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“Odds of winning depend on the number of eligible entries received”
A random-draw promotion admitting it cannot tell you the odds.
There are two kinds of prize promotion and this sentence tells you which one you are in.
In a random-draw sweepstakes, one entry is pulled from everything received. Nobody can state the odds in advance because nobody knows how many entries there will be, hence this formula. Your chance is one divided by however many people turn up, which for a heavily advertised promotion can be a genuinely enormous number.
In a matched-numbers or instant-win game, the odds are fixed by the design and the rules will state them outright: 1 in 13,346, or whatever it is. Those odds do not change with popularity.