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Comment by Pxtl | Hacker News Reader

You could just use a deck of cards with numbers on them. That's the simplest way to do "Gambler's Fallacy Dice" IRL. For example, there's a popular Catan expansion pack that replaces the dice with a deck of cards with numbers on them for just this reason, because in Catan each roll of 2D6 represents different regions of the map paying out so if a number never comes up it never pays out.

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One of our first house rules for Catan was to introduce a deck. Not quite sure why they went with dice for that game; the deck eliminates a lot of boring games.

Some purists insist that they role dice, so we just let 'em and the resulting game feels quite like you're using gambler's dice.

The thing about rolling 2D6, is the distribution isn't even.

I'm not sure that factors into the game (have played but its been a while). Cards seem like a more controlled way to distribute the results with some randomness.

only one way to get a 12 (6+6) but 7 much more likely.. (6+1, 5+2, 4+3, 3+4, 2+5, 1+6)

as someone who played a bit of online backgammon back in the day, We always suspected the random dice rolls behaved differently in the game than playing in real life...

Catan cards take that in account.

They basically made one card for each possiblity of pair of dices, so there is a 7 card for 6+1, another for 5+2, and so on...

Playing with it is MUCH better than with dice... when I played with the dice that came with my copy with catan, the dice were clearly defective (rolls weren't just random-looking, they were WILDLY wrong, it rolled 10s 2 times the amount of 7s...), and the game was super boring, it would end with everyone having the same materials and not having others, so not even trade would fix the game, we had stuff like 10 turns in a row where noone had one particular item while the 'bank' ran out of the other items because everyone had lots of them.

In Catan can't you trade any 4 identical resources for any one other resource? It slows down resource acquisition but should eliminate the situation you describe!?

You can, but if I remember the resource noone had was bricks, that is very important...

So the game pace slowed to a crawl... Also, the funky dice never rolling bricks meant people would quickly rack up random resources, sometimes like 3 of each, so they ended with 9 cards, and would then lose to robber rolls (7).

Then of course in one game where this happened there was an asshole cousin that thought it would be hilarious to hog resources and make the game worse, he would spend his whole turn making 'negotiations' with everyone, and them cancelling them, wasting like 5 minutes every time it was his turn, and sometimes if 7 was taking long enough have 20 cards on his hand...

We don't play with that cousin anymore either.

But yeah, not having a way to build roads make the game suuuuuper slow.

As I'm sure you know, understanding this distribution is critical to good backgammon play. For example, all else being equal it's better to leave your exposed blots closer to a threatening opponent checker than further away (within 6 pips of course). Also, you need to account for rolling doubles which results in the counter-intuitive average pip value of a roll being 49/6 (~8.16).

An interesting bit of trivia: In roman times it seems they played with 3 dice instead of 2: http://www.bkgm.com/variants/Tabula.html

If you look at the Catan number-circles that you use use to mark the tiles with their roll, they have a set of dots on them - 6 and 8 have 5 dots, while 2 and 12 have 1 dot. The dot is the numerator over 36 of its probability.

Likewise, if you use the Traders and Barbarians dice-deck, the same thing applies - there are 5X as many 6s and 8s in the deck as there are 2s and 12s.

Catan takes the distribution into account, and is pretty up front about it (There are dots on the numbers that represent the probability). I've played a lot of games of Catan and, every once in a while, you'll have a statistically unprobable game where 11 is rolled 10-15 times, but 6 is only rolled 3 times the whole game.

That's exactly what the pack of cards is designed to solve. With the cards it's guaranteed that the 6-7-8 will show up more often than everything else.

It very much does factor into Catan. Not only are there no spaces marked "7", which is instead used for a special type of result, the probability of the remaining rolls are described graphically on the number tokens:

http://www.catan.com/files/styles/lightboxy/public/gallery/d...

Notice that the 12 has one dot, the 9 (6+3, 5+4, 4+5, 3+6) has 4 dots, and the 3 (2+1, 1+2) has 2 dots. The gray robber piece is sitting on a red number token, which is either a 6 or an 8 and has 5 dots because it is more likely to be rolled.

In the game, you develop your pieces with the hopes of getting resources based on the adjacent numbers being rolled. It definitely creates a lot of stress in some people when "eights are being rolled all the time this game but never sixes!" or "your stupid 10 keeps getting rolled when it shouldn't, that's not fair!"

I think I'll give it a try tonight with some numbered cards. I just threw some together in Excel: 1-6 in B1-G1, 1-6 in A2-A7, and the formula

    =B$1&" + "&$A2&" = "&(B$1+$A2)

spread across the grid and printed that out, but on doing a little, ah, market research, it looks like you can buy official Catan decks like this at https://boardgamegeek.com/boardgameexpansion/20038/catan-eve.... Or download this: https://boardgamegeek.com/filepage/40420/deck-dice-separate-... (note: not the above). Or someone else pointed out that you can simulate it with two matching decks of cards with:

    one 2
    two 3S
    three 4S
    four 5S
    five 6S
    six 7S
    five 8S
    four 9S
    three 10S
    two Jacks
    one Queen

Other market research says that people start counting cards to see when their numbers are going to come up again....perhaps some compromise, with perhaps two or three such decks? Real dice are an approximation of an infinite number of shuffled decks of dice, and I imagine you'd go through on the order of 100 'cards' in a given game, so with more than 3 or 4 decks you could end up with certain cards/numbers that never appeared, which seems to happen frequently and cause ire in games with real dice...interesting. Science is required! Sorry for rambling/thinking out loud.

There's a little randomness in the Catan deck of cards: the bottom 5 cards of every shuffle are not used. Not as much as dice, but also not a guarantee for certain numbers to come up a certain amount.

I've never played in real life with the deck, but I first came across this version on a software version of Catan I had (I think Xbox?). I really enjoyed it and my guess is that in real life it adds a substantial angle to negotiating placement of the robber. In particular, bribing people to put/not put the robber in a given location - if the deck is 7-heavy or your good squares are already drawn, no big deal.

I don't think I'd want to start having to count cards in order to play Settlers well, in addition to keeping track of players' hands.

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