Exploring how the choice of cards, dice, tokens, coins and how the player physically interacts with can support (or break) the theme of a tabletop game. There's more to it than equivalent probability.
I think there is a clear difference between drawing cards and ticking a box to say roll a die later: with a deck of cards there is a finite and distinct set of outcomes. The player will never draw a King of Hearts twice.
Whether that difference is important in your game is a whole different question.
Narratively: using a deck contributes to the feeling of discovering unique objects.
Mechanically: if you had a mechanic that let players filter or modify the deck, it would contribute to a player's feeling that they are changing their odds (even though the the change in odds may not be very large).
This is absolutely true. While you could give dice a "memory" by using a list to check off or something, it's far easier when using a deck of cards. For the game, I think the deck of cards having memory is a bonus... but it might work with just dice.
As for how those two mechanisms FEEL, however... totally different!
One of the first games I made used coin flips because I wanted to keep the game as simple as possible, and what's easier than a d2? Turns out that coin flipping is a much harder dexterity game than dice-rolling, and what's worse, coins are harder to come by in this digital age than I'd expected.
As a poor coin flipper, can confirm. Rolling a d6 only requires dropping something on a table. Much easier. Hard (but not impossible) to miss the table.
And I’ve read that about coins. No one has a big jar of change anymore. Coins are for old people. 😅
A wonderful contraption that had completely flown under my radar, apparently mostly famous for its use in "Shogun" (even reviewed on Shut Up and Sit Down).
It's interesting how there is no analytical way to determine precise probabilities of its output. We can a only have rough estimates (see this interesting discussion on bgg:
Thank you for this comments! There's a lot for me to look into, especially checking out Shogun. I've heard of it, but never in the context of battle towers.
Yes, Space Gits looks very intriguing, indeed. So does most of Mike Hutchinson's work. I sadly haven't been able to try any of his games yet. But I've been a listener of "Rule of Carnage" for some time (the podcast he co-hosts). As the podcast is mostly about miniature game design, a lot of thought about the physicality of the components and its role on gameplay.
David Spiegelhalter's "The Art of Uncertainty" is a great introduction to probability and uncertainty very broadly.
Early on he talks about two kinds of uncertainty. Aleatory uncertainty is the future we cannot know - e.g. the roll of a dice. Epistemic uncertainty is about the present that we do not currently know - e.g. a card that we've drawn but not yet turned over.
Despite those very academic terms (they are the most cumbersome in the whole book, and I had to return to the book to check them for this comment) it's very accessible given the subject.
Thank you so much for this! I knew there had to be technical terms for what I was looking at. Seems like you nailed it! I’ll need to check out The Art of Uncertainty.
Fascinating as always :)! As a self-proclaimed math nerd, and PhD student in (basically) statistics, i think your use of probabilistic equivalence/probability distribution is very appropriate :D at least, it fits my understanding of the term :) (i could, of course, still be wrong ^^) thank you for sharing <3 it's super interesting to think about, what would i personally prefer? i have played most of my games online, so thinking about what would feel best physically is definitely interesting. i think i like rolling dice, but for 50/50 mechanism specifically it kind-of feels less fun, somehow, just in my mind? although, i would say that depends on the game, and overall i voted "not sure", as i like the idea of the feel of the game influencing the "best" feel!
Speaking of coinflips and probability. I once was entertaining a couple friends and flipped a coin (to catch on the air and then flip again) and it fell heads 12 times straight, then I stopped. One friend was flabbergasted and the other one kept telling him it was a trick. And yes it was, I pulled a Maverick
It also happened on a game of Magic, I had won the first game and the player was one of the top ones, so he had a whole army ready to squish me on the second game, and with no cards on my hands it was my turn to draw and I pulled another Maverick, I didnt knew what I neede but the deck provided
I think interaction helps bring a sense of ambience. Like using red dice to roll for damage, you feel the amount of splatter. I have this ongoing wip boardgame that I know can work with just cards, but there are also people (like me) that would download the papercraft popup scenarios and build them for the game.
Then theres also gameslike Scrapcat (Luca Negri) that added a bonus if you draw your character. And also “Every new thing” by the dungeonskey (onepagerpg submission) where you are told to use clay to build your golem. Its great to read your work as how the design of of the mechanic can bring it all together
I was at a Stephen Jay Gould lecture where he made the following claim: people were asked what was more likely, that a librarian [a] wore her hair in a bun, [b] wore glasses, or [c] wore glasses and her hair in a bun; a bunch of people picked [c]. The story is ‘showing its age,’ and for all I know he made up the survey/experiment to illustrate his point — people are really bad at judging probabilities.
When considering how things feel to players, don’t we have to wonder whether they know that two mechanisms are equivalent? If they don’t know the mechanisms are equivalent and they feel different to them, perhaps that is no surprise. Feel might still track their erroneous beliefs about probability, no? A difference of feel through obscurity?
