Popular Mechanics

[Navaren]

Since the wider BOLS audience tends to be caustic to discussion in the comments I thought I would throw up a thread to talk about the Popular Mechanics articles so I don't keep posting about them in an old 40k thread.

So this new one had me excited for the more in depth delve next week.

Two things I'm hoping to see:
1. Analysis of the pros and cons of "custom" dice
2. Analysis of which is the healthier mechanic "rerolls" or "bonuses"

[SALLstice]

I'm always down for additional discussion. There was A LOT that I cut from this article just for not having it be like 3000 words. Next week's is gonna be more on looking at games with random mechanics and how they do it well or not so well. So I probably won't really touch on that stuff at all there. So let's talk here.

So regarding custom dice. You could argue the weighting and balance of a custom dice is gonna throw off the true randomness of the die. But unless it's really egregiously unbalanced, I don't see it making a huge difference in your rolls. But what about the dice themselves? The symbols on the dice don't matter nearly as much as they might seem. Ultimately, it's just about how many of the sides of the dice will give you what you want and how many won't. So like, in Star Wars: Destiny each die has different symbols on each side but it could just as well have 1,2,3,4,5 and a reference sheet saying what each result means for that card.

Dice don't even [URL="http://starwars.wikia.com/wiki/Chance_cube"]need numbers[/URL]. I could have a die that has 3 red sides, 2 blue sides and 1 yellow side and still use that playing 40k. If I'm attacking and hitting on a 4+ with rerolling 1s; Red means I hit, Blue means I miss and Yellow means I get to reroll. Granted, having a more generalized die with numbers allows it to be used in more situations than with a Tau Fire Warrior with a Markerlight on the target. The reverse is true too. If you been watching our Harry Potter game on Board Game Bonanza, you'll know we're missing one of the custom dice the game comes with, the Slytherin Die. But we use a normal d6 and have a little post-it note which says "1: Draw, 2: Health, 3: Money, 4-6: Attack". It doesn't matter what the actual die is or says so long as you can fairly decide which die side means which game effect.

Rerolls vs Bonus Rolls: This is actually something I was specifically considering adding to the article on the initial outline, but ended up cutting. It occurred to me that the benefits of getting a reroll versus getting a bonus roll is pretty game dependant.

So if I'm rolling a die and aiming for a 3+, I expect to succeed 66% of the time so in 100 dice, 66 successes and 34 failures.
If I'm getting a reroll, I reroll those 34 dice and still have my 66% chance of success. So of those 34 dice, 22 of those should result in a success (66% of 34 = 22) and 12 will fail.
So adding my initial 66 successes with my 22 reroll successes I have 88 successes and 12 failures (88%).

If I'm getting bonus rolls, rather than rerolling the failures, I'll roll additional dice for each failed roll and add that to the total die pool. So I still have my initial 66% chance of success for aiming for a 3+.
I roll 100 dice and get 66 successes and 34 failures.
I push those 100 dice aside and I roll an additional 34 dice, which still have a 66% chance of success. Of those 34 dice, 22 will succeed and 12 will fail. Just as last time.
I add those additional bonus rolls to my initial roll of 100 dice. I have not rerolled my failures and they are still in my dice pool. Meaning I rolled 134 dice and have 88 successes as before (88/134 = 65%) , but I now have 46 failures (34 initial failures + 12 failed bonus rolls).

The rerolls have an 88% chance of total success.
The bonus rolls have a 65% chance of total success.

BUT keep in mind the number of successes didn't change, the number of failures did. Whether or not this would matter is down to the game itself. Does the game reward successes or punish failures? Every game I can think of rewards success. You're trying to achieve a certain result on a die and the failures are discarded with no game effect. In a game which rewards successes (as in 40k) rerolls or bonus rolls are the same. However in a game which punished failure, that would be different. Suppose in 40k every failed roll imposed a mortal wound on the shooter. If that were the case, players would be much less eager to jump at getting bonus attacks. It would mean rerolls are better because it reduces the odds of failure, which we just showed.

So ultimately, the only difference between rerolls and bonus rolls is if the game punished failed rolls in some way. When I first thought on this, I thought "they're totally functionally the same. There's not going to be any difference at all." But I'm glad I ran the numbers because I didn't really think about it all the way through and it's interesting to see how the chances of success actually go down if you do bonus rolls, but only because on average you increase your number of failures without increasing your number of successes! Interesting stuff! Funnily enough, because of the increased number of failures you technically are more successful if you don't take the bonus rolls at all. Granted, with 100 dice it's only 66.66% initially versus 65.67%, but still!

As an aside, doing all this thinking has given me lots of fun ideas for the game design part of this randomness chapter. So thanks for that!

[SALLstice]

So I actually did a quick spreadsheet thing and found out that bonus rolls do converge on having a 66% chance of success. The first row is stats on a reroll and the other rows are bonus rolls (note the additional number of failures in column F). So at a certain point, bonus rolls only add additional failures with no benefit at all!

[Navaren]

So are you familiar with Level 7: Escape?

Its actually why I was specifically asking about custom dice.

