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I went through a while ago and Grass/Fighting, Fire/Flying and Water/Rock form an almost perfect triangle even considering how the types and sub-types match up with each other. Apart from both Water and Rock dealing 1/2x Damage to Grass/Fighting, all three have a 2x and 4x effectiveness over one and 1/2x and 1/4x effectiveness on the other. Given that people probably wouldn't use the 1/4x damage move anyway most of the time that wouldn't matter much. I think the bigger problem with these is designing a pokémon for them that wouldn't be copying something else, especially the Fire and Water lines.

soble92 wrote:

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I have figured it out! I have developed 3 types that use 2 of the types in the polls.

Grass/Rock, Fire/Ice, Water/Ground

What do you think?

They don't match up well, since it favours the grass starter over the others:

Grass gets x4 and x0.5 on both water and fire
Fire gets x2 and x1 on grass and x1 and x0.5 on water
Water gets x2 and x1 on fire and x1 and x1 on grass

The grass starter actually comes out with an advantage over the fire one, which is not the way it's supposed to work. I know the generation 4 set tried to make the subtypes balance out, but in that case all moves learnt by level up did x2 at best.

With those three, and having the subtypes countering the weakness rather than amplifying it, I would say Grass/Ice, Fire/Ground and Water/Rock. In all cases, the primary type is strong over both types of the 'weak' starter, resulting in 4x damage, and the Fire and Water starters can deal 2x to the Water and Grass starters respectively. Grass unfortunately doesn't get that advantage, but both its types are neutral, whereas the others have a super effective and a not very effective type, which makes up for it to a degree. The Grass and Water starters both gain a resistance to the subtype of the 'strong' starter, whereas the fire one is 'only' neutral. This probably won't matter in practical terms though, since people would probably use the 4x effective move more anyway.

Overall it's not entirely balanced, but it at least keeps all the 'best' matchups in one direction, and spreads them. If the grass starter has the right design it could be given a move of a different type that would give it the x2 over the fire-type, which would push the balance closer. There also aren't any 'unique' combinations, but I would prefer a balanced team of repeated types than a set of new combinations where one dominates both of the others.