If you showed me a dice rolling procedure allegedly equivalent to pulling from a Jenga tower, I likely couldn’t tell you whether it really was. We like to think that the odds of future pulls from the tower collapsing it depend on our choices and skill in past pulls, but if you told me that in the absence of people making deliberately reckless pulls, there was a steady uptick of the chance of collapsing the tower, I wouldn’t dismiss it out of hand.
If a game only had 50:50 rolls would anyone really care whether they were done with a d14 or a d16 (the dice come in the box)? I am guessing not, but I am usually wrong about what other people think and feel.
Indeed. Humans are notoriously bad at estimating values and understanding randomness. As evidenced by most people believing "7" is the most "random" number when asked for a random number.
Although, to be fair to people — much as that pains me — what are they supposed to do with the request for a ‘random’ number? If you asked me for one, I would ask if I were allowed to roll a die first. ‘No, no. You have to pick it — but it must be random!’ ‘Sorry, mate, I can’t help you.’ Who has an internal RNG they can consult?
It is true that asking people to think of a number is not a substitute for a fair die, but why would we ever think that it was?
I guess the only thing to consider, which you, and many commenters alluded to, is other skills that come into play with other mechanisms like coin flipping or tower building. If that dexterity (or other skill) is part of the theme of the other game, I think it can work. But I can also see players getting frustrated if they don't have the dexterity, or in the case of Jenga, some external force knocks over the tower of blocks.
The only other thing to consider while choosing between these different options might be whether the same physical things can be used for other purposes in the game? If character movement, combat, and item storage all relied on dice or different uses of the dice, then that might make more sense for simplicity than introducing several different mechanisms, if that makes sense?
I think there is a clear difference between drawing cards and ticking a box to say roll a die later: with a deck of cards there is a finite and distinct set of outcomes. The player will never draw a King of Hearts twice.
Whether that difference is important in your game is a whole different question.
Narratively: using a deck contributes to the feeling of discovering unique objects.
Mechanically: if you had a mechanic that let players filter or modify the deck, it would contribute to a player's feeling that they are changing their odds (even though the the change in odds may not be very large).
This is absolutely true. While you could give dice a "memory" by using a list to check off or something, it's far easier when using a deck of cards. For the game, I think the deck of cards having memory is a bonus... but it might work with just dice.
As for how those two mechanisms FEEL, however... totally different!
Thank you for your comment!
One of the first games I made used coin flips because I wanted to keep the game as simple as possible, and what's easier than a d2? Turns out that coin flipping is a much harder dexterity game than dice-rolling, and what's worse, coins are harder to come by in this digital age than I'd expected.
As a poor coin flipper, can confirm. Rolling a d6 only requires dropping something on a table. Much easier. Hard (but not impossible) to miss the table.
And I’ve read that about coins. No one has a big jar of change anymore. Coins are for old people. 😅
Great comment. Thank you!
Somewhat related, Maurice Suckling has been experimenting with cube towers lately on Bluesky.
https://bsky.app/profile/writegameread.bsky.social/post/3luq55beswc2v
https://bsky.app/profile/writegameread.bsky.social/post/3lxhklwf2uc2u
A wonderful contraption that had completely flown under my radar, apparently mostly famous for its use in "Shogun" (even reviewed on Shut Up and Sit Down).
It's interesting how there is no analytical way to determine precise probabilities of its output. We can a only have rough estimates (see this interesting discussion on bgg:
https://boardgamegeek.com/thread/383097/the-mathematics-of-the-battle-tower
).
Still, it's a really fun artefact to toy with. And it surely has some untapped thematic potential.
Thank you for this comments! There's a lot for me to look into, especially checking out Shogun. I've heard of it, but never in the context of battle towers.
Space Gits comes to mind in how it uses stacking dice as a dexterity-based randomness element in the game: https://planetsmashergames.itch.io/space-gits
Yes, Space Gits looks very intriguing, indeed. So does most of Mike Hutchinson's work. I sadly haven't been able to try any of his games yet. But I've been a listener of "Rule of Carnage" for some time (the podcast he co-hosts). As the podcast is mostly about miniature game design, a lot of thought about the physicality of the components and its role on gameplay.
Oh! Didn't know he had a podcast. I should check that out too.
(So many podcasts.... so little podcast listening time.)
David Spiegelhalter's "The Art of Uncertainty" is a great introduction to probability and uncertainty very broadly.
Early on he talks about two kinds of uncertainty. Aleatory uncertainty is the future we cannot know - e.g. the roll of a dice. Epistemic uncertainty is about the present that we do not currently know - e.g. a card that we've drawn but not yet turned over.
