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I'm creating a live odds tracker and need to know the odds of making every possible hand at any point in the game, the information I have is:

Number of Outs
Number of cards left in the deck
Cards needed to make hand

I need to know how to combine these 3 elements in an equation to calculate the odds of making the hand, a flush in this case, so for example pre-flop, with 3 players and cards dealt to me being Jc Qc it would be:

Number of Outs - 11
Number of cards left in the deck - 46
Cards needed to make hand - 3

So far I have the following equations that I've found in other articles but I'm unsure how to combine them to do what I want:

    'The % chance of getting an out of the next hand can be calculated by (outs / remaining cards) * 100
    'To calculate the chance of getting 1 out on the turn or the river do the calculation above for each and add them together (3 / 45 = 0.0666) + (3 / 44 = 0.0681) = 0.1348 * 100 = 13.48%
    'To calculate the chance of getting 2 outs on the turn & river multiply the calculations by each other instead ((3 / 45 = 0.0666) * (3 / 44 = 0.0681) = 0.0045 * 100 = 0.45%
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    What precisely do you mean by number of outs? Why would being dealt JcQc mean you have 11 outs?
    – Andrew Chin
    Aug 13, 2020 at 18:33
  • Sorry, I've edited the question to show that I'm looking to make a flush, so with 13 cards in a suit, 2 of which I already have there are 11 left of that suit and I need 3 of them to make a flush.
    – user2096512
    Aug 13, 2020 at 18:37
  • Do you need precisely three of your suit on the board, or would four or five also be favourable?
    – Andrew Chin
    Aug 13, 2020 at 18:43
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    Also, "number of cards left in deck" is not useful. You need number of cards you haven't seen. Probability is a measure if information, so what's important is what you know and don't know. Whether the unseen cards are left in the deck, or your opponents' hands, or the burns, is not relevant.
    – Lee Daniel Crocker
    Aug 13, 2020 at 18:49
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    How would you know 11 of them are clubs? There may be as few as 7 if you have two other opponents.
    – Andrew Chin
    Aug 13, 2020 at 18:56

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