Reversed Cards

I have recently uploaded a Tarot deck into one of my games. In Tarot, it's totally cool (actually encouraged) to "69" your cards, and when you draw from the deck, there's a chance that the card may be upside-down... and that's actually relevant to the meaning of the card. Would it be too much trouble to add a Deck option that offers a 50% chance of displaying a card upside-down when drawn? (Yes, I have considered uploading two copies of the deck and reversing the second, but changing the deck size causes many more problems)

Hmmm, really what is upside down is a function of how you cut and shuffle the cards or how you flip the cards when dealing. Cut Example: If I have 52 cards and I cut the cards evenly (between the 26th and 27th cards) and then I flip the cards before shuffling them. I have just inverted 26 cards and that would be 50/50. However, if I cut them unevenly then a segment will be reversed and the ratio will not be 50/50. Flip example: Assuming all cards in the deck have the same orientation then if you flip sideways (like turning a page) you will never wind up with an upside down card. However, if you flip it bottom to top (like lifting a page up on a clipboard) or top to bottom then you guarantee an upside down card. This is not random so much as dealer's choice of which card to flip upside down. Which card that is is still random but it is under your control if you want it upside down or not. So lets assume you are going to go for the method that is random and use the Cut example. You would need to randomly roll where the cut is. It should be a random value centered on the center of the deck in order to not cut a single card. Something like 20+1d12 (for a 52 card deck) will focus the cut near the center but not always at the center of the deck. Then you would need to roll which half of the cut is upside down, a simple 50/50 die roll will work. Next, you shuffle the cards with the upside down cards going in upside down. Assuming you are shuffling many times you can repeat these steps for further randomization.

Yes, but once you've shuffled/recalled the deck, cards are no longer inverted. As crazy as this sounds, I've actually resorted to creating a "Tarot Table" room and spreading the cards face-down (and of all orientations) on the table. The subject selects cards, orients them in any way, then flips them one at a time to reveal faces, etc.

I wasn't referencing how the Roll20 deck works, I was stating that 50/50 does not replicate how real world cards become upside down and then went into the two methods that produce upside down cards in a real deck. Sorry if that wasn't clear. :) Basically, in order to get your cards to be upside down with any kind of randomness approaching real world methods 50/50 wouldn't work. If the Devs were to implement some method for upside down cards it would need to approach some kind of real world methodology.

…So you're saying that when you flip a card from a randomized, 69-ed deck, the statistical odds of normal and reversed are not 50/50? If so, what orientation do you suppose is more likely and why? I understand that in a deck of cards, "true random" does not mean that exactly half the cards are reversed. But on a card-by-card basis, this is essentially a coin flip. While each individual card is a perfect balance of 50/50, the entire deck is a mish-mash of true random, just like you're suggesting. Everybody wins! The principle I'm trying to employ is that in Tarot, a card may or may not be reversed, and both are equally likely. Sure, you can flip 3 cards and they may all be upright, or all reversed, or some combination thereof, but It's impossible for exactly half to to be upright, hence the macro sense of random you call "real world." On a card-by-card basis, "real world" is simpler than the complications of an entire deck. One of the things I imagined in my request is a little checkbox in Deck Editor that says "Cards might be reversed" as a deck, so that whenever you draw an individual card, it might be reversed, or maybe not.

Assuming that the cards were all one orientation to start with when you cut and then shuffle a deck the only way you wind up with flipped cards is if you flip them yourself. Many people do this without realizing it. So, based on that the number of "flipped" cards is not 50/50 but is determined by the cut. How many were flipped when cut and then shuffled? While there may only be two states a particular card can be in the odds of the next card being upside down change as you go through the deck. Of course, how the Devs would choose to implement this (if they choose to implement this) would be up to them. I was just commenting on my understanding of the odds.

Exactly. If each individual card has a 50% change, there is a possibility that none of the cards in the entire deck are reversed, or all of them, or any arrangement in between. Just like cutting and shuffling. To assume that the orientation of one card statistically affects the orientation of the next is gambler's fallacy.

The gambler's fallacy doesn't apply to counting cards in an unshuffled deck. When dealing from a finite deck without reshuffling, the orientation of one card does have an affect on the probability of subsequent draws, depending on the initial conditions of the cut (cut the deck evenly for 50%, in thirds for 33%, etc). Even if you start at 50% odds (half the cards up, half the cards down, 100 cards for simplicity), once you deal the first card (face up) the remaining cards are now at 49:50 to be face up. In the same way, once you've drawn the King of Spades from a deck, the probability that any subsequent card will be the King of Spades is 0.