Despite those very academic terms (they are the most cumbersome in the whole book, and I had to return to the book to check them for this comment) it's very accessible given the subject.
Thank you so much for this! I knew there had to be technical terms for what I was looking at. Seems like you nailed it! I’ll need to check out The Art of Uncertainty.
(I kind of want to rewrite this article now.)
Fascinating as always :)! As a self-proclaimed math nerd, and PhD student in (basically) statistics, i think your use of probabilistic equivalence/probability distribution is very appropriate :D at least, it fits my understanding of the term :) (i could, of course, still be wrong ^^) thank you for sharing <3 it's super interesting to think about, what would i personally prefer? i have played most of my games online, so thinking about what would feel best physically is definitely interesting. i think i like rolling dice, but for 50/50 mechanism specifically it kind-of feels less fun, somehow, just in my mind? although, i would say that depends on the game, and overall i voted "not sure", as i like the idea of the feel of the game influencing the "best" feel!
Well that makes me feel better about using the term! Glad to have a (friendly) math nerd as a reader. Thank you for the comment!
Nice! Cool to see another take on it. Have you read Goblin Punch's Take? (https://goblinpunch.blogspot.com/2023/03/critical-glog-base-resolution-mechanics.html)
and
Which system do *you* prefer?
I haven't! But I'll be sure to check it out. Thanks for sharing!
Speaking of coinflips and probability. I once was entertaining a couple friends and flipped a coin (to catch on the air and then flip again) and it fell heads 12 times straight, then I stopped. One friend was flabbergasted and the other one kept telling him it was a trick. And yes it was, I pulled a Maverick
It also happened on a game of Magic, I had won the first game and the player was one of the top ones, so he had a whole army ready to squish me on the second game, and with no cards on my hands it was my turn to draw and I pulled another Maverick, I didnt knew what I neede but the deck provided
I hope you played the lottery that day.
I think interaction helps bring a sense of ambience. Like using red dice to roll for damage, you feel the amount of splatter. I have this ongoing wip boardgame that I know can work with just cards, but there are also people (like me) that would download the papercraft popup scenarios and build them for the game.
Then theres also gameslike Scrapcat (Luca Negri) that added a bonus if you draw your character. And also “Every new thing” by the dungeonskey (onepagerpg submission) where you are told to use clay to build your golem. Its great to read your work as how the design of of the mechanic can bring it all together
Agree! I think small things like the color of dice really do matter.
Hmm …
I was at a Stephen Jay Gould lecture where he made the following claim: people were asked what was more likely, that a librarian [a] wore her hair in a bun, [b] wore glasses, or [c] wore glasses and her hair in a bun; a bunch of people picked [c]. The story is ‘showing its age,’ and for all I know he made up the survey/experiment to illustrate his point — people are really bad at judging probabilities.
When considering how things feel to players, don’t we have to wonder whether they know that two mechanisms are equivalent? If they don’t know the mechanisms are equivalent and they feel different to them, perhaps that is no surprise. Feel might still track their erroneous beliefs about probability, no? A difference of feel through obscurity?
If you showed me a dice rolling procedure allegedly equivalent to pulling from a Jenga tower, I likely couldn’t tell you whether it really was. We like to think that the odds of future pulls from the tower collapsing it depend on our choices and skill in past pulls, but if you told me that in the absence of people making deliberately reckless pulls, there was a steady uptick of the chance of collapsing the tower, I wouldn’t dismiss it out of hand.
If a game only had 50:50 rolls would anyone really care whether they were done with a d14 or a d16 (the dice come in the box)? I am guessing not, but I am usually wrong about what other people think and feel.
Indeed. Humans are notoriously bad at estimating values and understanding randomness. As evidenced by most people believing "7" is the most "random" number when asked for a random number.
Although, to be fair to people — much as that pains me — what are they supposed to do with the request for a ‘random’ number? If you asked me for one, I would ask if I were allowed to roll a die first. ‘No, no. You have to pick it — but it must be random!’ ‘Sorry, mate, I can’t help you.’ Who has an internal RNG they can consult?
It is true that asking people to think of a number is not a substitute for a fair die, but why would we ever think that it was?
Hah, your guess is as good as mine! :)
https://yougov.co.uk/society/articles/51866-seven-is-the-most-random-number
I guess the only thing to consider, which you, and many commenters alluded to, is other skills that come into play with other mechanisms like coin flipping or tower building. If that dexterity (or other skill) is part of the theme of the other game, I think it can work. But I can also see players getting frustrated if they don't have the dexterity, or in the case of Jenga, some external force knocks over the tower of blocks.
The only other thing to consider while choosing between these different options might be whether the same physical things can be used for other purposes in the game? If character movement, combat, and item storage all relied on dice or different uses of the dice, then that might make more sense for simplicity than introducing several different mechanisms, if that makes sense?