FFG board Game so custom dice are to be expected, but the dice themselves feel off to me in practice.

Without going into super detail there are basically 3 skills and 3 wild faces on each die but each non wild face is a double so you have the following:
1x Double 1
1x Double 2
1x Double 3
3× 1 or 2 or 3

Obviously its balanced, but it feels punishing when what is nominally the joker takes up half of the die and is worth half as much as a "full" roll. It makes me curious as to why we didn't see this instead:

1x 1
1x 2
1x3
1x 11
1x 22
1x 33

But I have no idea how to compare them statistically. I'm not a math guy.

Also that's a great analysis of bonus rolls and isn't something I ever thought of since it seems obvious to me (probably a gambler's fallacy) that rolling an additional die is always better than replacing a die for values of 2+ dice.

However, I actually meant like a FLAT bonus to a roll. I'm curious as to which is the more powerful mechanic in general and specifically why 40k chose to have refills trigger off of the raw die roll and then apply modifiers.

[SALLstice]

all that stuff you said

Oh dang, that makes more sense lol

yeah lemme look into this probably tomorrow. I should go to sleep. I have this whole thing I'm supposed to be doing tomorrow afternoon.

[Navaren]

I have this whole thing I'm supposed to be doing tomorrow afternoon.

Calling out sick and Interacting with *cough*gambling bees*cough* the community in chat?

[SALLstice]

I don't know that game at all so I'm gonna make a few assumptions but I think we can still calculate the amount of 1s, 2s and 3s.

So, naturally, each side of a d6 has a 1 in 6 chance of being rolled or a 16.6% chance. So you have a 16.6% for 11, 22, or 33, but a 50% chance of 1, 2 or 3. As I mentioned in the article, when you're looking for the odds for this OR that, you add the chances. So either a 16.6% chance of getting the double or a 50% chance of getting the wild single. So on this dice you should have a 66.6% chance of getting the number you want in some quantity. Like I said, I don't know this game so I'm assuming you're not looking for a 2+ or whatever. The odds here are with the thought that you are looking for 2s and only 2s.

But like another way to do the same thing would be looking for a 4+ and on a 6 you get a bonus success. Because you still have that flat 66.6% chance of success and from there it's only a question of how much success did you get; a single or a double? You could remove the need for having the 1s and 2s and 3s at all and just use standard d6s.

The way you've laid the die out would be worse for the player. Suppose I need 3s. In your layout there are only two sides of the die that will get me 3s, which is a 33% total chance of success with a 16.6% chance for double. Versus the original way, I had 66.6% total chance a 16.6% double success chance.

The best way to consider things like this is not look at the numbers or symbols on the die or whatever. Just consider, "How many of the six sides of this dice will get me what I need?"

FLAT bonus to a roll.

Okay, that should be pretty easy to math out here.

So lets say you're looking for a 5+. So with no modifiers or rerolls you're succeeding 33% of the time.
If you're granted a +1 modifier, then for all intents and purposes you're succeeding on a 4+ which you should get 50% of the time.
Otherwise, as we've looked at before, if you're looking for a 5+ with a reroll you have a 55.56% total chance of succeess.



Within each result, I highlighted which has a higher chance of success between rerolls and a +1 bonus. What's interesting is that sometimes rerolls are better and sometimes a +1 bonus is better. Once you get a +2 bonus, that is always significantly better.

Lemme know if I answered all your questions! I obviously enjoy discussing math stuff lol

[Icendar]

That was a great article on the front page, mate, and the extra stuff you've put here is very welcome also.

I obviously enjoy discussing math stuff lol

Don't ever talk to Matt about tau, though. In fact, it's probably safer to just avoid the topic of circles or spheres or anything round entirely.


I kid because I love.

[Navaren]

So melt down... I want to play it. I also want a heroic sacrifice player option to help further control them damn kids... I mean RUGRATs. Something like Automatically Succeed but skip your next two turns due to rad poisoning.

Also if you Crystal-punk the game out a bit you can ignore the "That's not how meltdowns work" bit. You are now a Steampunk Dam Con work party maintaining the power flow to the Aetheric Stabilzation Field of your Baryonic Dirgible.

[SALLstice]

heroic sacrifice player option

lol yeah, when I was going through the quick and dirty design stuff I had a bunch of ideas for additional game mechanics or abilities or options or whatever. But I ended up pulling them all out because the point was to focus on the random mechanics.

Crystal-punk the game

The theme actually came from trying to figure out a way that would allow the players to control the RUGRAT and that was the first idea I had. I'm sure there are other themes that would work too, but I feel like that's a mostly unused setting. I like when the players take the role of everyday people. Arkham Horror and such do a decent job of that, but they're all kinda exceptional in some way. I think it's fun when you're playing as a total schmoe. But yeah, anyway, if I had put more effort into the theme I think having a crystal punk theme could be fun and way easier to make up whatever. But I think it would also be cool to research actual nuclear reactors and such and make it at least semi-realistic. But yeah, I do like designing games and I have a lot of half-finished projects. It's not impossible I'll make a prototype version and maybe print-n-play it one day for distribution.