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12:59 AM
@murgatroid99 super easy. The basic game is played on a classic 9x9 Sudoku. And the gameboard is a heat map, so you can estimate points and regional polarity.
Last placement is red. There's an eye button so you can see the regional deltas, but some prefer that function disabled.
You don't even really need the big scoreboard numbers, since you can see which regions are dominated by which player (the regional cell borders are exactly neutral on the spectrum, and give a visual cue based on being darker or lighter than the region color.)
Does the score display there account for the square control changes that would happen if the scores were evaluated?
no. ;) that's something the player has to track.
but it's interesting you bring that up.
Right now, the AI's don't even track that, which is why they're semi-weak
(i've been working on that algorithm for a while)
but it's easy to derive that information after the first couple of games, once you start to become aware of how it may be used.
I'm not sure I would be capable of tracking something like that in my head
it's easier than you think. but that's a really useful poiint because I never considered and assist function for that.
I mean, it has that recursive cascade effect, where the order in which areas are resolved affects which squares change controller, which affects the order in which the remaining areas are resolved
1:09 AM
it's trivial procedurally to resolve the gameboard at any given state, and tell the player the predicted outcome
@murgatroid99 that's one of the most useful pieces of feedback, btw!
yeah, my programmer is opting for the auto-resolve to determine actual standing and benefit of placements as opposed to the Epistability and Metastability algorithms
(those are the ones I'm working on;)
Stability: Can the polarity be flipped with a single placement
Epistability: Will the region flip in prior resolution
Metastability: Can the position in the resolution order be shifted? Meaningfully?
That resolution procedure is a significant part of my worry about a human being able to evaluate any given game state. If the function game state->winner is too much of a black box, it seems like it would be difficult to learn move evaluation
and you have weak and strong conditions for those 3 basic stability states.
@murgatroid99 middle-schoolers pick it up faster than adults
it's definitely not for everybody, but it's only a 9 step chain.
the calculations are trivial, involving integers 1 through 8
also, the resolution chain is the FUN!
I don't think that you can reasonably claim that a 9 step recursive algorithm involving a total of 81 integers can be calculated in your head
people really enjoy when outcomes are unexpected
@murgatroid99 re recursive algorithm, the only thing you have to track is if a neighboring region resolves before, and has an opposing integer that will flip, will it flip this region?
all you care about is the 9 regional deltas
How often does the resolution sequence result in the actual winner being different from the projected winner based on the naive algorithm your app uses?
In general, it seems a little weird to me to display a score comparison like that if the player who ends the game with the top score (based on that calculation) is not necessarily the winner. It feels misleading
1:18 AM
It's pretty varied actually. Depends on the relative skill of the players in some cases, but not always. The more I play these AI, which are respectably weak, the more the outcome shifts as I take bigger risks than I would with a human, knowing their game breaks down mid-to-late game

PS- our current AI makes moves purely based on the Neutrality of a region (how small is the delta) with some tie-breaking from the 6th and 7th levels, and isn't even yet aware of Stability.
When I play humans, it's sometimes static, but again, varied.
It's partly a function of either:
1. How bad one player is
2. How much risk the players are willing to undertake
(i'm conservative, so against humans I go for 5/4, maybe 6/3, but never as Indigo.)
(my programmer and his friends "swing for the fences" and have these wild turns of events;)
i couldn't believe the regional scores from their tournament, because it's so counter to my style of play
there's a skill curve, but players advance rapidly at first, make huge breakthroughs each game.
later it gets more subtle. i've been playing for 4 years, and i still feel i've barely scratched the surface in terms of nuance
but the game definitely feels more random because of the cascade at first
and most people consider it to be the fun
Well, this was an interesting conversation, but I have to go. I'll probably try the game out at some point.
@murgatroid99 that was very, very helpful
thanks for taking the time!
1:39 AM
@AlexMitan re: http://anydice.com/

