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13

As long as neither player has information about the order of cards in a deck of cards, no player can gain an advantage from a "bad" shuffle. A "bad" shuffle could be defined as a shuffle that does not, by a reasonable standard, erase all information remaining from the end of the previous game, most notably the order of cards. This does not mean that there ...


10

As of the July 2021 Magic Tournament Rules Release Notes, spindowns are prohibited from being used as a randomized die at Competitive REL (though are seemingly being okay in casual play): Spindown life trackers are prohibited. We're not going to worry about it in casual play, but at Competitive REL, we expect the numbers to be distributed appropriately to ...


6

No player has a greater chance of drawing an even or uneven distribution than any other. One way of looking at it is to consider permutations of the tokens, where they are laid out in some sequence instead of jumbled in a bag or something. Then, if we shuffle the tokens up, so that they can be in any order, we can distribute the tokens, so that the first ...


4

Your wife is confusing 'random' with 'balanced' Human beings, in general, have a terrible understanding of probability. There's a rather popular probability demo that teachers use, where they'll give half their class coins and ask them to flip the coin 100 times and record the results. The other half the class is instructed to attempt to fool the teacher ...


4

There are certainly games in which a bad shuffle can benefit one player. I remember playing Ligretto, also called Dutch Blitz, against my teenage nieces who were winning far more frequently than even teenage reflexes would indicate likely. In Ligretto the cards end up stacked in order, and there is a distinct advantage to having low cards on the top of your ...


3

As long as you draw the whole deck before shuffling discards, it doesn't matter. Simply put, all cards in a well shuffled deck are equal. (Or have an equal probability of being this or that.) Splitting the deck, drawing in the wrong order, or intentionally drawing from the middle of the deck, or even shuffling the deck between draws does not matter, if ...


3

Deckbuilding is part of playing a CCG. Playing a game of Magic with a deck you had no control over is like playing a round of Bridge where someone else did the bidding for you. Any proposal for playing a duplicate CCG involves at some point playing a deck assigned to you by the format, created either by your opponent or by the competition's hosts. And that'...


3

Not sure this is an answer, but it certainly isn't a comment. Sentences in [brackets] are ignorable side-notes. In team-of-four bridge events, including the world championships, the two tables in the match are set up so that each team puts one pair N-S at their "home" table and E-W at the other team's home table. Then the same hands (6 is a "...


3

This game mechanic introduces the problem of trying to establish the expected result of a dynamic series of events that can't be readily repeated. For common terms through out, I'll be using the following to describe the game pieces. Tile Doors Effect A 1 -1 B 2 0 C 3 1 D 4 2 Additional variables are: M =...


3

Your sampling sequence is an example of an exchangeable sampling sequence. Exchangeable sequences are not independent. The outcome of earlier samples does affect the outcome of later samples. However the marginal distributions are identical. i.e. the probability of whether or not the first player gets a single color is identical to the probability the ...


3

The more dice you use to generate a single random value, the closer each random value will be to a certain average. You can see this happening in Catan: rolling two dice results in a lot more sevens than twos. If you do this with 4 dice, almost everything will be centered around the 14th coordinate. If you don't mind some normalization, you could use 2d12 ...


2

The answer to this question is going to depend on how you are shuffling the cards. If you are doing a standard riffle shuffle then as long as you can do a decent shuffle you should not need to do it more then 7 times. In most games shuffling the deck 3-4 time is enough to provide the randomness that the game needs. It should also be noted that even if you ...


2

It's true that there's no statistical difference between a card taken from the top of a perfectly shuffled deck and a card taken from the middle of the deck. (Assuming that no one has already looked at the top cards.) The caveat is perfectly shuffled. Humans, in general, are rather bad at shuffling cards. For a standard 52 card deck, it takes about 7 riffle ...


2

From the Ticket to Ride official rules: Draw Train Car Cards – The player may draw 2 Train Car cards. He may take any one of the face-up cards or he may draw the top card from the deck (this is a blind draw). If he draws a face up card, he immediately turns a replacement card face-up from the deck. He then draws his second card, either from the face ...


2

I've been working on an Excel sheet, and I think I'm ready to post it now. Here is the link, and you'll need to download it and enable macros. Here's how to use it: Enter the number of cards in the deck. Enter the ratio of 3 exit to 4 exit cards. In the example image a ratio of 2 means that there are 2 3 exit cards for each 4 exit card. The 1 and 2 exit ...


2

One of the things that makes duplicate bridge work is that, once the cards are dealt, the random factors are mostly fixed. The decisions people make in the middle of the game don't tend to change which unknown random factors are important and which are largely irrelevant. No matter what decisions people make throughout the bidding and play of a hand, if ...


1

First, duplicate bridge is played in teams of two because bridge itself is played in teams of 2. It is a feature of the game, not the duplicate tournament style, so there is not necessarily a reason to have teams of two here. In addition, the tournament setup described here does not really reflect duplicate bridge: in duplicate bridge, in different rounds ...


1

Duplicate bridge exists because bridge is a highly random game - if you don’t, then the deal determines who wins far more than the play. The deal is zero sum - opponents rarely have evenly matched hands. TCGs are totally different: each player makes their own deck, and they’re positive sum - both decks can have the best cards (equally). That’s most of the ...


1

You can't have it totally random, but you can make it random with slight boundaries. This all depends on the number of doors left in the maze/Labyrinth/dungeon. You start with X on the first tile and every tile afterwards adds (number of doors -2) to the number. So every tile with only one door removes an open door from the maze while a tile with two doors ...


1

I doubt you can keep your dungeon to a small range of sizes if you are drawing randomly. Even if you start with an entry card with three exits, the next three cards you draw might be dead end rooms and you have a very small dungeon. A real difficulty is that placing a card only uses up one door and unless it is a dead end it adds at least one so the number ...


1

There is no need for card runs to be long or for one person to have deck knowledge for a "shuffle" to be unfair for one player. Consider the case where high cards are placed on top of low cards during game play. If these alternations are then flipped over and dealt, the high cards will now be in the even-numbered positions and will be predominantly dealt ...


1

Since I don’t know Skip-Bo, I will give a more general answer: In deck-building games (like dominion) it is absolutely possible that a player benefits from a bad shuffle of their individual deck, because good cards, once close together, will tend to stay close and are more likely to be on their hand at the same turn, making for some really good and some ...


1

I think freekvd explained rather well why your probability distribution is not flat, but if you want a flat distribution, you could do one of the following: get a 24-sided and a 12-sided die and do basically the same thing you had already done. make cards numbered 1-24 and draw two of them for each token placement. Those on the 12-inch side can either be ...


1

So, after some discussion, this is the idea we're going with. We will create 12 (not concrete yet) set layouts for tokens that can be applied to any given board section. These layouts will be drawn onto cards and shuffled together to make a deck. When the game is started and the Board is tiles are placed, a card is drawn for each section and tokens will be ...


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