Games laboratory
Odds calculator
What are the chances of getting an As in your hand? And of receiving two oros (coins) in the first three cards? Configure the deck and what you are looking for: the calculator gives you the exact result, tells you how it was obtained and shows you how it changes as you draw more cards.
1. The deck
2. What you seek
Cards you seek
3. How to draw
Exact result
Result
Probability of getting at least 1 of the sought cards when drawing 3:
27.73 %
Approximately 1 in every 4 times.
Exact fraction: 137 / 494
Probability of the same goal according to the number of cards drawn.
Step-by-step calculation
There are 40 cards in the deck and 4 meet the condition. 3 are drawn without being returned, so we use the hypergeometric distribution: we count the ways to choose k good cards from 4 and the rest from the 36 that are not, and divide by all possible hands of 3 cards.
Formula: P(X = k) = C(4, k) · C(36, 3 − k) / C(40, 3)
| Sought cards obtained | Probability |
|---|---|
| 0 | 72.27 % |
| 1 | 25.51 % |
| 2 | 2.19 % |
| 3 | 0.0405 % |
What exactly it calculates
The calculator answers questions such as "if I draw n cards, what is the probability of getting k of those I seek?". It does not play for you or take into account what others will do: it only counts cases. That is why it helps to understand why some hands are rare and others appear often.
Everything is saved only on this device. You don't need an account and we don't send anything to any server.
FAQ
What is the probability of being dealt an As in Brisca?
With the 40-card deck and three cards in hand, the probability of having at least one As is around 28%. You can check this with the first example.
Why is it not enough to just multiply?
Because when drawing without returning, each card changes the deck: if an As has already come out, fewer remain. The hypergeometric distribution takes this change into account; multiplying as if they were independent draws gives approximate and sometimes very distant results.
Does it work for the poker deck?
Yes: choose the 52-card French deck. The figures are then the J, the Q and the K.