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If the receiver/transmitter is connected to a proper antenna so that nearly all of the power gets to the antenna then it's probably better than just a piece of wire.
Antennas radiate energy - that's their function. Their design must be such that they allow maximum transfer of power to/from the transmitter or receiver. Antennas also help to focus, where desired, the energy (or sensitivity) so that what little power you have is aimed at one point - or so that the sensitivity on the receive side, is greater that it would be in a non-focused arrangement. Directional antennas also have insentivities (or nulls) that can be of great benefit in excluding unwanted energy.
In this instance polarization might matter as well as height. Buildings, mountains, etc could be obstacles - or they could be good reflectors.
The wire or cable that connects the equipment to the antenna can be a signficant source of loss. At 433 mHz losses are significant if you use the wrong material.
So, an antenna could perform better than just a wire but it all depends on the situation.
You might seek out some amateur radio information on antennas - try 70 cm yagi - 70 cm refers to the nominal wavelength often used to indentify a particular band. Yagi is a type of directional antenna. Log-periodic is another type that might be used to describe a rooftop TV antenna for many frequencies.
Stevez explained the nitty gritty details above, I would just add that 10mW max radiated power is quite low as transmitters go. So, if you use a single band antenna (and a 'pice of wire' is an example of this), make sure its length is precisely tuned to the frequency to minimise transmission losses. At that frequency, a few millimeteres plus or minus make a big difference.
Also, the connection between the chip output and antenna is critical, odd bits of wire will not do :wink: this job. Use connectors suitable for 433MHz for your coax if you have planned to to include a connector.
You might want to visit your library and look at the ARRL antenna book, its in the electrical/ radio amateur section. Lots of good antenna information in that book.
Presumably 'karenthestudent' is in the UK (like me) as she quoted RS Components?. Licence free radio data transmitters in the UK (and probably many other places?) are subject to strict rules about usage. In particular the aerial is a crucial part of the design, the datasheets for the modules usually show exactly what you are allowed to use.
Personally I used the simplest possible - just a short whip of the correct length (using a piece of stiff copper wire), taken directly off the datasheet. However, I wasn't trying for any sort of range!.