What is not allowed in Over The Board (OTB) chess (because it might disturb a player), generally allowed in simuls (because they are supposed to be fun and entertaining), even more allowed in blindfold chess (because they are all about entertainment), and helps to save postage in correspondence chess?
It is announcing a forced mate.
For example, White would be completely justified in calling out a mate in three after Black’s 14th move.
Greco-N.N.
Rome 1620
1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.c3 Nf6 5.d4 exd4 6.cxd4 Bb4+ 7.Nc3 d6 8.O-O Bxc3 9.bxc3 Nxe4 10.Re1 d5 11.Rxe4+ dxe4 12.Ng5 O-O 13.Qh5 h6 14.Nxf7 Qf6

15.Nxh6+! Kh8 16.Nf7+ Kg8 17.Qh8mate 1-0
Such an announcement would be frown upon in an OTB tournament in these modern times. But hey, this was played in the 17th century, where the rules were a little more relaxed.
The English Master Blackburne was proficient in making these types of announcements in his blindfold simultaneous exhibitions. This one is from 1888.
J. B, Blackburne-John Norman Burt
Eight Game Blindfold Simul
Bristol, England, Mar. 2 1888
[Blackburne, Blackburne’s Chess Games, #367]
1.e4 e5 2.f4 exf4 3.Nf3 g5 4.h4 g4 5.Ne5 Nf6 6.Nxg4 Nxe4 7.d3 Ng3 8.Bxf4 Nxh1 9.Bg5 Be7 10.Qe2 h6 11.Qe5 hxg5 12.Qxh8+ Bf8 13.Nf6+ Ke7 14.Nc3 c6 15.Nfd5+ Ke6 16.O-O-O cxd5 17.Re1+ Kd6 18.Qe5+ Kc6 19.Qxd5+ Kc7 20.Nb5+ Kb6 21.Qb3 Nc6 22.Re8 Qf6 23.Nc3 Nb4 24.Nd5+ Kc6 25.Qc4+ Bc5 26.Nxb4+ Kd6

(Here, while making his move, Blackburne announced mate in six moves with 27.Qd5+ Kc7 28.Qxc5+ Qc6 29.Nd5+ Kb8 30.Rxc8+ Qxc8 31.Qd6+ Qc7 32.Qxc7#.) 27.Qd5+ 1-0 (Black resigned, no doubt due to Blackburne’s reputation in these situations.)
And Marshall announced a mate in 11 against Col. Moreau:
Marshall-Moreau
Monte Carlo, 1903
1.e4 e5 2.f4 exf4 3.Nf3 g5 4.Bc4 g4 5.O-O gxf3 6.Qxf3 Qf6 7.e5 Qxe5 8.Bxf7+ Kd8 9.d4 Qxd4+ 10.Kh1 Bh6 11.Bd2 Qg7 12.Bb3 Nc6 13.Bc3 Ne5 14.Qd5 d6 15.Rd1 Bd7 16.Ba4 Bc6 17.Bxc6 bxc6 18.Qxe5 Qg4 19.Na3 Kd7 20.Nc4 f3 (Here Marshall made his announcement)

Mate in 11 moves (at most)
21.Rxd6+! cxd6 22.Qxd6+ Kc8 23.Qxc6+ Kd8 24.Rd1+ Ke7 25.Qd6+ Ke8 26.Re1+ Kf7 27.Ne5+ Ke8 28.Ng6+ Kf7? (Col. Moreau could have prolonged the game with 28…Be3 29.Rxe3+ Qe6 30.Qxe6+ Kd8 31.Ba5#.) 29.Nxh8mate 1-0
Sometimes the announced mates are longer than the rest of the moves. A case in point:
Taylor-N.N.
London, 1862
[Chernev, 1000 Best Short Games of Chess, #3]
1.e4 e5 2.Nf3 Nf6 3.Bc4 Nxe4 4.Nc3 (The Boden–Kieseritzky Gambit.) 4…Nc5 5.Nxe5 f6? (White now announced a mate in eight moves, which is longer that the rest of moves. Apparently Black wanted to be shown and the game continued.) 6.Qh5+ g6 7.Bf7+ Ke7 8.Nd5+ Kd6 9.Nc4+ Kc6 10.Nb4+ Kb5 11.a4+ Kxb4 12.c3+ Kb3 13.Qd1mate 1-0
The longest announced mates, as you probably expected, occur in correspondence.
H.R. Barker-A.H. Owen
Midland Union vs. Southern Union
corres., England, 1906-7?
[This game was first published in the BCM, September 1907, pp. 434/5.]
1.e4 e5 2.Bc4 Bc5 3.Nf3 Nc6 4.c3 Nf6 5.O-O O-O 6.d3 d5 7.exd5 Nxd5 8.Bxd5 Qxd5 9.Be3 Bg4 10.Bxc5 Qxc5 11.h3 Bxf3 12.Qxf3 Rad8 13.Na3 Rd7 14.Rad1 Rfd8 15.Rd2 Qd6 16.Rfd1 Qg6 17.Qe2 h6 18.Nc4 Re7 19.Re1 b5 20.Ne3 a6 21.b4 f5 22.Qd1 Red7 23.Nc2 f4 24.Re4 (BCM reports: “Black with this move announced mate in 25 moves or less. White replied, I resign after your 36th move, Of course, I could vary the forms of checks, and drive your King to shelter, but this would be as futile as unsportsmanlike.” The other notes are from me.)

24…Qxe4 25.dxe4 Rxd2 26.Qg4 Rxc2 27.Qe6+ Kh7 28.Qxc6 Rd1+ 29.Kh2 Rxf2 30.Qe6 Rff1 31.Qf5+ Kg8 32.Qe6+ Kf8 33.Qf5+ Ke8 34.Qxe5+ Kd8 35.Qd5+ Rxd5 36.exd5 (Notice how nicely Black’s f-pawn keeps White’s king from fleeing.) 36…Ra1 0-1 [Let’s see the rest of Barker’s analysis as we long as we here. 37.a3 Kd7 38.g4 Ra2+ 39.Kg1 Kd6 40.h4 Kxd5 41.g5 Ke4 42.gxh6 gxh6 43.Kf1 Kf3 44.Ke1 Kg2 45.Kd1 f3 46.Kc1 f2 47.Kb1 Re2 48.~ (The symbol “~” is sometimes used to indicate “any move”.) 48…f1=Qmate.]