Tuesday, May 21, 2019

Why You Should Draw from the Deck of Many Things

Because Ozymandias, or Simon Jester (name that book), has written two posts on the Deck of Many Things (here and here), now I feel compelled.  For those not familiar with the deck, or have no copy of it, you can see it on this link, page 142.  On the right, you'll find a screen shot of the deck (the notes are from whomever put it on the web). Follow the link for the descriptions.

All told, there are 22 cards.  Gygax and party are playing off the Tarot Arcana, which I posted just a couple days ago, but the names are, well, "creative."  The names don't matter.

Let's break this down a moment, because the most important thing when making a decision like this is to know the odds.

There are 6 very good possibilities: the sun, the moon, the star, the throne, the jester and the fates.  Arguably, depending on the DM, the two wishes may bite you on the ass, but then you should quit playing with assholes.

There are 5 okay possibilities: the comet, the key, the knight, the gem and the vizier.  These are all positive but, when compared with the six above, they're so-so.  Which would you prefer?  A magic item and 50,000 x.p. or a magic item and a treasure map?

There are 6 cards that will make you go ouch: the talons, the ruin, the euryale, the rogue, the balance and the idiot.  True, the "ouch" is relative, depending on what magic items you have and how much property you can lose.  And hey, you'll survive with 4 less intelligence.

Arguably, you can include the void here, as well.  I mean, what's a soul?  It really depends on how the DM plays it.  Chances are, your DM never brought up your soul before, so why does it suddenly matter now?

And equally arguably, the fool only makes you lose 10,000 x.p.;  AND then you get the same odds as before.  Slightly if your DM discards the fool card from the pack as dictated.

That leaves only 3 truly bad cards: the flames, the skull and the donjon.  Everything else you recover from.

Out of 22 cards, half are perfectly good.  8 hurt, but you're basically fine.  There are only 3 bad cards.  That's only a 13.6% chance of pulling a truly bad card.  And what happens?  You maybe die and you maybe don't.  Ultimately, a devil is just a monster you fight.  The card implies that death might be defeated ~ and hey, what does that mean exactly, hm?  None of us actually defeat death, but it takes a long time to lose.  And however we might get imprisoned, we've got these great adventurers who just love rescuing people from prison.

With these odds, you'd be NUTS not to play.  If gambling worked on these odds, Las Vegas would be a flat empty plain in Nevada.


11 comments:

kimbo said...

Better odds than russian roulette. Maybe worth it for ones henchmen.

Ozymandias said...

Context matters, nyet? I hadn't really thought about the circumstances of players, such as party level, total wealth, etc. Those bad cards become more and more a nuisance than a real threat, the higher up you go.

Thinking about this more, especially what you said about the cards being like a virus (self-replicating), and I'm leaning toward making charts to randomly generate a deck each time. That way the players are taking a big risk by drawing blind. It's in their interest to do the research first, to see what cards and effects are available.

Ozymandias said...

and the reference is to The Moon is a Harsh Mistress.

Alexis Smolensk said...

Well of course, you know Ozymandias. When I hold up two fingers, I need Mrs. Riley ~ and only Mrs. Riley ~ to answer the question. Heh.

Ozymandias said...

sorry, couldn't help myself ;)

Alexis Smolensk said...

Well, Oz, you're entitled to name the film I related with my previous comment.

Ozymandias said...

I want to say October Sky but I have a feeling I'm wrong . . .

Discord said...

Thanks for sharing the fascinating articles!

For the diegetic reason for the Deck existing, I'm learning towards the idea that some kind of trickster deity created them. Maybe not to sow chaos in general, but this entity benefits from having cards drawn. I'll need to work through the idea more, though.

Homer2101 said...

How many times will a player draw from the deck in a campaign?

Your analysis is good if a player draws from the deck many times during a campaign. If she draws from the deck an infinite number of times, she will get 50% good cards and 50% mediocre or worse cards. These are quite good odds.