As Gauss pointed out, the actual chance of a card being inverted is not quite exactly random; it depends entirely upon the method used to shuffle. It's possible to use a certain shuffling method, carefully doing so each time, and never invert any cards at all. It's possible, by the same method and knowledge of the deck's initial orientation, to invert only selected cards. A truly skilled magician (muggle-magic, not sorcery!) could potentially invert only a single card in a deck with extremely careful shuffling, as well as positioning it where he wants it within the deck. However, Tarot is not poker; presumably some of the magic (sorcery, not muggle-magic) of a Tarot deck comes from the subconscious actions of the participants, subtly affecting the choice and placement of each card. While seemingly random, the fates, gods, supernatural forces, or what have you are actually making choices in such a way as to reveal ultimate truth to the Tarot user. I"m not entirely sure that a computerized simulation of this would be effective; the supernatural tends to not play well with technology! But then, on the gripping hand, you have the fact that there's no such thing as sorcery, and very few people are muggle-magicians. A simple simulation, with a pseudo-random shuffling of cards and a pseudo-random 50-50 chance of each card, when played, being inverted or not, would be quite sufficient for the purposes of this proposed system; the average user would be extremely hard-pressed to find any effective difference whatsoever between that and a 'real' Tarot dealing. So, yes, simply put a 50% chance of inversion on each card, when dealt, and you have a simulation that would work just fine. Whether this is something enough people want to be worth whatever amount of difficulty this would pose the developers is another question entirely. -Phnord

Yes. I'm not suggesting that the entire deck be 50% inverted. That's stastically improbable. The orientation of the deck is a phenomenon stemming from a random number derived from an individual card's statistics. John M. You are talking about replacement, which is already managed just fine by the card deck rules. Gambler's fallacy does not apply to the faces of cards, but it does apply to orientation. initial conditions of the cut do not matter, since they can perfectly simulated on the draw. Your deck order statistics refer to the possibility of drawing a single card, and do not require any indication if initial conditions of the deck. Likewise, orientation is simply another variable. in a true random situation, the deck is not fitted with a balance of reversed and upright cards, as a deck might be fitted with a perfect balance of suits. The act of inverting cards is a series of simple binary randomization that is multiplied against the laws of replacement that come with a card deck. Think of it as [coin flip] * [card draw] your card draw concerns are already addressed in roll20's system; my coin flip concerns are not

Perhaps this example will help: Start with a 52 card deck. Cut 20 cards and then shuffle so that after the shuffle 20 cards are inverted. The odds of any card being inverted is now 20 in 52 (~38%). Draw a card, if it is inverted the odds of drawing the next card inverted is 19 in 51 (~37%). If not inverted the odds of drawing the next card inverted is 20 in 51 (~39%). While each card can only have two states and thus may seem like 50/50 the cut and method of shuffle (did you invert the cards or not?) affects the probability of how many cards are inverted. That in turn affects the probability that each card will be inverted. This is really not like flipping a coin. Because the cut is usually uneven the odds are not 50/50.

But with the law of large numbers, all decks should average out at 50/50, and this is the same idea. Your example assumes that you intentionally invert only exactly 20 cards. True randomness assumes that you don't know which cards are inverted (so the ratio doesn't matter until they are revealed), and you continue to invert and shuffle ad infinitum until eventually only the law of large numbers justifies the assumption that only half are inverted. In reality, if you were to do this, you're just as likely to end up with 20 of 52 inverted, just as in your example, or any other number for that matter, but the core of the idea is that it doesn't matter whether the card is inverted until the exact moment you draw it. Perhaps this example will help: Start with a 52 card deck. Due to true randomness, let's say that only 20 of them were inverted. This gives you the illusion that the odds of any card being inverted is now ~38%, but in reality the odds were 50% all along and this is simply the result of random chance. You're giving me the impression that you think probabilities are 100% accurate in predicting outcomes. You are simply applying the wrong principles. Here's the problem! If you shuffle a deck, invert, and keep shuffling until the world ends, you know that the deck contains exactly 52 cards, 4 of which are Kings, 13 of which are Spades, etc. Bingo! You'd be golden if that's all there was to it. However, if you shuffle a deck, invert, and keep shuffling until the world ends, you don't know how many cards are inverted, so you don't have enough information to logically deduce the probability that the top card is, say, inverted. As long as you don't correlate inversion to faces, it is exactly the same as flipping 52 coins. At this point, each individual card, poses the question: Am I inverted or not? All things considered, the chances are equal. Each card is in a "cat state," à la Schrödinger. Your permutations are completely accurate and supplemental to the idea, but they aren't necessary to solve the problem. The real beauty of this situation is that since it is so much simpler than you think it is, it will probably be pretty easy to implement in roll20.

All of my examples were for a single shuffle, not for many shuffles. I agree that if you shuffled infinitely that statistically you will eventually approach 50/50 distribution of the number of inverted to non-inverted cards. But it will still not be exactly 50/50. Also, I don't know that a d20 will roll a 20 on the next roll, but if it has greater than normal or less than normal distribution then there may be something wrong with the die (like the die is weighted or lopsided). In any case, as I stated earlier, this is entirely up to the Devs.

Shuffles are not discrete. Ether you sufficiently randomize or you do not. You're missing the point: even if the distribution is not 50/50, the blind card-per-card probability is . You are referring to stacking a deck at this point. All I am asking is for realistic card drawing.

+1 for the original idea. Not interested in the statistical likelyhoods of real world decks so much as just a base 50/50 chance (per card) of a card being played upside down.