:
	> if not in control, always monster
	> if empty board, always trap
	> if in control, dice roll (50/50?)
- if he has monster and magic, dice roll for which (might vary by duelist/distribution)
	> magic seems to have less priority (when compared only to monster) than trap