According to the BBB a Full Burst against three targets is supposed to be handled like one short bursts against each target (SR4A p. 154). Does that mean that the shooter only suffers 8 recoil and and spends only 9 bullets? Why can't I do three short burst against one target? That should be easier than the above.

No, you still are firing 10 Bullets, they are just resolved as 3 separate 3-round bursts. You "lose" a bullet in the exchange due to waste.

So no to the bullets but yes to the lesser recoil?

You still fire 10 Bullets (while only 9 potentially impact the targtets), so the recoil is the same (-9), and the expenditure of bullets (Total of 10) is the same...

This is something else than Neither do three short bursts or a long and a short burst incur a -9 recoil penalty nor do they use 10 bullets. In case of two targets this reading would make no sense at all since the shooter could just as well use actual short and long bursts for less penalty and ammo waste.

But you are not talking about a FUll Burst against 2 Targets. You may Treat it as X for resolution purposes, but the fact remains that you are still firing a FULL BURST. To treat the attack against 3 targets as 3 Short Bursts, you must still fulfill the prerequisite of firing a Full Burst. Full Bursts fire 10 Rounds.

That FULL BURST is supposed to be "treated as separate burst fire attacks against each target (one short and one long against two targets, or three short against three targets)". If I treat it as such, I don't use 10 bullets and do not receive -9 for recoil (its 9 bullets and -2/-5 for the first and -8 for the second, depending which burst goes first). If I use ten bullet and get a -9, I'm not treating the full burst as separate bursts.

In case of two targets this becomes especially stupid. If someone declares a full burst against two targets he gets the whole full burst package, if he instead declares a short burst against one and a long burst against another, he is better off. Its not that he would have to switch mods or anything for those two bursts.
Moreover with the latter declaration the targets needn't even be within 1m of one another.

It seems illogical that you get two different results for two situations that should be treated equally.

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It is not illogical, however. A Full Burst (1 Complex Action) <> a Short Burst and a Long Burst (2 Simple Actions). They are not equivalent.

I know that generally they are not the same, but according to the book they are supposed to be treated equally in case of two or three targets. Your opinion simply does not reflect that. The way you put it, it is just a case of declaring the optimal or less than optimal action.

Actually there are whole classes of weapons that would need to be modded in order to do the latter of those 2 options.

Can't any FA weapon do either?

Nope, FA can fire short, long and full bursts:

FA short bursts only cannot use Called Shots by RAW, BF bursts can.

And now "burst" no longer looks like a word. Great job, everyone!

Semantic satiation, or verbal weirding?