diff --git a/src/crypto/internal/randutil/randutil.go b/src/crypto/internal/randutil/randutil.go
index 84b1295a87..5a8b096d15 100644
--- a/src/crypto/internal/randutil/randutil.go
+++ b/src/crypto/internal/randutil/randutil.go
@@ -8,31 +8,19 @@ package randutil
 
 import (
 	"io"
-	"sync"
+	"math/rand/v2"
 )
 
-var (
-	closedChanOnce sync.Once
-	closedChan     chan struct{}
-)
-
-// MaybeReadByte reads a single byte from r with ~50% probability. This is used
+// MaybeReadByte reads a single byte from r with 50% probability. This is used
 // to ensure that callers do not depend on non-guaranteed behaviour, e.g.
 // assuming that rsa.GenerateKey is deterministic w.r.t. a given random stream.
 //
 // This does not affect tests that pass a stream of fixed bytes as the random
 // source (e.g. a zeroReader).
 func MaybeReadByte(r io.Reader) {
-	closedChanOnce.Do(func() {
-		closedChan = make(chan struct{})
-		close(closedChan)
-	})
-
-	select {
-	case <-closedChan:
+	if rand.Uint64()&1 == 1 {
 		return
-	case <-closedChan:
-		var buf [1]byte
-		r.Read(buf[:])
 	}
+	var buf [1]byte
+	r.Read(buf[:])
 }
diff --git a/src/go/build/deps_test.go b/src/go/build/deps_test.go
index 40034263cc..e233535f75 100644
--- a/src/go/build/deps_test.go
+++ b/src/go/build/deps_test.go
@@ -460,7 +460,7 @@ var depsRules = `
 	< crypto/internal/boring
 	< crypto/boring;
 
-	crypto/internal/alias
+	crypto/internal/alias, math/rand/v2
 	< crypto/internal/randutil
 	< crypto/internal/nistec/fiat
 	< crypto/internal/nistec