What is a round robin bet

A round robin turns a handful of picks into every parlay of a chosen size. Three picks "by 2s" is three two-leg parlays: A with B, A with C, B with C. You are not placing one bet, you are placing all of them, and the count grows fast:

Taking all the picks at once ("by 6s" on six picks) is a single parlay, not a round robin.

So the first thing to check is the total at risk. At 25 a ticket, three picks by 2s is 75, not 25.

When it helps and when it does not

With fair legs a round robin cannot help: the book's margin is charged on every ticket, so it buys a different shape of result, not a better average. The calculator shows that case at −110.

With legs that each carry an edge, it is different. Three even-money legs that each win 53% of the time, by 2s at 25 a ticket:

Parlaying edges multiplies them, which is why the round robin's expectation is higher. The price is the last row: nearly half the time the whole stake is gone. That is a bankroll question, not a betting one, so size it with fractional Kelly, and only when the edge on each leg is real rather than hoped for. These figures assume the legs are independent; legs from the same game are not, and books price that in.