But as the number of draws decreases, the deviation from the ideal increases. If she draws from the deck ten (or twenty) times or less, odds are good she will experience streaks which will grossly deviate from the ideal 50/50. Just like how a d20 will roll each number with equal frequency over numerous rolls, but might roll nothing above a 10 in a particular session.

So a player should draw from the deck if she's going to draw many cards. Otherwise she should recognize that drawing from the deck is a crapshoot.

Alexis Smolensk said...

Homer,

The rule in the DMs Guide states, first, that the number of times you pull from the deck must be named before the first card is drawn. You can't change the number of times once the first draw is made.

As well, also stated by the DMG, with the exception of the Fool card, a drawn card is ALWAYS reinserted into the deck before another card can be drawn. So the odds don't change, except for that one card, which increases the chance of the three very bad cards to slightly more than 14%.

Homer2101 said...

Yes. And the player should declare she will draw 400 cards and keep drawing until she runs into the Void or the Donjon, which block further draws, to take advantage of the law of large numbers. I would not draw from the Deck because of the existence of those two cards, but that's the best way to try and maximize the odds of getting 50% good cards to hopefully offset the bad.

It's not that the odds change as the player draws more cards. It's that the variance gets smaller as the player draws more cards, and the distribution of cards approaches the ideal probability distribution. You're arguing that the player has a 50% chance of drawing a good card, and only a 14% chance of drawing a really awful one, but this is only guaranteed over a very large number of card draws. Players shouldn't expect to get 50% good cards unless they draw several dozen times from the Deck due to how probability works.

Perhaps this will explain more-clearly:

For any game of chance, like the Deck, there's an ideal probability distribution. For a coin toss, the ideal distribution is 50 Tails/50 Heads. For the Deck, it's 50% good, 36% bad, 14% awful. This distribution is only obtainable with an infinite number of observations -- draws of cards, rolls of dice, and so forth. Draw from the Deck a million times, and you'll likely get the above distribution. This is the law of large numbers.

But the law also states that there is no guarantee a small number of observations, or any series excerpted from a large set of observations, will have an ideal distribution. Assuming that any small set of observations will have an ideal probability distribution is a common logical fallacy. Since each draw is an independent event, as you've pointed out, there is also no prohibition on streaks of bad or good luck.

For example, consider a coin toss. The ideal distribution is 50% heads and 50% tails. This does not guarantee that any small sample will have the above distribution of outcomes, as the quick demonstration below illustrates.

On the first toss, I get: Heads

Because each toss is an independent event, like draws from a deck with replacement of cards, this does not guarantee the next toss will result in a T, and does not change the odds of future results.

After the second toss, I get: Heads, Heads

And after five coin tosses, I get: Heads, Heads, Tails, Heads, Heads (80/20)

We can run the same example using the Deck. The ideal distribution according to your post is 50% good, 36% bad, 14% awful, rounded to the nearest percentage point. WotC provides a deck generator. Running it, I obtained, in order from left to right:

Void, Talons, Throne, Talons, Idiot

Since Void blocks further card draws, this is 100% bad. Only two cards stop further draws, but a player can very well draw one at the very start. If we remove the no-draw feature, we get:

80% bad, 20% good.

If we call the second Talons a wash, because the first Talons ate all of our magic items, it's 75% bad, 25% good.

Still not really close to the ideal distribution.

Drawing 40 cards and pretending none of them stop further draws, I get:

45% good, 38% bad, and 13% awful.

This is a somewhat better outcome, but it also includes a Donjon as the 8th, 32nd, and 39th cards. This is twice the expected rate for a 40-card draw but, again nothing prevents this sort of thing.

So the player should draw as many cards as she can in order to reduce the effect of bad streaks of luck inherent in drawing a small number of cards. This won't prevent her from getting a bad card right at the start, nor from being blocked from further draws by the Void or the Donjon after a bad streak, but it will be less of a crapshoot than drawing 4 cards and hoping for the best.

To truly favor the player, we would have to remove the no-draw feature of the Donjon and the Void.