What Are the Odds? Hypergeometric Probability and You

[Rainmaker]

Yes, probability is a KEY tool when playing any card game (from BLackJack, Poker, etc to Elements).
The thing is "its just probability". It help on the theoretical side; but after having a solid build, decision are made on the experience of the deck.

I'll use an example to explain myself:
Suppose you are playing Blackjack 1v1 (vs croupier).
According to probability the best strategy is to call for a card if you sum up 16 or less, and stay if you get 17 to 21.
Nevertheless, sometimes you may want to draw a card although you have 17 (running a high risk of going over 21)
And that is based on experiencie.

Yet as humans we are faulty, and there are many ways to exploits your human flaws. For example: using gambler falacy; trick you with the way you may win money (only costs you $1 to play and you can win $50, though odds of winning are 0,12).

Also I want to explain that when we express probability; for example 30%. That means the chances of something happening is THAT (a relative number). It doesn't mean that if you repeat it 100 times, 30 of them will succed. (That has its own probability, which is by the way: chances of having 30 succes in 100 trys, with a p=0,3: 0.086783864 or 8,7%)

[QuantumT]

is there a way to calculate different cards in your first draw?
i have a fire rush deck which needs photons, immolations/cremations, and lava golemns/lava destroyers on the first turn.
this would be kinda complicated cuz you have to calculate the probability of the photon, then the probability of the next card assuming one photon is drawn, and then the probability assuming 2 photons are drawn, and so on.

and when you all are calculating probabilities, dont forget that you have 8 cards if you lose the spin and 7 if you win.

I talked about how that would work in my thread on probability (http://elementscommunity.org/forum/index.php/topic,16010.0.html). If you want, you can post your deck and the hand you want, and I could use it as a specific example.

Yes, probability is a KEY tool when playing any card game (from BLackJack, Poker, etc to Elements).
The thing is "its just probability". It help on the theoretical side; but after having a solid build, decision are made on the experience of the deck.

The reason probability isn't everything in elements (and poker) is because you have to interact with your opponents, which is something that probability holds little influence over.

I'll use an example to explain myself:
Suppose you are playing Blackjack 1v1 (vs croupier).
According to probability the best strategy is to call for a card if you sum up 16 or less, and stay if you get 17 to 21.
Nevertheless, sometimes you may want to draw a card although you have 17 (running a high risk of going over 21)
And that is based on experiencie.

I don't really think blackjack is a good example. With its rigid rule structure, you should always follow the probabilities. Any departure from the probabilities will lead to losses in the long run.

Also I want to explain that when we express probability; for example 30%. That means the chances of something happening is THAT (a relative number). It doesn't mean that if you repeat it 100 times, 30 of them will succed. (That has its own probability, which is by the way: chances of having 30 succes in 100 trys, with a p=0,3: 0.086783864 or 8,7%)

But the chances of having 25-35 successes is 77%, and chances for 20-40 successes is 98%, so it still gives a pretty good guideline.

[Captain Scibra]

Well, instead of some super-complicated calculating program, you could always check out my theoretical formula of how many cards to add in a deck based on when you need them and how to get it by that turn theoretically.  The link is in my signature.

[teffy]

A slightly different approach to deck-building: http://elementscommunity.org/forum/index.php/topic,20069.0.html

In case you change the sig later...

[Raptor6789]

using this handy dandy tool, i find that i am an odd defier. but not for the better, for i get more bad draws than i should.  ???

for example - my 30 card deck has 6 immolations. 4 of them show up in the first 8 cards of my hand(0.027233 chance). in a different game, 5 of them showed up in the first 9 cards(0.004457 chance).

this type of situation has occured to me many times before. not just with immolations.

[badivan1]

I have discovered that spreadsheet programs, such as Microsoft Excel, can somewhat simulate a hypergeometric distribution.  I only just found the function, so I don't know how to plot a graph of it.  The function :

=HYPGEOMDIST (X; n_sample; successes; n_population)

X : number you want to draw
n_sample : number of copies
successes : starting hand
n_population : deck size

[Dragoon]

That function in Excel/Google Docs will only calculate the probability for drawing exactly what you ask for and no more.  In other words if you want to know the odds of drawing exactly 3 Pillars in your opening hand and no more, it can tell you.  If you want to know the odds of drawing 3 or more Pillars in your opening hand, you'll have to do some more Excel gymnastics to show that.  I recommend using the link Coinich gave or use the Card Probability Calculator in my UDBT (see sig). [/shameless plug]

[Tea is good]

when's that zip file for the graphs coming out? I need to explain to someone that Elements is a learning experience. Sorry for bump.

[coinich]

Sorry about that.  Just the graphs for now: http://www.megaupload.com/?d=C84OBPZ7

[Tea is good]

Thaaaaanks !