It says riders pay up to $10 per ride and drivers get up to $10 per ride. This makes me think that Lyft won't be taking a cut from the carpool rides. If that's the case, then Lyft is also providing a super easy way to pay the driver without having to remember to bring cash.

The "up to" parts make me think they will be taking a cut ;-)

Well the math says they won't. If the most a rider can pay is $10, and if Lyft takes a cut, then the max the driver will receive will be less than $10, which is not what they say.

It says "drivers earn up to $10 per trip", which means a driver can earn nothing! Or the rider can pay "from $4-10"; Lyft takes no more than the rider(s) pay; and the driver takes the rest.

The terms of service have a section reserving the right to impose a service fee. Not sure if there will be a fee at launch.

"Service Fee. In exchange for providing the Carpool Platform, Clara Rides may assess a service fee on each Carpool Ride (on either or both of the Carpool Rider or Carpool Driver). The amount of the applicable service fee shall be communicated to you in writing."

If 3 riders paid $5 each and Lyft took one third of that, the driver would get $10.

I think the convenience of having Lyft manage the logistics will mitigate this to some extent. Lyft carpools are scheduled as late as an hour in advance; if you've entered into a more long-term arrangement, more notice is required especially if you're the driver.

That is a fact of life for all marketplaces. Historically speaking, it has already been proven that the power users who look to form relationships outside of a marketplace are usually edge cases and have little effect on the viability of the business