Thursday, 26 April 2012

what are the odds?

Before I start, I just want to say I wrote this some time ago.
I've ummed and I've aaahd and I've decided that I will publish it.
But I nearly didn't.
I nearly didn't because Malifaux is a brilliant game with so much more to it than the cards.  Because, stripping out and looking at the cards in this way is perhaps not how I want to view my beautiful game.  But, I have written it, it is part of the game, and as I'm an entirely un-educated statistician it's probably meaningless anyway.

So, read it if you want.  Correct me if it's needed.  But don't get too worked up about it.  Malifaux is so much more than a card game that this is barely worth the effort.


Malifaux is a card game.  Well, at least partially, and as such is subject to chance, and these chances are measurable.
(c) Wyrd Miniatures
Do you know what the chances are of you picking up the Red Joker in a hand you draw?
Do you know the chance of getting the red joker on any given flip?
Do you want to know?
Any card player who plays bridge or poker or any other card game with any degree of seriousness will know the odds of key events happening.  Perhaps we should too?
I'm no mathematician or card sharp so anything I say here may be misguided and inaccurate but I do have some thoughts.

Basics - 54 cards 4*13 cards suits + 2 jokers.  Playing with the jokers gives slightly longer odds than standard card games that aren't played with jokers.

Chance of drawing the Red Joker in a 6 card hand?  6 chances from 54 cards = 6/54 or 11.1%  Which means that approximately one in 10 hands drawn will contain the Red joker.  Except that when we draw our hands some cards have already been flipped/ discarded.  Might just be one you discarded from previous hand - 6/53 or 11.3% or 2 6/52 or 11.5% or more, all of which increase the chance of you getting the Red Joker in your hand.
There are other factors too, such as ability to hold more cards in the hand such as minions or masters who add to your hand size.  Arcane Effigy lets you hold an extra card, combine that with a master who holds an extra card (Rasputina i think?) and you have 8 cards in your hand rather than 6.  that's 33% more cards.  but is it 33% more chance of drawing the Red Joker?
Hand Size Cards Chance %
6 54 1/9 11.1
6 53 1/8.83 11.3
6 52 1/8.67 11.5
7 54 1/7.7 12.9
7 53 1/7.57 13.2
7 52 1/7.43 13.5
8 54 1/6.75 14.8
8 53 1/6.63 15.0
8 52 1/6.515.4
please excuse the fraction decimal hibrid.

So that's a reasonable increase in chance of picking out that coveted card.  Also, with a larger hand size the odds grow faster as you loose cards to choose from.  So the change over 3 cards (54 - 52) at 6 card hand size is 0.4%, at 8 card hand size it's 0.6%.

Does this make the Arcane Effigy worth taking?  Well, it costs 4SS.  So that's 4 SS to increase your chance of drawing by a couple of %.  What else could you do with those 4SS?  take them as Soul Stones for one.  Each one giving you a better chance than any single card in your hand, of being the red Joker.
If the Red joker hasn't been played, as cards are played from your deck you get an increased chance of drawing the Red.  Two cards flipped, 6 in your hand chance of Red Joker being next is 1 in 46 or just under 2.17%.  2 Flipped 8 in hand it's 1 in 44 or 2.27%.  But, if half the decks been played without it popping up?
6 in hand 23 played 1 in 23 or 4.34%  Still not great is it?  But it is twice what it was before. For any given card in a 6 card hand the chances at the time of drawing your card are between 1/ 52 (assuming 2 cards flipped) 1.9% and 1/46 or 2.17%.  the thing with Souls Stones is though only one or maybe two models in a typical crew can use them.  If the RJ is in your hand anyone has access to it.

Apply that extra card in hand to a requirement for high cards in a specific suit, or even just high cards in any suit and it becomes even more useful.  I think I may well be acquiring an Arcane Effigy to run alongside Rasputina in the hope that the shortened odds will give me an upper hand, a lightly increased chance at least.  Of course, in play these odds may not bear fruit.  We're talking about shortening long odds by only a little, but I reckon it's worth looking at.

The point of this article then, is not to tell you the odds, I've probably got them wrong, but to get you thinking about them.  The card mechanic is core to the game we love and should be given due consideration, go give it some thought and try and calculate the odds that matter to you..  What are the chance of me flipping a certain suit for instance, might be worth knowing that one.
Nor am I claiming that the odds are more important than crew selection, crew knowledge and good tactics because I don't think they are.  But I do think having an idea of them is a worthwhile exercise. If you're hoping for a good flip, at least have some idea what hope you have.

Now I just need some mathematician to shoot me down in flames ;-)

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