Hello everyone,


I am reading book from Owen Gaines named Poker maths that matters. And there is lesson about combination of villians hole cards. there are few questions in the end of lesson which i need help with. the answers to the question doesnt match mine plus there is no explanation given about the answers.



5. Hero: A♦J♠
Villain: AA
Board: 7♥5♥2♣4♣
How many combinations are there in villain's range?
Answer: 4


however i believe it should be 6 as 6 combination of AA can happen.


7. Hero: 6♥7♠
Villain: QQ, A♦3♦
Board: 4♠7♦Q♦2♠
How many combinations are there in villain's range?

Answer: 4


can anyone who read the book help me understand why the answer is 4 for both questions?
for the second question it says if two cards of same suits are exposed then 55 cobinations can happen and for qq as one Q is on board the combinations that can happen is 3 so i am confused about the answer posted at back of the book.



Thank you

For the first scenario. I think there is only 3 combos of AA. You hold the Ace of diamonds. So, that removes some of the combos. I don't know where the 4th combo comes from. It's either a typo in the book, or you didn't include something.






He can't have:



because you hold one of those aces in your hand.


A similar thing happens in the second scenario. With one Queen on the board, there are only 3 combos of QQ left, and the one combo of Ad3d makes 4 total combos.

thanks for replying.


yes in first question three combos. you are right.
can you explain how just one combination of Ad3d is only possible? i am sorry i didnt understand it

There is only one in a deck and only one in a deck. There's only one combination of that specific holding. Any other A-3 combination won't be suited in diamonds. That leaves the following possible hands for the villain.









Note: I haven't read the book, so I am going to assume there's a reason for these ridiculously narrow hand ranges. I assume it's to give you an idea about how knowledge of one card can dramatically reduce the number of certain combinations you opponent can have. But, in real life, there's never a situation where you know a player's range is limited to exactly Ad3d or QQ.

Thank you for explaining.
Yes, it is to help beginners understand how combination works.


My reason for asking particularly about A♦3♦ was, it is written in that book if 2 cards of same suits are exposed and as i don't have diamond card, 55 combinations is possible(11,2). that's the reason I was confused how just 1 combination is possible.

Originally Posted by blacknight92

Thank you for explaining.
Yes, it is to help beginners understand how combination works.


My reason for asking particularly about A♦3♦ was, it is written in that book if 2 cards of same suits are exposed and as i don't have diamond card, 55 combinations is possible(11,2). that's the reason I was confused how just 1 combination is possible.

Yes, if you can see 2 of a suit, and don't have the suit yourself, there are 55 combinations of suited cards. Those include Ad3d as one combination. It includes a bunch of nonsense combinations that you only need to worry about if someone plays all suited cards. Most people won't play Jd3d or Td4d. People shouldn't play stuff like 9d5d, but they might because it could make a straight (lol).

As an example: On a flop of where you hold no hearts, your opponent could have the following 55 combinations.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Hopefully, you recognize that some of those combinations are less likely to be played than others. I have only met one person who truly played all suited hands. Most people will toss about half this junk.