# Hold'em poker calculator

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### Calculator

enter expression, e.g. 2+2
supported extra functions:
• C(n,r) binomial function (also notated as nCr, eg. C(6,3) = 6C3 = 20)
• h(x,n,a,N) hypergeometric distribution, eg. with a pair hit a set on flop h(1,3,2,50) = 0.115
• hs(x1,x2,n,a,N) cumulative version, eg. with pair hit set or quads on flop hs(1,2,3,2,50) = 0.118

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

#### 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

#### 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

#### 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

#### 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

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

#### 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

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.

### Hand ranking

 AA AKo AQo AJo ATo A9o A8o A7o A6o A5o A4o A3o A2o AKs KK KQo KJo KTo K9o K8o K7o K6o K5o K4o K3o K2o AQs KQs QQ QJo QTo Q9o Q8o Q7o Q6o Q5o Q4o Q3o Q2o AJs KJs QJs JJ JTo J9o J8o J7o J6o J5o J4o J3o J2o ATs KTs QTs JTs TT T9o T8o T7o T6o T5o T4o T3o T2o A9s K9s Q9s J9s T9s 99 98o 97o 96o 95o 94o 93o 92o A8s K8s Q8s J8s T8s 98s 88 87o 86o 85o 84o 83o 82o A7s K7s Q7s J7s T7s 97s 87s 77 76o 75o 74o 73o 72o A6s K6s Q6s J6s T6s 96s 86s 76s 66 65o 64o 63o 62o A5s K5s Q5s J5s T5s 95s 85s 75s 65s 55 54o 53o 52o A4s K4s Q4s J4s T4s 94s 84s 74s 64s 54s 44 43o 42o A3s K3s Q3s J3s T3s 93s 83s 73s 63s 53s 43s 33 32o A2s K2s Q2s J2s T2s 92s 82s 72s 62s 52s 42s 32s 22
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