dude, that is really effing cool. re: choice between risky, high-reward mining hits or steady-flow, but costing time(turns), that is bas@ss imo
@AlexMitan I love resource management games. acquisition should definitely be more swingy, and definitely a bit tactical. I'd have to throw those numbers into a spreadsheet (which i will probably do!) it sounds like a bad@ss, fundamental game. Are dice and tokens the only equipment?
like just that mechanic on it's own is an excellent game imo, which is what I think you're going for? in the context of a larger game?
2 hours later…
3:43 AM
@AlexMitan I ran the numbers on what it looks like with 1&2 dice. (I was afraid to tackle 3 dice in excel;)
Because the penalty is constant, but the reward is exponential, it's already showing signs of heavy incentive to max attempts in terms of the payoff matrix, but with the probability distribution for a given roll, it feels like it pulls toward net loss, although I haven't attempted the numbers on that yet.
Just for fun I tried this formula:

payout=attempt*difficulty for each successful_attempt - attempt*difficulty for each failed_attempt

The ultimate payouts are probably bigger numbers than you were intending to work with, but the reward/penalty ratio is only slightly weighted toward more risk in the payoff matrix. I posted the spreadsheet at http://www.fundamentalcombinatronics.com/DiceMining_DZs_Tweak.xlsx is you want to take a peek.
I'd be totally happy to discuss this with you ad nauseam lol--it's a really cool idea. Feel free to invite me to a separate chat if you want to avoid spamming the main chat!
4:35 AM
I just had a Commander game that lasted two and a half hours, and ended with me taking the last turn before everyone packed up, drawing my card, and saying "Deadeye Navigator, I win"
I was playing my super janky Mairsil deck, and I had about 25 cards caged and was just waiting for a way to combo forever
Honestly, I'm not entirely sure I was guaranteed to be able to do more than flicker forever, but I think I had a pretty good shot
I was able to draw 3 cards for 3 mana with Arcanis + Skithiryx + Deadeye, and there were several cards that would bring me above parity with mana generation
4 hours later…
8:39 AM
@DukeZhou damn! I'd definitely love to chat, today and tomorrow are quite full but on the other hand, I have a bunch of visualisations done for this!
by the look of it, this looks to be the gain heatmap
9:17 AM
Haven't modelled std, but now I'm experimenting with a more elegant mechanic
Since this one does tend to blow up sometimes
9:30 AM
i got some crazy distributions some of the time
Plus, there's a bit more than just probabilities to model... I mean expending resources to boost attack is still a way to incapacitate yourself, and the enemy overdefending to your attack is also a gain, since they lose resources
The bottom-right square shows this: I attack with 1 die, you defend with 6... Sure, I probably won't win, but I made you waste 6 dice
1 hour later…
10:47 AM
@murgatroid99 there's a friend of mine here in London who played EDH for several years in Seattle. Apparently in Seattle there's a popular way to win: bring the other players into a sort of lockdown position in which their defeat is assured, but it will take several boring turns to get there. So people play this position, suggest they now win, and others scoop and agree.
This friend dislikes 1v1 immensely, and when a multiplayer comes down to 1v1 and isn't pretty much within a turn or two of someone winning, they prefer to forfeit, congratulate the other player on their victory, and shuffle up for a new multiplayer game. The 1v1 showdown is just a part they like to skip to get back to multiplayer. I can respect that.
However, out of sheer determination and spite, they will never scoop to a lockdown play. They will stay in the game and require the other player to go through the motions to actually seal off that victory. He'll look for an opportunity to break through it, of course, but he'll keep playing even if he can't.
From what I gather of his motivations, he was frustrated by games in Seattle frequently ending prematurely. And since "I played a group of cards, now I win right?" strategies frequently ended games earlier than other strategies, just because people would scoop rather than go through a few more turns (during which someone else might actually win!), the whole "play a lockdown strategy and suggest everyone scoops" became an even more popular way of playing because it gave someone a chance of a win.
So his motivation is that he doesn't want that to catch on here, so he will force people to experience how boring and lackluster that kind of victory is, so that it doesn't catch on as a fun & exciting way to win. It turns into a way to spend ten turns going "alright I do that again."
1 hour later…
12:13 PM
Hey folks, I've got an MTG combat damage question to check.
The other night, we were in this situation:
- Them, attacking: one 6/5 attacker with trample and first strike.
- Me, defending: a 1/1, 2/2, and 5/5 blocker. I assign all three as blockers in that order: 1/1 first, 2/2 second, 5/5 third. (There's benefits for me if the 1/1 and 2/2 die.)

