"If you should find that book, could you keep it for me?"

Such a sentence could be said to contain a first conditional (hypothetical but probable)

"If, by any chance, you find that book, can (or 'could', for the sake of politeness) you keep it for me?"

or a second conditional (purely hypothetical)

"If, by any chance, you found that book, could you keep it for me?"

Which is more likely?

The example sentences I found in different dictionaries all contained 'If, by any chance' followed by a verb in the present, so first conditional. But I could not find a rule which said it had to be so…

"If you should find that book, could you keep it for me?"

Such a sentence could be said to contain a first conditional (hypothetical but probable)

"If, by any chance, you find that book, can (or 'could', for the sake of politeness) you keep it for me?"

or a second conditional (purely hypothetical)

"If, by any chance, you found that book, could (here, 'can' would not work) you keep it for me?"

Which is more likely?

The example sentences I found in different dictionaries all contained 'If, by any chance' followed by a verb in the present, so first conditional. But I could not find a rule which said it had to be so…

"If you should find that book, could you keep it for me?"

Such a sentence could be said to contain a first conditional (hypothetical but probable)

"If, by any chance, you find that book, can (or 'could', for the sake of politeness) you keep it for me?"

or a second conditional (purely hypothetical)

"If by any chance, you found that book, could you keep it for me?"

Which is more likely?

The example sentences I found in different dictionaries all contained 'If, by any chance' followed by a verb in the present, so first conditional. But I did not find a rule which said it had to be so…

"If you should find that book, could you keep it for me?"

Such a sentence could be said to contain a first conditional (hypothetical but probable)

"If, by any chance, you find that book, can (or 'could', for the sake of politeness) you keep it for me?"

or a second conditional (purely hypothetical)

"If, by any chance, you found that book, could you keep it for me?"

Which is more likely?

The example sentences I found in different dictionaries all contained 'If, by any chance' followed by a verb in the present, so first conditional. But I could not find a rule which said it had to be so…