Showing posts with label Probabilities. Show all posts
Showing posts with label Probabilities. Show all posts

Tuesday, October 13, 2015

The value of bell curves

A while back I started talking to some friends about starting up a regular game again. To fill some time, after realizing that it would need some discussion to find a game everyone agreed on, we picked a game we had played before as a starter. 3:16 Carnage Amongst the Stars was that game.

For those who have not played this game, I can summarize a key point of the rules system. All rolls are one 1d10, roll under but high is good, against a Trait. I guess you see what this means. Right. No bell curve.

We started to play and since it is very much driven by black humour and creative narration by the players, it worked quite fine with some cynicism and beer. But, after a few sessions a pattern started to emerge. One of my players rolled really shitty. Like some of us say, he storked it, repeatedly. The thing is, he rolled maybe 10 dice rolls a night and missed all but one. Even after changing dice, we are not superstitious, he kept rolling like that in session after session. It just was not fun any more. In the end the game was not just a chore, it was actively un-fun to roll dice for him.

Now, I guess you have all heard of games where the narrative is as much in the hands of the players as the GM? You would imagine that maybe that would alleviate the problem, maybe? The problem here is that 3:16 is just such a game. I as the GM could only limit the stiffness of the opposition, and the players still had to sit there and narrate the hell out of repeated failures. Kind of sucks after a while.

We decided to fade to black after a few missions, and now I had pitched a new game which all seemed to like. It was all down to the weird imagination of Ken Hite, since who can resist a game with both nazis and the Midgard Serpent? Savage Worlds it was.

I guess you see one thing that differs from 3:16? In Savage Worlds you roll multiple dice, and if you fail you can spend a token and roll again. Once again you roll multiple dice. Multiple dice, i.e. more chances to succeed, since you get to pick which to use.

That choice of game system was intentional.

As you probably know, there are more than one way to skin a cat. The cat I wanted to skin was player enjoyment. While I do not subscribe to the school of design that say encounters should be "balanced" and that the players are entitled to this or that, I do believe game system matters for how much fun you can have.Clearly linear probabilities do have some potential to screw up your game night.

Savage Worlds and Fate are two game systems that have decided to let you have all that wild and intense fun you get by rolling dice, but have also included some way to take the edge of Those Nights(tm). I think that is good game design for a game for modern adults, for whom game night is time you clawed back from all the necessities of family, work and other obligations. Narrative control is one thing, but getting to describe your failure yourself over and over again does not make it more fun. Maybe the first time. I think some game mechanic that works as a "safety net" should be in your mind when you design a game for my kind of gamer.

Are there other ways? Let's go back to those dice, and our subject line.

I know I am not the first one to notice that some games are really swingy, and D&D with its d20 based to hit roll is one of those. As those of us than own a AD&D 1st ed DMG know, there are more ways to roll dice, and one of them produce a bell curve. Such a probability distribution skews towards the middle, making it harder to get those extremes. On the other hand, it also makes it likelier to get above that first hump of lower target numbers. Is this possibly the way to increase player enjoyment? I will leave off dice pool systems, since I find the probabilities of those headache inducing, instead focusing on rolling multiple dice and adding them before comparing to a target number.

Strangely enough, there are few games I can think of where you roll multiple dice of a similar kind and add them, as a basic mechanic. Sure, it's used for damage, but more seldom for other things. Off the top of my head I can only remember five game systems that use this, and two of them are closely related.
  • The Fantasy Trip (TFT) - roll 3d6
  • GURPS - roll 3d6
  • Traveller - roll 2d6
  • Tunnels & Trolls (T&T) - roll 2d6 for Saving Rolls, in combat roll weapon dice and add stat bonus.
  • HERO - roll 3d6
Maybe these games are actually kinder to gamers who just want to succeed once in a while?

Next topic: Are these thus newbie friendly games?

Friday, May 28, 2010

What's the probability?

That is one of my most common questions. I very often wonder just that. What's the probability of something happening? I'd like to tell before rolling dice about probabilities. I one took down the math books for some basic high school mathematics, and even though I had once studied that I couldn't make head or tail out of it. 