As I understood it, this would have to happen (let's call this Interpretation A):
- Their attacker must assign at least 1 damage to the 1/1 before it can assign damage to any other blocker.
- Then it must assign at least 2 damage to the 2/2 before it can assign damage to the 5/5.
12:51 PM
I don't get it...
I made this program to simulate rerolling a die if it's below a certain threshold
why does it say there's a lower value on "reroll ones" than "reroll ones and twos"?
1:07 PM
@AlexMitan i don't know entirely how your script is working but i do not think it is outputting correct results. if you're rerolling 1's, you should have 0% in the 1's column. a d6 reroll 1's should have a 20% chance of each of 2, 3, 4, 5, and 6, with 0% chance of 1.
so something in your script is fundamentally incorrect
1:34 PM
rerolling just once
the question is, "if I have a die, and reroll it if it's below a threshold, what's my average value gain?"
that looks fine then
logically, it should be higher for a 1... right?
or maybe by only rerolling ones, you're passing up the opportunity to gain value from rerolling twos
damn, that must be it
i don't really understand what you're looking at that seems incorrect to you
1:38 PM
@AlexMitan yes, rerolling ones and twos results in a higher expected value
because you're more likely to increase the value of the two than to decrease it
Thaaaat makes sense, okay
"reroll at 1 (3.92 / 1.48)" has an average result of 3.92 (that 1.48 is the standard deviation); reroll at 2 has an average result 4.17; at 4 or higher rerolling reduces your average score back toward normal.
I want to simplify my game and I wanted to know how much value a reroll basically generates, if it's free
instead of fiddling with counters and rolls to increase them, I thought that maybe you can just reroll dice on the board
rerolling a 1 always generates value; you have a 5/6 chance of something better and a 1/6 chance of something equal.
rerolling a 2 almost always generates value: you have a 4/6 chance of something better, a 1/6 chance of something equal, and a 1/6 chance of something worse.
rerolling a 3 is sometimes valuable: you have a 50% chance of rolling better, 50% of rolling same or worse. 33% of the time you will get something worse.
rerolling a 4 has a 50% chance of getting worse so is only worth doing if a 4 just doesn't count, i.e. you need 5's and 6's.
given free choice i would reroll 1's and 2's, but not 3's, if i were trying to maximize my overall results. if i needed to maximize the number of dice meeting a certain value or higher, i would just reroll everything beneath that value.
now I'm imagining a dice game like Fluxx, where you can have a bunch of localised rules for reroll < n, reroll n dice of your choice, flip n dice of your choice, etc.
2:20 PM
..it crossed my mind
it crossed my mind that dice could represent charged, but unstable cores, and flipping it would be basically (7 - value)... do you keep 3s and 4s with nothing to lose, or do you carry around 6s at the risk that they might enter meltdown for whatever reason?
^ Relevant questions for game development. (source)
I don't understand that one last program
Nd{0,2} >= N isn't always 50%
2:57 PM
You don't determine the blocking order, the opponent does:
509.2. Second, for each attacking creature that’s become blocked, the active player announces that creature’s damage assignment order, which consists of the creatures blocking it in an order of that player’s choice. (During the combat damage step, an attacking creature can’t assign combat damage to a creature that’s blocking it unless each creature ahead of that blocking creature in its order is assigned lethal damage.) This turn-based action doesn’t use the stack. #
Guys, I need help
why is this so jagged? shouldn't it be all 50%?
@doppelgreener I would be interested in have this as a Q on the main site (if there isn't a close duplicate). I have always found combat damage assignment kind of confusing, and a long form answer of what JonTheMon wrote would probably be useful to others
3:13 PM
Q: Does the attack or defender decide the order of damage assignment to blockers?

