Probability Revised - Fate Egg Statistics!

[Kuroaitou]

First off; I'm not a deck tester. I'm not very good when it comes down to analyzing what card could be replaced in order to make a deck .003 turns faster than normal, not to mention we already have plenty of dedicated testers for the turns-to-win study (*hint hint *). That said, I decided to take up a small (and probably more trivial) study to look at, regarding the probability of Fate Eggs (and in the future, Nymph's Tears, Mutations, or other statistics hopefully).

So without further ado, here's the study.

The objective of this study was to figure out what creatures most commonly hatch from eggs, and more importantly, the probability of having a Fate Egg hatch into either a Dragon of a Nymph of any element. (The reason being that dragons and Nymphs are generally the most potentially powerful creatures (in attack power or utility) compared to the rest of their element's creatures)

Specialized Egg Hatchery

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The above deck was just randomly thrown together to pump out as many (potential) eggs as possible against a Level 1 A.I., the easiest* computer player with the least amount of creature control. For the most part, my tactic was to first put as many eggs out on the field (ignoring potential AOE creature control such as Unstable Gas or Plague) and then all hatch them in a turn when the field was as full as it could get, then write down what creatures were hatched in a excel sheet. I often lost, because I hatched the eggs to late to deal 100 damage in a turn, but that variable is irrelevant as win-loss ratio was insignificant - the most important part was to figure out the probabilities, not improve the win rate of a fate egg deck.

* = Note that while 'Level 0' or dueling a random player's 'suicide' deck would be more guaranteed to have 23 eggs on the field to hatch simultaneously, I didn't want to detract another player's time from playing the game (nor be bothered by tutorials while I'm spamming the Hatch ability on the field).

Creature Tables and Distribution

Element	Creature	Hatched #	Element	Creature	Hatched #	Element	Creature	Hatched #
	Ball Lightning	4		Damselfly	11		Pest	6
	Phase Recluse	8		Elite Wyrm	10		Bloodsucker	4
	Immortal	0		Elite Firefly	3		Vampire	5
	Elite Phase Dragon	9		Elite Queen	5		Gargoyle	6
	Aether Nymph	7		Sky Dragon	8		Voodoo Doll	5
	Retrovirus	5		Air Nymph	5		Obsidian Dragon	4
	Elite Skeleton	5		Gnome Gemfinder	11		Dark Nymph	10
	Flesh Recluse	2		Antlion	7		Micro Abomination	4
	Condor	6		Steel Golem	0		Werewolf	6
	Elite Mummy	6		Elite Graboid	8		Maxwell's Demon	8
	Deathstalker	15		Elite Shrieker	6		Fallen Druid	8
	Ivory Dragon	7		Basalt Dragon	10		Schrödinger’s Cat	12
	Death Nymph	11		Earth Nymph	10		Amethyst Dragon	6
	Brimstone Eater	9		Graviton Guard	5		Purple Nymph	4
	Fire Spectre	4		Elite Armagio	9		Giant Frog	2
	Lava Destroyer	7		Elite Charger	5		Elite Cockatrice	7
	Minor Phoenix	5		Elite Otyugh	3		Leaf Dragon	6
	Ruby Dragon	5		Graviton Firemaster	7		Forest Spectre	7
	Fire Nymph	10		Massive Dragon	7		Scorpion	7
	Ray of Light	8		Gravity Nymph	4		Jade Dragon	7
	Elite Pegasus	11		Elite Deja Vu	8		Life Nymph	4
	Archangel	6		Fate Egg	0		Physalia	6
	Crusader	5		Elite Scarab	0		Abyss Crawler	6
	Light Dragon	10		Elite Anubis	8		Puffer Fish	5
	Light Nymph	7		Dune Scorpion	3		Ulitharid	3
				Pharaoh	6		Steam Machine	9
				Silurian Dragon	0		Arctic Octopus	3
				Golden Nymph	8		Arctic Dragon	5
							Water Nymph	5

