Hold'em poker calculator

using hypergeometric distribution


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Calculator

enter expression, e.g. 2+2
supported extra functions:


     
Result

Hypergeometric distribution sum from x1 to x2 both included:

Sumx1 to x2 h(x; n, a, N)

x1 x2 (the needed outs, e.g. if you need at least 3 and can get max 5 outs, then x1=3 and x2=5)
n (cards to come, from preflop to river the n is 5)
a (outs available)
N (deck, for preflop the deck is 50, where 2 is delt to you)

     
Result

Example of use

1: What are the odds that you get at least a pair at the showdown?

> Fill in
At least hitting a pair, two pair, triple or fullhouse.
Lets say you get the following cards A and J
x1 = 1 You need at least 1 of the outs to get a pair
x2 = 2 You dont mind getting more than one pair, (you still get minimum a pair).
To include those odds you set x2 = n.
If you only want a pair in total, then you set x2 to same as x1
n = 5 There are 5 cards to come from the preflop state
a = 6 There are three A and three J left in the deck, you have 6 outs
N = 50 You have received two cards, then the deck size is now 50
Click Fill in and you get the probability ~0.49
About 50% chance

2: What are the odds that you get a flush at the showdown?

> Fill in
Lets say you get the following cards T and 3
You only want 3 hearts on the board.
x1 = 3 You need at least 3 of the outs to get a flush
x2 = 3 You want to hit maximum 3 flush cards
n = 5 There are 5 cards to come from the preflop state
a = 11 Since you got two of the suited, there are 11 left in the deck
N = 50 You have received two cards, then the deck size is now 50
Click Fill in and you get the probability ~0.058
About 6% chance

3: What are the odds that that somebody has a 5 on the flop?

> Fill in
Lets say you are 4 players for the flop and you get the following cards Q and Q

You know nothing about the players, the flop comes 5 5 9

x1 = 1 The players need at least 1 of the outs
x2 = 2 Any player could have 1 or 2 of those 5's
n = 6 There are 6 cards to be given to the 3 other players
a = 2 Since two 5's are on the board, there are 2 left in the deck
N = 47 You have received two cards, and 3 cards on the flop, the deck size is now 47
Click Fill in and you get the probability ~0.24
About 24% chance of at least one 5 is out there

4: What are the odds for a runner straight?

> Fill in
Lets say you get the following cards J and T

The flop comes 2 9 A

This is solved by Combinations without repetition:
You need at least 2 of the outs to get a straight, the runner cards for straight are 7,8 or 8,Q or Q,K
You take all the possibilites outcome for the running straight
and divide by all the possible combinations for the next 2 cards.
The calculations is (7,8 combo or 8,Q combo or Q,k combo)
divided by all possible combos for next 2 cards.
Possible combinations for 7,8 combo is C(4,1) * C(4,1) = 24, picking 1 out of 4 is C(4,1)
Possible combinations for 8,Q combo is C(4,1) * C(4,1) = 24
Possible combinations for Q,K combo is C(4,1) * C(4,1) = 24
You have the 2 cards, the flops has 3, then there's 47 cards left in the deck.
Combinations of picking 2 out of 47 is calculated by the function C(n,r). C(47,2) = 1081
(C(4,1)*C(4,1) + C(4,1)*C(4,1) + C(4,1)*C(4,1)) / C(47,2) = (24 + 24 + 24) / 1081
Click Fill in and you get the probability ~0.04
About 4% chance

5: What are the odds for a runner flush?

> Fill in
Lets say you get the following cards J and T

The flop comes 2 9 A

x1 = 2 You need to hit minimum 2 flush cards
x2 = 2 You can hit maximum 2 flush cards
n = 2 There are 2 cards to come after the flop
a = 10 The flop has the 2 flush cards, you have 1, then the're 10 flush cards left
N = 47 You have received two cards, and 3 cards on the flop, the deck size is now 47
Click Fill in and you get the probability ~0.04
About 4% chance

6: What are the odds for not flopping overcards?

> Fill in
Lets say you get the following cards T and T
x1 = 0 0 overcard to hit
x2 = 0 maximum 0 overcards on the flop
n = 3 There are 3 cards to come for the flop
a = 16 There are four Aces, four Kings, four Queens and four Jacks in the deck, that's 16 outs.
N = 50 You have received two cards, then the deck size is now 50
Click Fill in and you get the probability ~0.305
About 31% chance

Notice, though, that those probabilities would be lower
if we consider that at least one opponent happens to hold one of those overcards.

7: Formula - odds when two cards to come?

> Fill in
Lets say you get the following cards A and Q

The flop comes 2 7 J

This is solved by the formula:

1 - ((47 - outs) / 47 ) * ((46 - outs) / 46 )
Where outs is a value between 1 and 21.
You have 6 outs to get a pair (3 aces and 3 queens)

outs = 6;   1 - ((47 - outs) / 47 ) * ((46 - outs) / 46 )
Nb. for the turn only the formula is: 1 - ((47 - outs) / 47 )
Nb. for the river only the formula is: 1 - ((46 - outs) / 46 )
Click Fill in and you get the probability ~0.24

About 24% chance

8: Formula - what are the odds for not flopping overcards?

> Fill in
Lets say you get the following cards T and T
This is solved by the formula:

C( 4 * x - 6 , 3 ) / C( 50 , 3 )
Where x is a value between 3 and 13.
e.g. if you have pocket 3 the value x is 3
e.g. if you have pocket tens the value x is 10
e.g. if you have pocket kings the value x is 13
You have pocket tens, then you set x = 10

x = 10;   C( 4 * x - 6 , 3 ) / C( 50 , 3 )
Click Fill in and you get the probability ~0.305
About 31% chance

Notice, though, that those probabilities would be lower
if we consider that at least one opponent happens to hold one of those overcards.

9: Lotto probability?

> Fill in
Lets say there are 36 numbers, and there are 6 winner numbers. You have to hit atleast 3 correct out of 6.
x1 = 3 minimum
x2 = 6 maximum
n = 6 There are 6 numbers to be drawed
a = 6 There are 6 correct numbers
N = 36 There are 36 possible numbers
Click Fill in and you get the probability ~0.0451.
About 4.51% chance

Hand ranking

AAAKoAQoAJoAToA9oA8oA7oA6oA5oA4oA3oA2o
AKsKKKQoKJoKToK9oK8oK7oK6oK5oK4oK3oK2o
AQsKQsQQQJoQToQ9oQ8oQ7oQ6oQ5oQ4oQ3oQ2o
AJsKJsQJsJJJToJ9oJ8oJ7oJ6oJ5oJ4oJ3oJ2o
ATsKTsQTsJTsTTT9oT8oT7oT6oT5oT4oT3oT2o
A9sK9sQ9sJ9sT9s9998o97o96o95o94o93o92o
A8sK8sQ8sJ8sT8s98s8887o86o85o84o83o82o
A7sK7sQ7sJ7sT7s97s87s7776o75o74o73o72o
A6sK6sQ6sJ6sT6s96s86s76s6665o64o63o62o
A5sK5sQ5sJ5sT5s95s85s75s65s5554o53o52o
A4sK4sQ4sJ4sT4s94s84s74s64s54s4443o42o
A3sK3sQ3sJ3sT3s93s83s73s63s53s43s3332o
A2sK2sQ2sJ2sT2s92s82s72s62s52s42s32s22
Sklansky's adjusted starting hands ranking by groups 1-9 (from wikipedia)
1 2 3 4 5 6 7 8 9

Pokerstove top starting hands ranking, displays top 1,2,3,4,5,10,15,20,25,30,40,50 percent


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