Card Draw
Draw random cards from a virtual 52-card deck
How to Use
- Select how many cards you want to draw (1-5)
- Click "Draw Card" to draw from the deck
- The deck will deplete as you draw cards
- Click "Shuffle New Deck" to start fresh with a new 52-card deck
Perfect For
- • Card game decisions
- • Magic trick practice
- • Random selection
- • Teaching probability
- • Party games
The probabilities behind a 5-card draw
A 52-card deck has C(52,5) = 2,598,960 distinct 5-card combinations. The standard poker-hand frequencies, drawn without replacement (which is what this tool does — each drawn card is removed from the deck):
- Royal flush: 4 / 2,598,960 ≈ 1 in 649,740 (0.000154%)
- Straight flush (non-royal): 36 / 2,598,960 ≈ 1 in 72,193
- Four of a kind: 624 / 2,598,960 ≈ 1 in 4,165
- Full house: 3,744 / 2,598,960 ≈ 1 in 694
- Flush (non-straight): 5,108 / 2,598,960 ≈ 1 in 509
- Three of a kind: 54,912 / 2,598,960 ≈ 2.11% (1 in 47)
- One pair: 1,098,240 / 2,598,960 ≈ 42.26%
- No pair (high card): 1,302,540 / 2,598,960 ≈ 50.12%
Card counting (the Hi-Lo system popularized by Edward Thorp in Beat the Dealer, 1962) works because blackjack deals without replacement from a shoe, so the conditional probability of each rank shifts as cards leave. +1 for 2–6, 0 for 7–9, −1 for 10–A; a running count scaled by decks remaining (the "true count") shifts the player's edge by about +0.5% per unit. That's why real casinos now use 6–8 deck shoes and cut ~1.5 decks behind the cut card — depth of penetration collapses the signal. With this tool's single-deck, full-penetration draw, counting works perfectly, but there's also no bet to place.
Edge case: "Draw 5, then draw 5 more" from this tool is not the same as drawing 10 up front. The first draw alters the conditional distribution of the second. If you're simulating a game, draw all cards for a hand in one shot.