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TheWesson

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Dual Pillars https://elementscommunity.org/forum/index.php?topic=5348.msg53940#msg53940
« on: April 15, 2010, 11:59:24 pm »

Here's a suggestion to bump up the power of dual decks - bringing them a bit closer to rainbow decks.

Allow us to 'craft' dual pillars out of two pillars of different colors.  You would choose two pillars and craft them (or maybe make such a choice in the bazaar.)

Such a dual pillar would randomly emit one quantum of one of its colors each turn.

Objection #1: "What's the difference between that and having pillars of different colors in your deck?"

The difference is that you are less likely (or much less likely) to be shafted with dual-color pillars.  The sense is that in any particular game, dual-pillars will distribute your quantums more evenly between the two colors, and it is much less likely to be starved of one color.   (In fact, this is a great advantage of rainbow decks over dual-color decks using mono pillars:  less quantum starvation.)

I didn't want to do the math so I just ran a sim.  Let's suppose you want to play a bone wall (5  :death quantums needed) and an elite otyugh (5  :gravity quantums needed.)  If you draw 5 pillars from a mixed batch of gravity/death pillars you have about 63% chance of having the quantums you need for each after 3 turns.  If you draw 5 dual gravity/death pillars you have about 88% chance of having the quantums you need after 3 turns.

Another sim: suppose you want to play something costing 7 :death quantum.  What is the chance you will be able to play it after 3 turns, given 5 pillars?  With mono-pillars, the chance is 48%; with dual-pillars, the chance is 69%.

Objection #2 (from Zanz): "Graphics for sixty new cards?  Help!"

I would just have the machine generate the dual-pillar graphics, each pillar graphic from each of the two source pillars laid side-by-side in the new dual-pillar graphic.  Maybe you could even generate them at runtime, if that helps.

---------------

Anyhow, I think this is a good idea because I think dual-decks would be a very interesting area for players to explore (I would like to explore this area more) and the rainbow arena is pretty well explored and maybe somewhat OP relative to duo or mono. 



Offline jmizzle7

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Re: Dual Pillars https://elementscommunity.org/forum/index.php?topic=5348.msg53958#msg53958
« Reply #1 on: April 16, 2010, 12:54:14 am »
Welcome to the forums, Wesson. This has been suggested a great many times in several different threads already. That's not to say that your idea is bad or unwanted - just unnecessary in this particular case.

There are actually a lot of viable decks that use two or three types of quanta. I feel you may be underestimating the power of good deckbuilding to overcome the drawback that exists when one decides to play with multiple types of pillars/towers.

Ashebrethafe

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Re: Dual Pillars https://elementscommunity.org/forum/index.php?topic=5348.msg54006#msg54006
« Reply #2 on: April 16, 2010, 02:01:06 am »
I didn't want to do the math so I just ran a sim.  Let's suppose you want to play a bone wall (5  :death quantums needed) and an elite otyugh (5  :gravity quantums needed.)  If you draw 5 pillars from a mixed batch of gravity/death pillars you have about 63% chance of having the quantums you need for each after 3 turns.  If you draw 5 dual gravity/death pillars you have about 88% chance of having the quantums you need after 3 turns.
Based on your estimates, it looks like you did do the math! Or at least had tons of trials. The explanation is below if anyone is interested -- if not, skip down to the "****".

With mono-pillars, you essentially need to get 2 or 3 heads out of 5 fair coin flips (heads is gravity, tails is death). There are 2^5 = 32 equally likely sequences of flips, including 1 each with 0 and 5 heads, 5 each with 1 and 4 heads, and (5 * 4)/(2 * 1) = 10 each with 2 and 3 heads, so the probability of success is 10 * 2 / 32 = 5/8 or 62.5%.

With dual pillars, you need between 5 and 10 heads out of 15 flips. There are 2^15 = 32,768 possibilities, including 15!/(10! * 5!) = 3,003 each with 5 and 10 heads, 15!/(9! * 6!) = 5,005 each with 6 and 9 heads, and 15!/(8! * 7!) = 6,435 each with 7 and 8 heads, so the probability of success is (3,003 + 5,005 + 6,435) * 2 / 32,768 = 14,443/16,384 or 88.153076171875%.

Another sim: suppose you want to play something costing 7 :death quantum.  What is the chance you will be able to play it after 3 turns, given 5 pillars?  With mono-pillars, the chance is 48%; with dual-pillars, the chance is 69%.
The sim wasn't quite as close here. Now you need 2 or fewer out of 5 heads with mono-pillars (chance of success 1/2 -- you just need more tails than heads), or 8 or fewer out of 15 heads with dual pillars (chance of success 1/2 + 6,435/32,768 = 69.6380615234375%).

Also, **** that 7 :death shows up as the cost of bone wall, when I look in the bazaar. Is the 5 :death for an upgraded bone wall?

Objection #2 (from Zanz): "Graphics for sixty new cards?  Help!"

I would just have the machine generate the dual-pillar graphics, each pillar graphic from each of the two source pillars laid side-by-side in the new dual-pillar graphic.  Maybe you could even generate them at runtime, if that helps.
Putting them side-by-side, even compressed into one frame, would look to me like the card was equivalent to 2 pillars, producing one of each quantum per turn. If this idea is implemented, perhaps superimposing the images would be more intuitive.

TheWesson

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Re: Dual Pillars https://elementscommunity.org/forum/index.php?topic=5348.msg54013#msg54013
« Reply #3 on: April 16, 2010, 02:19:21 am »

Jmizzle7
- Oh, I didn't know the idea was well explored already.  Looked at the first couple of pages but didn't see a post titled "Dual Pillars" or the like ... :)  Perhaps I should have exploited the "search" feature, eh.
- You can have a reasonable dual deck but I wanted to attempt FG's with a dual deck - or a variety of dual decks.  Maybe I should explore deeper but it seems like rainbow is the main option there.

Ashbrethafe
- Thanks for doing the math for me :)
- The dual pillar graphics should have the left half of one pillar and the right half of another pillar, side by side.

 

blarg: