EvenQ[1]

EvenQ[2]

step={
n_ /; EvenQ[n] :> n/2,
n_ /; OddQ[n] :> 3n+1
}

11 /. step

34 /. step

17 /. step

11 //. step

step1={
n_ /; EvenQ[n] :> n/2,
n_ /; OddQ[n] :> 3n+1,
1 -> Bingo
}

11 //. step1

step2={
1 -> Bingo,
n_ /; EvenQ[n] :> n/2,
n_ /; OddQ[n] :> 3n+1
}

11 //. step2

31 //. step2

11 //. n_Integer :> (Print[n]; n/. step2)

31 //. n_Integer :> (Print[n]; n/. step2)