advice: hit back button before your head asplodes
We've all seen the riddles when we were kids about how if you add and subtract x amount of dollars, you come up short by a dollar or so at the end. I took that brilliant idea and applied it to card combos!
note: scroll down 3 or 4 paragraphs if u already know what i'm talking about.
There are 1326 distinct (meaning suits are of importance) starting hands in hold'em. We take 52 (any card) x 51 (any remaining card after the first is picked) = 2652. Then we divide by 2 because order does not matter. 7d 7s is, for all practical intents and purposes, the same hand as 7s 7d.
We can do the same thing for a specific hand. For example, for all combos of AK (suited and unsuited), we have 8 cards to choose from, then 4 to choose from = 32, divide by 2 since order does not matter. We come up with 16 combos of AK.
If we take this a step further, if we want to find out how many AKo combos there are, we can take any one of the 8 A's or K's, and there will be 3 of the offsuit matching variety. 8x3/2 = 12. It should be simple to figure out that there are only 4 combos of AKs, but the maths are very simple... any A or K can make an AKs combo, but only the matching A or K suited will complete it... so 8x1/2 = 4.
NOW, say we hold exactly Ac Kd, and we are trying to count up all of villain's AK combos. It should be obvious that we have to take away all of the AK combos that contain either Ac or Kd. This is not much of a big deal. There are 4 combos that contain the Ac, so we have to knock all of those out. There are also 4 combos that contain the Kd, so we have to knock those out. There is one combo that contains both, but we don't want to count it twice, so in total we knock out 7 of his possible combos.
So know we want to figure out all of his. He has 6 remaining A's and K's to choose from. First we want to figure out all of his AKo combos-- any of those 6, multiplied by 2 (since the 3rd one would make an AKs combo), then divided by 2 since order does not matter = 6. The suited combos are easy to figure out since we have already knocked out AcKc and AdKd by holding one of each suit.
So we knocked out 7 combos, and villain has 6 possible combos of AKo and 2 possible combos of AKs. WHERE DID THE LAST CARD COMBO GO??????
head asplode