I have posted about my Wednesday game before, and the great fun of playing 3:16. One reason it have been fun is that one of my players, who usually don't complain about dice or luck, in the session last week rolled amazingly bad!

Imagine rolling 20-something d20 rolls a night, and having 14 of those turn up a 0!

That guy missed a lot, but when he managed to roll under 8 for his Fighting Ability check, his kill number were impressive. His ability to roll high was consistent. In a game system where you should roll low, but higher than the opposition, his rolls where hilarious. Of course I had him narrate all his failures.

But, what's the probability?

Apparently poker buffs don't talk about luck, they talk about "variance". The same guy who rolled all those zeroes told me, that some have kept statistics on all their hands to calculate "variance". Even though it should even out, they have decided that there seem to be such a thing as luck. Everything should even out, eventually, right? The question is how close to infinity you have to get.

But, rolling 14 0 out of 20 something rolls? What's the probability of that happening? Amazing. I love dice.

Thursday, November 12, 2009

Some ideas about stat checks, from Frank Menzter and me

I peeked in at Dragonsfoot today. Usually it's not of my hangouts, but I felt like seeing what was going on that end of the world. As some of you might now, some hobby Big Names have their own Q&A threads there. Not all of them are very lively, and some are just open house chatting and rambling. Anyway, I checked what Frank Mentzer had to say to the world, being a bit curios about that business plan of his. Nothing new seems to have happened on that, but he was answering questions and pontificating upon other matters. One thing he said was how they handles ability check in his game.

Since the games of yesteryear usually didn't have skill systems, you used some other mechanic when you wanted to do something not specifically covered by the rules. Rolling a d6 (grumbling grognard method), rolling a d20, rolling against a save of some kind or rolling against some stat. Those are the classics.

I grew up in BRP land, where there were skills aplenty. But, if for some reason no skill covered it, it was time to roll against a stat. There's a Resistance Table in the rules, used for e.g. arm wrestling (I promise, it's the first thing I've ever seen anyone use as an example, or used in actual play!) which can be used when pitting two basic stats against each other, so the idea to use roll against the stats are there. Frankly, the stats usually don't do that much in BRP (unless you count the Idea Roll and relatives, recently expanded in the big BRP tome), so sometimes you feel like using them.

There are some fairly interesting ways to roll a stat check. My favourite one is to roll a different amount of d6 depending on difficulty. Try to roll below 13 with 7d6!

Now, Frank didn't do stat checks. He had used "roll a d20, get above 12" as a standard, but also liked the idea of using saves. Personally I find the saves for AD&D to be so bizarre and non-intutive that I get a migraine just trying to remember what those crazy categories are! I think the unified saves in 3rd ed was a stroke of genius. Much have been written about saves and how they work or not. I think they are a mess in anything pre 3rd ed D&D. There, I said it. Anyway. Frank Mentzer didn't use stat checks.

Why did Mentzer think stat checks was a bad idea? Well, he actually had his reasons. However you twist and turn saves on their heads, they are a factor of a class based system. In D&D everyone have saves, and they are set before hand, equal for all. Rolling against a save is same for every 4th level Cleric, but the stats are individual and based on luck. Well, rolling dice is random, of course, but the way I understood Frank's reasoning, he felt the player should bring some skill to the table. Rolling against stats felt like to much randomness, since you would be better at saving if you was lucky when rolling your stats.

I'm not sure I buy that argument, but it's an interesting way of seeing it. Of course it's interesting to compare all of this to T&T, where everything you do will be a stat check. I do think Frank Mentzer have a point about randomness, but I still think it makes sense in T&T. Since there's nothing not based on stats, there will be a common base for everyone. Rolling enough dice will actually make the outcome drift toward the average. I find that kind of weird myself, but I know that the law of averages will make it even out. Also, I have seen by my own game table that smart players go further in T&T.

Choosing when to roll, and make it count when you're in a postion of strength is very important. That's one lesson I learnt from Advanced Squad Leader. If you take every opportunity to roll, bad things happen. Attack from strength, it's a proven maxim. How you roll them bones, that's another kettle of fish. Food for thought.
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