Probabilities Gone Wild! (or, How I Finally Fixed Playthings)

After giving the issues with Playthings some breathing room for a couple weeks I decided to get back to it by giving the system, which I’m now calling the Hit ’n’ Miss System™, the same treatment that I gave to the Knockout System™ from my last post so that I could take a peek at the probabilities.

In my playtests I have been using pools of six-sided dice. Each die was successful on a roll of 4, 5, or 6 (Hit) or a failure on 1, 2, or 3 (Miss). To replicate this on a spreadsheet I created eight columns of 1000 random numbers between one and six. I then checked each die for a hit and totaled the number of hits for different numbers of dice per line.

Spreadsheet: the most boring thing whose name sounds vaguely dirty

Spreadsheet: the most boring thing whose name sounds vaguely dirty

Long story short (too late) I plotted out the percent of hits for different values of dice and came up with the following.

This explained a lot. During playtests the players frequently had a hard time rolling successes, even on a difficulty of 1. A difficulty of one should be super easy. With eight dice it should be all but guaranteed, but here we see that the best chance a player has is 88%. Not good enough, in my estimation. I want there to be a chance of failure, but I want those chances skewed in favor of the players.

So I had the distribution, now I needed to fiddle with the numbers. I set up the spreadsheet with two variables: one to represent the value of the dice being rolled and the other to represent the success threshold. By changing the die value to 8 I got a much better distribution:

But 'octohedron' is so much harder for kids to say than 'cube'

But ‘octohedron’ is so much harder for kids to say than ‘cube’

This is more like what I wanted to see. However, the whole point of using a d6 was that almost everyone can scare up a few of them by pilaging other games. So I returned to a d6 and tried lowering the hit threshold to 2. Low and behold:



So the moral of the story is that the system was sound, but I needed to change how I defined a hit. Now a roll is a hit on 3, 4, 5, or 6 and a roll is a miss on a 1 or 2.

The other crucial bit is that I was making challenging tasks difficulty 3, 4, or 5. (I think I even had a 6 in there somewhere.) And before you say it, yes, I know that the highest an attribute can be is 4. I was counting on the players either 1.) having skills that increased their stats beyond 4, or 2.) working together to accomplish tasks, in essence adding their attributes together. But look at the old distribution. On a difficulty 3 the best they could do using eight dice is 54%. It’s in their favor, but only just. And don’t get me started on difficulty 4 and 5. I want those to be hard, but not nigh impossible. By lowering the hit threshold to 2 it boosts their chances to 71% on difficulty 3. Much more in line with what I wanted to see.

The players eventually figured out that they could work together to pool their attributes and that got them out of a few jams, but I didn’t like how frequently they had to rely on that. For me it underscored the need for me to create a list of items that characters can use to increase their dice pools. A well placed +2 Thumbtack Of Stabiness or a +1 Dental Floss Of Climbing could go a long way.

It’s crazy that such small changes could make such a huge difference to the game, but they really do. And I may never have figured it out without plotting it all out. Math, kids, learn it. It does matter.

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