confusedaboutmtgI read from the comprehensive rules guide that there is a damage assignment order, but I've always played the game as if there was a blocking order. Here is the relevant text: 509.2. Second, for each attacking creature that's become blocked, the active player announces that creature's damage ...

3:34 PM
guys </3
3:47 PM
It looks uneven because your victory conditions are uneven. Your die has either 0 or 2.
One die roll, half fails, half succeeds.
Two die rolls, only one of your two die have to roll 2.
Three dice, you have to roll a 4 to win, which is 2 of your 3 die. Which means you have to beat the average to succeed.
Hm, okay
I'm basically doing something along the lines of... you have a pool of dice... you can use them as-is for guaranteed hits, or you can use them as coin-flips for 2 hits each if they roll 4,5,6
4:27 PM
That would be http://anydice.com/program/dd9a
Compare that to Nd{1}
Oo, thank you!
Okay... and are there clear implications of that in terms of game mechanics?
I mean
stuff like "it's always better to roll even numbers"
...no but it'd seem that there's always a choice
Let's say you need a 7 for something. if you have 5 d2's, you'd need to have 4/5 success. However, if you used 1x d1 and 4x d2's, you'd only need 3/4 to succeed.
4:43 PM
Ooo... okay, so splitting the pile didn't really come to me much, I've thought in terms of all flip or all static
I feel like that'd add a bit too much overhead to my game
I mean in terms of "I have 4" or "I have 3". Is there ever really a case where I should always flip or always roll?
depends on the goal
...ok, I was hoping for that.
ok, and a pile of 6 "build/green", can, in my context, generate at most 3 new resources on its own
this is the most elegant mechanic I've had so far
Well, I was thinking more like "well, if I get my rolls to 2, I can have this nice perk" In that case, if you kinda want it but are fine w/o, roll 1x d2. If you really want it and don't want to chance it, use 2x d1
mhm... I'm tinkering now
I'm taking an idea of mine from above with resource nodes providing opposition, and if you "conquer" them, their "defense" gets added to the result
so if I roll 4 hits against a 3-node, I get 7 "magnitude" of success
and this is good because it mimics attacking someone, too
it goes with one of my design goals: battles of large pools have chances similar to proportionally smaller pools, but higher stakes
5:11 PM
I'm so proud
5:32 PM
@JonTheMon Thanks very much, that makes sense out of it. Somehow I thought I did assign blocking order...
@doppelgreener have you been touching the icky icky banding?
You choose the order in which your blockers deal combat damage, not the order in which they take damage
@JonTheMon i haven't, it's just been literal years since i last had to deal with a situation with multiple blockers
Each player chooses how their own creatures deal damage
5:44 PM
last few times it was just, like, an army of identical tokens, so it didn't matter in practice which ones took which damage
6:01 PM
@murgatroid99 I do want to go on record as not being against RNG--I think dice are a legit way to simulate a chaotic systems (weather, etc.) in a physical medium such as traditional boardgames. Possibly my bias re: computer board games is that, once you're in a computing context, it's fairly easy to to generate complexity and create actual chaotic systems.

