Probability Revised - Fate Egg Statistics!

[gavsword]

This is really cool. + Karma for statistics

How many games is this across?

[ratcharmer]

I'd be willing to lend a hand with this if you'd like one. Mayhaps I'll start running tests with unnupped fate egg?

Very interesting. I thought the only creatures on the no-hatch list were fate egg and chimera.

Earlier I ran the math assuming an even chance for each creature, but it really looks like that's a non-random distribution. Seems (at a glance, haven't done the math yet) that mid-hitters are under represented, while a lot of small fry are over represented (deathstalker, cat, damselfly, gemfinder etc.).

A couple types of dragon/nymph seem slightly over represented, but others seem slightly under represented. Really most of what I'm seeing could just be random variation though.

I'll try to calculate the average attack, hp etc. of a hatched creature later tonight.

*edit*
Results are in. I stopped at 213 hatches for reasons that should soon be apparent.

Previously I calculated the following, assuming there was no bias in creature selection:
Average Attack: 3.37
Average HP: 4.05
Average cost: 4.95
17% chance of a rare creature
15% chance of a dragon
15% chance of a nymph
47% chance of a useful* creature

After running enough games to get data I ran the stats on what I was actually getting out of fate eggs:
Average Attack: 3.27
Average HP: 4.1
Average cost: 4.94
21% chance of a rare creature
15% chance of a dragon
16% chance of a nymph
48% chance of a useful* creature

Basically, so far fate egg is behaving exactly as predicted.

Here's the gritty details if you want them:

First off, I was using this deck:

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5ri 5ri 5ri 5ri 5ri 5ri 7qb 7qb 7qb 7qb 7qb 7qb 808 808 808 808 808 808 808 80i 80i 80i 80i 80i 80i 81q 81q 81q 81q 81q
I blatantly copied this table from kuro and just changed the numbers, hence even though the table gives the upgraded names, these are all the unupgraded versions of these cards.

Element	Creature	Hatched #	Element	Creature	Hatched #	Element	Creature	Hatched #
	Ball Lightning	2		Damselfly	6		Pest	4
	Phase Recluse	1		Elite Wyrm	3		Bloodsucker	4
	Immortal	0		Elite Firefly	2		Vampire	2
	Elite Phase Dragon	1		Elite Queen	1		Gargoyle	1
	Aether Nymph	3		Sky Dragon	2		Voodoo Doll	1
	Retrovirus	3		Air Nymph	1		Obsidian Dragon	6
	Elite Skeleton	5		Gnome Gemfinder	4		Dark Nymph	3
	Flesh Recluse	1		Antlion	7		Micro Abomination	1
	Condor	5		Steel Golem	2		Werewolf	0
	Elite Mummy	1		Elite Graboid	2		Maxwell's Demon	2
	Deathstalker	0		Elite Shrieker	3		Fallen Druid	2
	Ivory Dragon	1		Basalt Dragon	4		Schrödinger’s Cat	2
	Death Nymph	2		Earth Nymph	1		Amethyst Dragon	3
	Brimstone Eater	3		Graviton Guard	2		Purple Nymph	3
	Fire Spectre	3		Elite Armagio	3		Giant Frog	1
	Lava Destroyer	6		Elite Charger	0		Elite Cockatrice	4
	Minor Phoenix	4		Elite Otyugh	0		Leaf Dragon	1
	Ruby Dragon	1		Graviton Firemaster	2		Forest Spectre	4
	Fire Nymph	4		Massive Dragon	6		Scorpion	1
	Ray of Light	2		Gravity Nymph	4		Jade Dragon	3
	Elite Pegasus	4		Elite Deja Vu	1		Life Nymph	3
	Archangel	1		Fate Egg	0		Physalia	5
	Crusader	1		Elite Scarab	0		Abyss Crawler	4
	Light Dragon	3		Elite Anubis	1		Puffer Fish	6
	Light Nymph	5		Dune Scorpion	4		Ulitharid	3
				Pharaoh	3		Steam Machine	3
				Silurian Dragon	0		Arctic Octopus	8
				Golden Nymph	2		Arctic Dragon	2
							Water Nymph	3

My apologies in advance if I flumoxed the table. I'll post my excel sheet of work once I've finished crunching the numbers for elite fate egg.

*- a "useful creature" is here defined as a creature that is either rare or costs more than 4 quantum to play. While a non-rare creature costing 4 or less quantum to play can still help you, you would have been much better off playing that creature directly instead of getting it through a fate egg.