Element Distribution

ELEMENT	Hatched	ELEMENT	Hatched
	28		42
	40		57
	52		48
	40		40
	40		47
	34		42

Dragons Hatched	78	Nymphs Hatched	85	TOTAL EGGS HATCHED	510
Percentage of Dragons	0.152941176 (15.3%)	Percentage of Nymphs	0.166666667 (16.7% or 1/6)	TOTAL	100%

A few notes:

• The creatures that are italicized never hatched once during the study. While some of them may seem logical (Fate Egg hatching into a Fate Egg shouldn't happen), others are a bit strange (Steel Golem, Silurian Dragon, Elite Scarab, & Elite Immortal) A good chunk of non-hatchable creatures come from the Time element.
• Again, these are only accounting for upgraded creatures. Regular Fate Egg distribution should be somewhat the same.

Comments, Suggestions, Questions, and Feedback appreciated.

[Memorystick]

I'd like to point out that the no-hatch list includes chimera (for obvious reasons), immortal, scarab, devonian dragon, and fate egg. I don't know why you didn't get any golems, but I've gotten quite a few hematite golems from eggs (and seems to have been the old / elder's favorite hatch) In my opinion, though, 510 eggs might not be a large enough sample for the number of other creatures.

[TheCrazyMango]

Most hatched element, death. Most hatched card, Deathstalker.
(for those of you who got scared by the wall of text)

[Kuroaitou]

I'd like to point out that the no-hatch list includes chimera (for obvious reasons), immortal, scarab, devonian dragon, and fate egg. I don't know why you didn't get any golems, but I've gotten quite a few hematite golems from eggs (and seems to have been the old / elder's favorite hatch) In my opinion, though, 510 eggs might not be a large enough sample for the number of other creatures.

Ah, yes. Forgot to include Chimera in the table... >_< Ugh.

That said, I guess the stats could be increased to ~1000 instead of 500, so I could hopefully get a Steel Golem during one of those hatches, but aside from that, I don't recall why the other creatures (immortal, scarab, and devonian dragon) aren't allowed to hatch from a Fate Egg. I'm guessing it involves something regarding exploitation of playing a Fate Egg to obtain another stronger creature, but that's just an awkward assumption...

I'll see if I can get a few more games in to increase the total to over 1k.

[Kamietsu]

Great study! I like the table you have there, it's a really interesting look at Fate Egg and what comes out of it. Karma for it

[Van Cleef]

I have to ask, is there a difference between the actual game fate egg and the trainer fate egg?  It'd be so much easier there with this deck:

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And 100x quanta and the whole shebang.  The matches seem to take a little more than 2 minutes.  If anything it would find another discrepancy between the trainer and the actual game.  Mark of time works just as well...

[WakSkylicker]

Problem: Won't you have to restart every time new cards are added?

[Raptor6789]

very interesting.
i wonder if the distribution is significantly different for un-upped fate eggs.

fate egg SHOULD be random though, so my hypothesis is if we do it 1 million times  , or some other large number, each creature would have the same percentage. but of course, no one has the time to do it 1 million times.

[Daytripper]

Nice idea.

I would not go as far as that. There are some 75 ish creatures in that sample, which means the chance for a particular creature isn't mch more than 1% if random. Statistically, 500 is a decent sample. 1000 is even better, but certainly you dont need a million tests.

Now the lowest tests are 2, the highest 15. Looks like a huge gap to me. It would not surprise me if anyone with an ANOVA could show that that distribution is not random.   

[GG]

I loled at the 'specialized egg hatchery'.

Funny (and pertaining to your element) investigation you're doing, Kuro. I like.

That field of yours full of totally random creatures just seem damn awesome.

[ninjamaster1991]

put in 3 upped and 3 unupped eggs in ur deck, then try.

[chum3]

I was just wondering about this the other day. Good stuff.

So would you say that each creature, individually, has the same chance of coming from a Fate Egg as any other creature? I might have missed this somewhere in your post, so sorry if I did.