When I was researching randomness in nature, it was suggested to me that true randomness, as in outcomes not based on causality, are restricted to quantum phenomenon (in some models) and only interact with the macro world in areas like
6:14 PM
It depends on what you mean by randomness
1 hour later…
7:34 PM
@murgatroid99 yeah. I'm finding I need two lexicons--one for game theory/CGT and one for video games. I'm not entirely happy with Garfield's definition of "luck", but I get why he's going that direction. For me, true randomness is a purely stochastic process, with outcomes unrelated to causality. In that definition, while hidden information creates uncertainty, the uncertainty is not a function of randomness.
My attempt (work in progress) to define "deterministic game": deterministicgames.info
but Garfield's point is that classical chaotic systems (factors beyond calculation, or, intractability) create uncertainty in outcomes, so that even deterministic games, if non-trivial to the participants, involve "luck"
8:19 PM
From the point of view of someone playing a game, a roll of a D6 is functionally equivalent to getting a number between 1 and 6 generated by a quantum noise reader
And I don't really think there's a meaningful theoretical difference between randomness in board/card games and randomness in computer games
2 hours later…
10:09 PM
@murgatroid99 my point is, for a system like Dice Mining, in a computational context, the chaotic system simulated by RNG can be generated fairly easily. (Balancing is a different problem, but in my experience, symmetry is a powerful tool in that regard.)
in other words, it might be more expedient to simulate chaotic systems in computing context for games, but part of my drive as a designer is to move away from that, in favor of actual chaotic systems.
I'm not sure what you mean by "the chaotic system simulated by RNG". It looks to me like that's an independently existing probability distribution that doesn't directly correspond to any physical process
Well, physical dice are a chaotic system (factors beyond calculation influencing the roll) but not random in the true sense, as in quantum randomness
OK, this goes back to what I said before: in the context of the game, there is no meaningful difference between the randomness generated by rolling a die and by a quantum system
I strongly disagree
10:17 PM
RNG is a simulation of the chaotic system that's meant to be expressed. Take weather, a chaotic system. There is a quantitative difference between generating weather conditions in a game using RNG, and creating sufficient complexity to have a deterministic weather system, where the expression is chaotic because the system that generates the weather is computationally intractable
I thought we were talking about dice
we are, but in two different contexts. Physical dice for boardgames, and computational RNG for computer games. Physical dice are an RNG also.
Also, having a real weather system would require a detailed simulation of the atmosphere, which isn't really worth doing for most games that would want to have weather
@murgatroid99 but the in-game weather system doesn't have to be nearly as complex as real weather
it's quite easy to harness conminatorics to produce intractability
that's why I'm so obsessed with Latin squares and Sudoku
OK, I've lost track of what you're getting at
10:20 PM
they are complexity engines par excellence
Are you familiar with pseudo-random number generators? Because I can't help but think that they are exactly the chaotic systems you are looking for
Just that dice aren't strictly necessary, although significantly more necessary for a vast array of physical boardgames, to keep the physical games simple. but in a computing context, that complexity can be "under the covers". That's basically what I'm getting at.
@murgatroid99 actually, I've been reading that there are some computer processes that aren't pseudo, because computers use electricity, and quantum randomness can be channeled using certain techniques.
Well, yes, you can generate truly random numbers with some computer hardware modules, but usually it's not worth the trouble
but I'm partly saying that computer RNG is a process outside the logical structure of the game mechanics--it's integrated into the mechanics, but the output does not arise out of deterministic game state conditions.
what I'm saying is that with certain combinatorial structures, one can get around the need for RNG
OK, that's true. And what I'm saying is that creating a system like that simply isn't worth the trouble in most cases
10:26 PM
@murgatroid99 agreed
How would you even implement a weather system that is simple enough to be feasible to implement, but deterministic and also unpredictable?
What factors would you use to calculate its behavior?
@murgatroid99 (this may make you laugh, but the only reason I cracked the [M] mechanics was naivete. when I started recognizing the balancing issues for deterministic game, much less developing novel, fundamental mechanics, I just though the difficulty was based on my own lack of skill as a designer.)
and to answer you question, I'm chipping away at such a system.
gotta log, but I'll check back later!

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