Are there ways to guess credit card details?

  It's quite possible to guess credit card details. Choose a known BIN (first six), generate 9 random digits, and then append the appropriate check digit. That's only 1,000,000,000 combinations - high, but listing every single one is certainly doable even on a personal computer.

  Checking whether your guess is actually valid is harder. Almost every single website will ask for your expiration date and most will also ask for your CVV. Assuming that the card in question will expire within the next four years (standard lifetime of a card), that's still 12*4 possible valid expiration dates. And the CVV is another three digits you would need to guess. All told, that's 10^9*(12*4)*10^3=48,000,000,000,000 combinations - much less feasible.

Additionally, you would need to spread your guesses around - throwing them all at a single merchant's website will likely get them shut down by their payment processor for permitting exactly this kind of attack.