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The Three Axes Model of Action Analysis

Model Thomas Kelvin quote

Model Thomas Kelvin quoteYou’ve got an action. Let’s call it “build Blooper”. You’ve got a second action. Let’s call it “buy Blooper”. You put your actions before your playtesters and in very short time you notice that nobody is building Bloopers. Your whole Blooper economy, your cute BloopBuilders, everything is just pointless.

And you’ve got no idea why.

So you make building Bloopers less expensive. Now everyone should build Bloopers all the time. Except they don’t. They’re still buying Bloopers.

So you make buying Bloopers really, really expensive. And now your game is stalling out and your playtesters are complaining. Nobody wants to build Bloopers and all the BloopBuilder concept art you commissioned is just so much dollars down the drain. What the hell is going on?

Welcome to the wonderful world of action analysis.

Fortunately there’s a quick and dirty tool you can use to graph your actions and compare them to each other. All you need are three simple axes* of analysis: Cost, Benefit and Risk.

The 3 Axes

Cost is what it takes for a player to perform the action, what the player loses. It goes from High (bad for the player) through Low (better) to Negative (hey, they’re paying me to do this shit!). The lower the cost the more beneficial (obviously) the action is for the player.

Benefit this the opposite of cost: it’s what the player gets out of the action. The amount and size of the Bloopers. It goes from Negative (bad, baaaad!) through low (ok if cheap) to high (get it, get it now!).

Risk is the chance of the action succeeding. It goes from Certain (yay, let’s do it) through Possible (ok, let’s try) to Impossible (why the hell is this stupid thing even included in this game?).

A Note on the Impossible

Beauty of Mathematics quoteIf you’ve got an action that is impossible, or near impossible, then you’ve got a problem. Impossible actions are meaningless since they’ll, by definition, never succeed. If you’ve got anything that’s impossible (you shouldn’t, you’re not completely daft after all) then cut it and be done with it.

Actions that are next to impossible are throwaways. If the cost is low you’ll get a gambling situation: try, try, try again and you’ll succeed by sheer probability theory. You should save your players the time by combining the cost and raising the chance of success. Yes, that contorts your cute probability curve but it’s worth it – who’d want to spend ten minutes trying just to succeed by probability? It’s not dramatically correct.

Actions that are next to impossible but have low benefit are even more of a throwaway. This is the “I’ve got so much resources that I don’t care and the graphics are cool so lets try it” action. Cut or change as above.

Then you’ve got the insidious “one-in-a-million” action that costs like crazy and gives more benefits than the four handed blessing of Lord Vishnu. WARNING! WARNING! Game breaking moment approaching! AWOOOoooo! AWOOOoooo! [insert appropriate panicky noise here]. The one-in-a-mil action make the rest of the game meaningless. If you’re losing the one-in-a-million action is a no brainier: I can’t win but I could have a chance at winning if this succeed. So the game becomes about going all in and blowing up the Death Star. Everybody get their Jedi farmhand ready, here comes the random game victory.

Negative Values

Ok, now that we’ve done the impossible lets take a look at another oddity: negative costs and negative benefits. Simply stated, negative costs with a positive benefit are no brainers. Keep hitting that mole over and over again until it’s dead, then continue to game with your newly found free resources.

Actions with negative benefits and positive costs are dumb. Suggest them to your kid brother and watch the tantrum unfold.

That leaves us with negative costs with negative benefits. Shovel all the manure out of the playtesting yard and you get a donut. No, you don’t get to wash your hands. Enjoy your sugary norovirus and return the spew pail in pristine order. Instant interesting choice.

Now, you could define the end of the scale as zero (see below) but there’s a little bit more than that. With negative cost you are able to perform an action which you would not be able to perform otherwise. You get freedom of movement, which is a benefit in and off itself. It must be compensated.

So if you’ve got buy Blooper that cost one BongBuck, and you’ve got sell Blooper that gains you one BongBuck the sell Blooper action must have an additional cost associated with it otherwise its strictly better than the buy action. The cost can have the form of a restraint: you can’t sell Bloopers you don’t have, but that effectively makes Bloopers cash and you don’t need Bongs. Or you can twist it so that you get less Bongs for selling Bloopers than you have to pay for buying them (which is the way it’s normally done – don’t you know anything about Bloopers?).

Calculating Equal Values

Simple math. Cost minus Benefit. Multiply by Risk (which should be in probability format: 1 for certain, 0 for impossible). Now you’ve got the relative expected value of the action. Do this for every action and you get a nice progression of what it takes to win the game. Yay, you!

But hold on, how do we subtract Bongs from Bloopers? Easy. Find a currency that works for every item in your game. It might be Bongs. It might be Bloopers. It might be actions (hey, if you’ve got a limited amount of actions then actions are a currency like any other). It might even be movement, or player order, or position (don’t believe me? Talk to a Chess master). Whatever it is, make sure that you can convert every resource you have into your currency or convert in into a resource that can be converted into currency.

And don’t forget the risk. If you’re converting Bloopers into Bongs, but you only have a 50% chance to do that then your expected Blooper value in Bongs just got sliced in half.

And then you encounter circular conversion. For two Bongs you get a Blooper but a Blooper can only be sold for a single Bong 50% of the time then two Bongs are worth a Blooper which is worth half a Bong. And don’t forget that your BloopBuilders can convert into Bongs but it may be more efficient to convert into Bloopers first. Makes your head spin. Don’t touch that bong.

Making the Model Real

Human nature Stephen Hawking quoteOk, so that’s the model. Does it work in real life? Well…

It’s a model, an idealized version of what actually goes on in a game to the point where it’s easily understandable. You can even do a nice 3D graph of it (just remember to multiply negative costs unless you have an associated action cost). But then you apply it to your game. You want to see your Bloopers marching across the screen, crushing all opposition, so you feed everything into the model.

And you discover that it’s not a perfect fit.

See, as with any model the 3 axes simplify reality in order to make it graspable. Conversions between different resources are never perfect in real life. You always get some resource that’s got a hidden benefit or a hidden cost that isn’t obvious until you’ve playtested the game dozens of times. You get a combinations of resources that lets you Bong, Bong, Blooper,Right paddle, Finishing move your opponents. You get group think where even a perfectly balanced game can be unhorsed because the theme causes players to believe that some action is much stronger than the math would suggest. So, yeah, the model is only a model.

But so is the weather channel and every grandma in Jersey is watching that (and it’s got nothing to do with the hot bald guy presenting the thunderstorms). And as with any tool, the 3 axes action model can help you along the way but it will not do the work for you.

If you ever figure out a tool that does that let me know and I’ll let my computer crank out Half-Doom Fallout XXVI over the summer…

Big thanks to Kevin B. Smith (peakhope) for the idea way, way back.

*Yeah, axes is plural of axis. Dude, check out my 1337 barbarian axes.

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