Draw Probability Index

[EvaRia]

Basically, I've discovered a way to determine what card you are most likely going to draw next.
For the sake of this thread, I will call this Draw Probability Index, or DPI.

DPI=(1/Number of Cards Remaining in your Deck )*Number of Specific Card Remaining in your Deck

For example, you have 5 photons remaining in your deck. You have 15 cards left in your deck.
DPI
=(1/15)*5
=5/15
=33.3% chance that your next draw will be a photon.

The card left in your deck that has the highest DPI will be the card you are most likely going to draw next.
Simple enough?

WHAT YOU CAN DO WITH THIS!

You can use this to calculate your absolute average start hand.
Basically for every draw, calculate the DPI of each different card in your deck, and for each draw add the card with the highest DPI to your (imaginary) hand.
Repeat this for 7/8 times and you have your AVERAGE START HAND.
Recalculate DPI after each draw and you can even find out what your AVERAGE GAME against an opponent doing nothing is, INCLUDING YOUR INTEGER TTW WITH AVERAGE DRAWS.
Heck, if you calculated by turn DPI with TWO decks, you could create and find out WHICH DECK WOULD WIN IN AN AVERAGE GAME.
Somebody make a program for this? Please?

[Demagog]

Haha I'm pretty sure everyone knows about probability already. Great players can guess what card they will draw next most of the time, without even needing to think about it.

[Mastermind79]

This is somewhat similar to coinich's  Hypergeommetric Draw Probability  (http://elementscommunity.org/forum/index.php/topic,7893.0.html). I'd prefer to use hypergeommetric probability, but only because I'm lazy and there's a nice internet app thingie.

I like the idea of mock battles, but many games don't go as expected.

[teffy]

This idea is definitely wrong.
lets say you get a starting hand of 7 and have more than 12 pillars in the deck.
say 6 of all other cards, 31 cards in the deck (edit: thanks for finding this small mistake)

Then:

13/30 > 6/30 -> pillar
12/29 > 6/29 -> pillar
and so on
7/24>6/24 -> pillar

-> average hand = 7 pillars

do you want to accept that?

Simply use the rule of three for calculating an average starting hand
That means:
12 pillars, 6 of card A,B and C, average starting hand with 7: 2,8 (12*7/30) pillars, 1,4 (6*7/30)of all other cards.

[EvaRia]

Yah, I just realized it too.
Probabilities are weird >=O.

For starting hand try (7or8/deck size)*# of specific card
Then try taking all the ones that have DPI of at least 1, and putting them in your hand.

The reason that didn't work is because I guess you have the probability of drawing a specific card is highest, but the probability of drawing something else is higher.
At this point I have no idea what works ><

[Krahhl]

The problem is the probability of drawing a card compared to drawing another card is different than the probability of drawing a card compared to not drawing it.

Following the example with 13 pillars and 6 of every other card (though I'm not sure how that can add up to a 30 card deck..so we'll say 31 cards).

13/31 > 6/31, but 13/31 < 18/31.

Therefore you are more like to draw a pillar than any other specific card, but you are more like to draw any other card in general than a pillar.


To figure out your average starting hand, you take each card proportionately to how many of that card there are total.

Example:
You have 12 copies of card A, 6 of card B, 6 of card C, 3 of card D, and 3 of card E for a 30 card deck.
So in any 10 given cards, you are likely to have 4 copies of card A, 2 of card B, 2 of card C, 1 of card D, and 1 of card E.

This means in a 7 card starting hand, you should have 2.8 card A, 1.4 card B, 1.4 card C, 0.7 card D, and 0.7 card E.
This rounds to averaging 3 card A, 2 card B or C and 1 of the other, and 1 card D or E.
But this is all probability, so the actual numbers will usually be different.


I think I hurt my brain too much thinking about something that's not gonna help anyone.

As a general rule: The more copies of a card you have, the more likely you are to draw one.