[juvenal]

Just how much of a gamble is sowing saved F1 tomato seed. 50% chance of a 'true' crop, or doomed to fail, or..what?

[Aunt Sally]

I’m afraid you’ll probably only get poor quality plants 

[Subversive_plot]

The seeds will most likely grow into plants that yield fruit that are different from the F1 plant in appearance and flavor.

In the past, I have grown F1 hybrid tomatoes, and occasionally a fruit is not harvested or is damaged in the field for some reason, and the seed is dropped onto the soil. If the seeds grow into a plant that bears fruit, my experience is that the fruit is often small compared to the fruit on the F1 plant. Still edible, but not the same as the F1 plant.

It is worth mentioning that what we call heirloom tomatoes started out, generations ago, as the product of parent tomatoes that may not be similar.  Selection of tomatoes with desired qualities over many generations, and inbreeding of these plants, results in tomatoes with reinforced plant and fruit characteristics.

Wikipedia provides information on F1 hybrids (the section on Production of F1 hybrids is useful):
 https://en.wikipedia.org/wiki/F1_hybrid#Production_of_F1_hybrids

Wikipedia also provides information on "hybrid vigor", or heterosis, the reason F1 hybrids are made:
https://en.wikipedia.org/wiki/Heterosis

[snowdrops]

I agree with the other replies, the only way I think would be to grow on some of the side shoots & over winter them, which is similar to cloning them. You might need to do it once or twice to get them through the winter

[AndyRVTR]

Am I the odd one out... I've saved & used Shirley F1 seeds for the past five years and always had decent crops?

[Aunt Sally]

John has a good article here:

https://www.allotment-garden.org/gardening-information/seed-saving/seed-saving-tomatoes/

[Subversive_plot]

Am O the odd one out... I've saved & used Shirley F1 seeds for the past five years and always had decent crops?

Maybe that's good luck?  Or good gardening!

[Snow]

I grew out some seeds from a supermarket piccolo tomato and they were orange, not red like piccolo. But they were very tasty and lasted ages on the  truss once picked.

If you have the space it's worth a try if you don't mind that they may not be ideal

[Growster...]

I certainly finished up with two distictively different plants when I kept Crimson Crush seeds from a previous year!

And what was an added bonus, was that one of the types didn't get even touched by late blight, while it's 'other half' plants died off within days!

Like Snow says, if you have the space then try it, the plants have two choices in the end...