Set up the shoe and draw. Cards are dealt server-side without replacement — a dealt card is gone until you reset, exactly like a physical shoe.
A real shoe, honestly shuffled
Cards are drawn without replacement: once dealt, a card is gone, so a duplicate can only appear when more than one deck is in the shoe. That is the same dependency card counters exploit — and the reason online blackjack reshuffles every hand.
The named-card odds use the hypergeometric distribution — the probability that at least one copy of a specific card lands in your draw given the shoe size and the number of copies it holds.
Methodology
Each draw removes a uniformly random card from the remaining shoe via PHP's random_int (CSPRNG). The named-card probability is hypergeometric: 1 − C(pool−copies, n) / C(pool, n), where copies equals the number of decks.
Two draws, two different questions
Card problems split into two kinds and the tool answers both. The first asks about a specific card: the ace of spades is 1 in 52 on a fresh deck, and after three irrelevant cards are gone it is 1 in 49 — a real but small improvement. The second asks about a category: any ace is 4 in 52, about 7.7%, and that number moves much faster as aces leave the deck.
This is the arithmetic behind the only legal advantage play in a casino. Blackjack counting works because removing low cards from a shoe shifts the odds of the next hand measurably; it fails at six or eight decks with an early shuffle, because the proportion barely moves before the cards are gathered again. Run the draw with one deck and then with six to see how quickly the effect disappears.
FAQ
Why does drawing without replacement change the odds?
Because every card removed changes the deck. The chance of a specific card is 1 in 52 on the first draw and 1 in 51 after a different card is gone, which is the whole basis of card counting in blackjack.
Does this tool model a real casino shoe?
It models a single deck unless you set otherwise. Live games typically use six or eight decks and shuffle before depletion matters, which is why real-game probabilities move far less than a single-deck calculation suggests.
How is the probability of a named card over several draws derived?
As one minus the chance of missing it every time. Over four draws from a full deck that is 1 − (51/52 × 50/51 × 49/50 × 48/49), which is about 7.7%.
Can this tell me the next card?
No. It shows how likely each outcome is before the draw, which is a different and more useful thing than a prediction.