An Entertaining Diversion

I’ve found in the past that if I get stuck on a problem it sometimes helps to walk away from it for a while, do something else, and come back to the problem later with a clearer mind. Following Who’s Yer Con I was jazzed about how well things had gone with the Playthings playtest and I set to work straightaway trying to correct the few issues that I had identified. Some were simple to resolve, others were not. I hit a wall when trying to address an issue with the probabilities in the core mechanic, so I decided to take a break and do something else.

The “something else” turned out to be a new system mechanic that for now I am calling the Knockout System (for reasons I hope will become apparent). The idea came about while I was playing Pokemon Master Trainer with Beth and the kids. To catch a Pokemon you roll a single d6 and you have to roll one of the numbers listed. For the easier Pokemon there are three numbers for success, for harder Pokemon there were two numbers for success, and for powerful and legendary Pokemon you have to roll one specific number.

I started by pondering the probabilities of the dice rolls, ’cause I’m weird like that. Even on the easy Pokemon you only had a 50/50 shot of catching the little bastards. I started musing about how the odds might be skewed more toward the player’s favor, the most obvious being adding more dice to the mix. Then I started thinking that it was sort of odd that as the difficulty gets larger there are fewer numbers for success. That led me to think that you could turn it on its head, so instead of trying to roll specified numbers, you had to avoid specified numbers. The more numbers that are knocked out **wink, wink**, the more difficult the roll. Then I started thinking about making the numbers you had to avoid variable by rolling dice to establish the difficulty.

As it wasn’t my turn in the game I surreptitiously pulled out a container of d6s and started rolling, playing out some basic scenarios. One die vs. one die, one die vs. two dice, two dice vs. one die, two dice vs. two dice. Then one of the rolls landed on a pair of sixes. I paused, wondering what should be done with that. If the difficulty is two dice and they both come up as the same number, should that just be a lucky break for the other player?

I kept rolling dice and started to notice an interesting pattern: it seemed like the more dice the attacker used the less likely they were to succeed, which is exactly the opposite of what you normally see in RPGs.

Soon I was in full-on obsession mode. Once our game ended we shooed the kids off to bed and I broke out the laptop to work out the probabilities.

WARNING: POTENTIALLY DULL MATH-STUFFS AHEAD.

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Yes, I can really be this anal.

The only way to establish a pattern is through a whooooole bunch of rolls, which can take a long time. Thankfully, our friend Microsoft Excel has a formula for that: RANDBETWEEN. It gives you a random number between a given start and end point. To simulate a d6 you just set the start as one and the end as six. A few cuts and pastes later I had eight columns and 1000 rows. (I’m not sure why I chose eight columns. It just seemed right.) Each column represented a single die rolling 1000 times. These eight dice were my attacker. I then repeated the process to get another eight columns representing the defender.

Hello, Mr. Bell Curve

Hello, Mr. Bell Curve

Since we’re talking about the defender avoiding the numbers rolled by the attacker it’s a simple success/fail scenario. I just had to compare whether any of the dice rolled by the defender matched those of the attacker. If not, it was a success (1), if so, it was a failure (0). This took a bit more time to set up because I needed to set up different scenarios to get the full picture. Once I had my results I plotted them out in a chart of percentages showing the likelihood of the Defender winning. I was pleased to see that my initial impression was correct. Adding more dice to either the attacker or defender decreased the chances of the defender succeeding. In fact, multiple dice on both sides decreased chances even further, creating a bell curve in the middle. Suddenly things began to click into place.

It lays out like this: the Defender gets one die. The defender’s goal is to keep his defenses up. The attacker rolls a number of dice equal to the attribute being used (strength, intelligence, whatever; I haven’t worked that out yet). His goal is to take out the defense by matching one of his numbers to the defender’s roll. If the attacker rolls multiples (two or more of the same number) then the defender must roll that many dice for the defense.

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Wait, d-what?…

That all tracks pretty well. The main problem I see is that according to the chart above anything beyond six dice is basically impossible. Of course that is if both sides are using d6s. I decided to try other dice values. The sweet spot turned out to be d12. That gave a very nice curve and made just about every number combination possible. That appeals to me. The d12 is sort of the lonely outcast among dice, so I like the idea of showing it some love by creating a system that uses d12s exclusively.

Obviously this is a long way from being a fully functional system, but it was a fun exercise. I think I’m now ready to go back and tackle the remaining issues with Playthings. Hopefully a little distance will prove to give me a bit more perspective.

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