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Mathematical probabilities. There are a number of quotes from the Epicurean texts that address this idea, especially:
[133] "Who, then, is superior in thy judgement to such a man ? He holds a holy belief concerning the gods, and is altogether free from the fear of death. He has diligently considered the end fixed by nature, and understands how easily the limit of good things can be reached and attained, and how either the duration or the intensity of evils is but slight. Destiny, which some introduce as sovereign over all things, he laughs to scorn, affirming rather that some things happen of necessity, others by chance, others through our own agency. For he sees that necessity destroys responsibility and that chance or fortune is inconstant ; whereas our own actions are free, and it is to them that praise and blame naturally attach. [134] It were better, indeed, to accept the legends of the gods than to bow beneath that yoke of destiny which the natural philosophers have imposed. The one holds out some faint hope that we may escape if we honour the gods, while the necessity of the naturalists is deaf to all entreaties. Nor does he hold chance to be a god, as the world in general does, for in the acts of a god there is no disorder ; nor to be a cause, though an uncertain one, for he believes that no good or evil is dispensed by chance to men so as to make life blessed, though it supplies the starting-point of great good and great evil. He believes that the misfortune of the wise is better than the prosperity of the fool. [135] It is better, in short, that what is well judged in action should not owe its successful issue to the aid of chance.
Replace "chance" with "luck" and that's a pretty good summary of Epicurus's views.
Yes I agree with Don. That's the key passage, mainly on the topic that we should organize our lives so that we are as little affected by negative chance as possible, because there are things which are not in our control (where lightning will strike) that are essentially to us matters of chance, but to which we can minimize our exposure.
I think there may be others directed against the idea that there is a "force" in the universe that dispenses favorable or unfavorable luck, along the lines of a "goddess of fortune," which would also be ruled out by Epicurean philosophy.
More examples...
U489
489. Nature teaches us to think nothing of what fortune brings, to understand that when prospering we are unfortunate and when not prospering we are fortunate, to receive undisturbed the good things that fortune brings and to stand ready for its seeming evils. For what is good or evil to most people is fleeting, and wisdom has nothing in common with fortune.
καὶ τὰ παρὰ τῆς τύχης μικρότερα (ἡ φύσις) διδάσκει νομίζειν, καὶ εὐτυχοῦντας μὲν γινώσκειν ἀτυχεῖν, δυστυχοῦντας δὲ μὴ παρὰ μέγα τίθεσθαι ὄν τὸ εὐτυχεῖν, καὶ δέχεσθαι μὲν ἀθορύβως τὰ παρὰ τῆς τύχης ἀγαθά, παρατετάχσθαι δὲ πρὸς τὰ παρʼ αὐτῆς δοκοῦντα εἶναι κακά· ὡς ἐφήμερον μὲν πᾶν τὸ τῶν πολλῶν ἀγαθόν ἐστι καὶ κακὸν, σοφία δὲ οὐδαμῶς τύχῃ κοινωνεῖ.
VS17
It is not the young man who is most happy, but the old man who has lived beautifully; for despite being at his very peak the young man stumbles around by chance as if he were of many minds, whereas the old man has settled into old age as if in a harbor, secure in his gratitude for the good things he was once unsure of.
οὐ νέος μακαριστὸς ἀλλὰ γέρων βεβιωκὼς καλῶς· ὁ γὰρ νέος ἀκμῇ πολὺς ὑπὸ τῆς τύχης ἑτεροφρονῶν πλάζεται· ὁ δὲ γέρων καθάπερ ἐν λιμένι τῷ γήρᾳ καθώρμικεν, τὰ πρότερον δυσελπιστούμενα τῶν ἀγαθῶν ἀσφαλεῖ κατακλείσας χάριτι.
VS67
67. A free person is unable to acquire great wealth, because that is not easily achieved without enslavement to the masses or to the powers that be. Instead, he already has everything he needs, and in abundance. But if by chance he should have great wealth, he could easily share it with his fellows to win their goodwill.
ἐλεύθερος βίος οὐ δύναται κτήσασθαι χρήματα πολλὰ διὰ τὸ τὸ πρᾶγμα <μὴ> ῥᾴδιον εἶναι χωρὶς θητείας ὄχλων ἢ δυναστῶv, ἀλλὰ συνεχεῖ δαψιλείᾳ πάντα κέκτηται· ἄν δέ που καὶ τύχῃ χρημάτων πολλῶv, καὶ ταῦτα ῥᾳδίως ἃν εἰς τὴν τοῦ πλησίον εὔνοιαν διαμετρήσαι.
U489
489. Nature teaches us to think nothing of what fortune brings, to understand that when prospering we are unfortunate and when not prospering we are fortunate, to receive undisturbed the good things that fortune brings and to stand ready for its seeming evils. For what is good or evil to most people is fleeting, and wisdom has nothing in common with fortune.
Don ...this sounds "stoic"...and it is from: Porphyry, Letter to Marcella, 30 [p.209.12 Nauck].
While parts of it are okay, other parts do not sound Epicurean to me. Porphyry is not quoting Epicurus, but instead he is giving his own thoughts on Epicurus.
Epicurus recommends gratitude for what is good. (There is a Vatican Saying on that, if I recall.)
Here's a prior thread on the letter to Marcella: We've discussed this before as the source of the "vain is the word of a philosopher which does not heal...." and that the letter is not represented to be a direct quote from Epicurus. I've come around to a somewhat more favorable opinion of it lately, but there's no doubt in my mind that it is mashup of Stoic and Epicurean and may simply Porphyry's own views, so in my view it has to be taken with caution. I agree with your reservations on this part Kalosyni. I think that a close reading of *exactly* what it is saying largely rescues it from sounding Stoic, and for that reason it's useful for discussion. But a too-superficial reading of it can definitely be made to sound like a recommendation to being indifferent to pleasure and pain, which I don't think is accurate Epicureanism.
Second thread, same general reservations:
See also in particular this part for discussion that Porphyry seems to be recommending abstinence from food and sex:
Also PD 16 (unless I missed it):
PD16. In but few things chance hinders a wise man, but the greatest and most important matters, reason has ordained, and throughout the whole period of life does and will ordain.
βραχέα σοφῷ τύχη παρεμπίπτει, τὰ δὲ μέγιστα καὶ κυριώτατα ὁ λογισμὸς διῴκηκε καὶ κατὰ τὸν συνεχῆ χρόνον τοῦ βίου διοικεῖ καὶ διοικήσει.
