Combat Cards


A Balancing Fantasy? by docboffin
8 +00002007-02-02T12:12:10+00:00282007bUTCFri, 02 Feb 2007 12:12:10 +0000 2006, 12:12 pm
Filed under: Balancing, Doc Boffin, Game Design

After thinking about balancing the scenario where one player has all of all the 2 turn fantasy combos and the other has all of the 2 turn horror combos, I started thinking about the more common scenario when each player has 2 out of 3 of the combos available, rather than all 3. Normally once a player has 2 out of 3 combos they will stop trying to draw the 3rd combo and just alternate between the combos they have.

This case initially seems more complex as the scissors-paper-stone relationship means that pairs of cards with be good against some opponent pairs and bad against others, but there are only 3 combinations of 2 cards, so I only had to work out how each pair fared against the 3 pairs in the other set: 9 sets of results.

I started with Redeswire Rip and Couture’s Cosh Vs Dragon Swipe and Demonic Spear:

High	Redeswire Rip    18	 8	Dragon Swipe 	Mid
Mid    	Couture's Cosh   15   	14   	Dragon Swipe   	Mid
High 	Redeswire Rip     0	12    	Demonic Spear  	Low
Mid	Couture's Cosh   15    	 6	Demonic Spear  	Low

Here the horror deck is more powerful, doing 6 DPT vs 5 DPT for fantasy.

I began listing out all the other combinations and then noticed that I was repeating myself. There were identical lines in the results. As I was going to divide the whole thing by the number of results anyway I decided to skip the duplicates and divide by a smaller number at the end. Once I’d removed the duplicates I ended up with 9 combinations:

High	Redeswire Rip    18	 8      Dragon Swipe    Mid
High	Redeswire Rip     0	12      Demonic Spear   Low
High	Redeswire Rip    18   	10      Tiger Pounce    High
Mid	Couture's Cosh   15     14      Dragon Swipe    Mid
Mid	Couture's Cosh   15    	 6     	Demonic Spear   Low
Mid  	Couture's Cosh    0     10     	Tiger Pounce    High
Low     Sick Sumo Slap	  0     14      Dragon Swipe    Mid
Low     Sick Sumo Slap   12     12      Demonic Spear   Low
Low     Sick Sumo Slap   12  	 4      Tiger Pounce    High

I was pleasantly surprised to see that on average, both sets balance at 5 DPT just like in the 3 card scenario, until I realised that I’m just comparing each card in 1 set with each card in the other, just as I was doing with the 3 card scenario. By balancing the 3 simple card scenario equations I had balanced the 2 card scenario which I thought I had to work out result by result!

Next I started thinking about the 1 card scenario (each player has a 2 turn combo) but listing all the combinations in that scenario would produce the same table as above. By balancing the 3 card scenario I had balanced the 2 and 1 card scenarios which initially seem more complicated!

Sound reasonable? If so, it’s a balancing fantasy 😀

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The Horror Of Balancing by docboffin
8 +00002007-02-01T12:41:08+00:00282007bUTCThu, 01 Feb 2007 12:41:08 +0000 2006, 12:41 pm
Filed under: Balancing, Doc Boffin, Game Design

Last week at Friday Fights we noticed that the horror demo deck seemed to be more powerful than the fantasy demo deck. I started thinking that it must be possible to work out if there is an imbalance and fix it with a spreadsheet, but last time I tried that my brain melted. This time I started small and here’s where I got to:

Imagine 1 player has all the 2 turn fantasy combos and the other has all of the 2 turn horror combos. They both play random combos.

Redeswire Rip does 14 damage and regenerates 6 health when it’s unblocked and 0 damage and 0 regeneration when blocked by a fantasy 2 turn combo.

Let’s add regeneration to damage for now, as they both increase the health differential between you and your opponent, regeneration just makes the game take longer.

On average the card will be blocked 1/3 of the time as each fantasy 2 turn combo card blocks 1 location.

So, on average Redeswire Rip does (14 + 6) * (2/3) + 0 * (1/3) = 13.33 damage per use against a 2 turn fantasy combo card.

The best fantasy 2 turn combo card is Demonic Spear which has no regeneration, but does a small amount of damage when blocked by a 2 turn horror combo card.

On average Demonic Spear does 14 * (2/3) + 4 * (1/3) = 10.66 damage per use against a 2 turn horror combo card.

Aha! Bingo! The horror cards seem to be more powerful in this scenario. Working out the numbers for all the horror and fantasy cards it turns out that the horror cards will do 5.67 damage per turn (DPT) average and the fantasy cards will do 4.33 DPT.

Tweaking the numbers I can make both sets do 5 DPT average without changing the fantasy card stats by reducing the defence and regeneration of the horror cards.

Using the same method on the 3 turn cards I can get the sets to balance at 6.44 DPT without changing the fantasy stats, which makes 3 turn combos more powerful per turn than 2 turn combos, as they should be.

Factoring in regeneration again: on average a 2 turn horror combo will regenerate 1.5 health per turn while letting 1.0 DTP through when blocking, so games with horror cards will be slightly longer on average, but I think that’s OK.

The cool thing about developing Combat Cards in SL is that it’s really easy to tweak the numbers and then play some more games to find out if the theory works in practice. I just need to copy the new numbers to a notecard and we can try them out at Friday Fights tomorrow!