On building roads and bridges

[Ravingdork]

The Terrain Improvements table in the Kingdom Building rules states the following: Road cost represents the BP cost to establish a Road that crosses a hex and connects to all adjacent hexes.

Doesn't this mean I only need to build roads in every other hex to connect everything?

The rules also state in several places that building a road in a hex with a river doubles the price, since you need to build bridges to cross said river.

What if I don't want to build a bridge in that hex? Do I have the option of building a road through the hex without the bridge? There are numerous reasons why I might want to do this rangin from the road simply going alongside the river through the hex, to trying to maintain a strategic advantage over a nearby enemy across the water.

If I can choose to not build bridges, how does this impact/interact with the road's ability to "connect to all adjacent hexes"?

[Chemlak]

No: connects to all adjacent hexes simply means that if that adjacent hex has roads, too, they're connected together.

Second question is house-rule territory. The RAW answer is that you must bridge rivers if you're building roads in a hex.

My personal house rule is that if a river passes through a hex you are building roads on, you may pay the normal terrain cost for roads to have them on only one side of the river. You can later pay again for the other side, which includes bridges in the cost. Any hex-sides that are completely cut off from roads by the river are not connected to the road network.

[Simon Hayes]

Situations may vary a lot, usually rivers are borders, if you don't build bridges you can't cross, at least not easily, so somebody may argue that you don't control the other side of the hex

[boring7]

The road still costs double because of erosion. It might not be a good excuse, but it is an excuse.

The main issue is that roads (presumably) have effects, and as the rules are written the moment you build a road on a hex that benefit effect affects every neighboring hex, including the ones on the opposite side of the river. To avoid that you would have to make up an additional rule for the road's effects not crossing the river. I'm not familiar with the road rules so I don't know what benefit they offer in the first place. Looks like it's only real use is travel speed and the overall bonus to the kingdom (which is applied regardless of the roads' actual placements). As such there is probably no need to build a road tile ON a river, since your marching army (or whatnot) will get TO that hex at the same speed.