50/50

[thehedglin]

To be fair, not many people really understand probability, it is a bastard of a field of study. Essentially the error here is one most people tend to make, they look at the odds of a single event, and assume that the individual probability of that event isn't effected by the frequency or sequence. Like with the cards, we went from 1/52 odds of a single card being dealt, to 1 in over six hundred billion in a seven card hand.

The number of events matter.

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But I started out with the assumption that the chance that you will pick a card to begin with is 50/50. I do not think this is the case at all, but even if it is, the chance it is a certain card is 0, since it is an infinite deck with all different cards.

While the chance of a certain card is 0, in your scenario, the chance of getting a card is still 50/50. Since we haven't really specified a card, any card is still a card, you have to specify a single value before the infinite deck comes into play. It is essentially the difference between any god being correct, and a specific god being correct.

In probability, a large range does not always decrease a probability, at least not until you specify a value or sequence.