Draw odds

How likely you are to see the cards you built around.

Exact hypergeometric math for a shuffled deck. No games are used.

50 cards, four copies

The questions players ask

35.3%
At least one of your 4 copies in the opening hand
4.5%
Two or more of your 4 copies in the opening hand
2.2%
Three or more of your 4 copies in your first 10 cards
0.1%
All 4 copies in your first 10 cards

Any number of copies

Chance of at least this many copies

At least 1 copy
Copies	Cards seen (5 = opening hand)
Copies	5	6	7	8	10	12	15
1	10%	12%	14%	16%	20%	24%	30%
2	19%	23%	26%	30%	36%	43%	51%
3	28%	32%	37%	41%	50%	57%	67%
4	35%	41%	46%	51%	60%	68%	77%

At least 2 copies
Copies	Cards seen (5 = opening hand)
Copies	5	6	7	8	10	12	15
1	–	–	–	–	–	–	–
2	0.8%	1.2%	1.7%	2.3%	3.7%	5.4%	8.6%
3	2.3%	3.5%	4.8%	6.3%	9.8%	14%	21%
4	4.5%	6.6%	8.9%	12%	17%	24%	35%

At least 3 copies
Copies	Cards seen (5 = opening hand)
Copies	5	6	7	8	10	12	15
1	–	–	–	–	–	–	–
2	–	–	–	–	–	–	–
3	<0.1%	0.1%	0.2%	0.3%	0.6%	1.1%	2.3%
4	0.2%	0.4%	0.7%	1.1%	2.2%	3.8%	7.5%

At least 4 copies
Copies	Cards seen (5 = opening hand)
Copies	5	6	7	8	10	12	15
1	–	–	–	–	–	–	–
2	–	–	–	–	–	–	–
3	–	–	–	–	–	–	–
4	<0.1%	<0.1%	<0.1%	<0.1%	<0.1%	0.2%	0.6%

Deck sizes from 20 to 100. A main deck is 50 cards.

Method

What these numbers assume

Your deck is shuffled uniformly and you see cards from the top. The opening hand is 5 cards and every card drawn afterwards adds one to the count, so a column is cards seen, not a turn number: extra draws and the mulligan move the turn on which you reach it.

The mulligan is not included. Redrawing a weak hand improves your odds of a good one, so treat these as the odds of the first hand you are dealt.

These are exact figures, not simulations. We do not yet publish an observed column from real deals; when it exists it will sit beside these as a check that our game shuffles fairly.