Calculating poker hand probabilities

[@sophomoremd]

Exactly what I was looking for! I wish I could find something like this for 7 card games like Texas Hold 'Em, although I assume the math is mostly similar.

[@mathaha2922]

@@sophomoremd Glad to hear it! Yes, the principles remain the same for other types of poker.

[@giwdul]

Does this mean that the calculations (values) change in Texas Hold 'Em or do you mean that they stay the same?

[@mathaha2922]

@@giwdul I would say the exact probabilities would not remain exactly the same, but their ordering would.

[@giwdul]

@@mathaha2922 Thanks, How should you change in the equations to get these new probabilities? Could you give an example?

[@mathaha2922]

@giwdul Sorry, you'll have to do some searching, I think. But it's a good question.

[@iliabh4176]

Beautiful insight to the game of poker

[@mathaha2922]

@@iliabh4176 Thanks for the kind comment!

[@coderassistant]

Good explained, thank you. I love mathematic too

[@mathaha2922]

Glad to hear it!

[@Y7Y01]

Hey! I wonder if you can clarify why you chose (10 1) while we need 5 cards. it was in minute 4:52 Thanks

[@mathaha2922]

Because if you don't consider the suit, there are exactly 10 different straights: A2345, 23456, 34567, 45678, 56789, etc. It is true that we need 5 cards, but once we have chosen, for example, the lowest one, the others are already clear. Hope that helps.

[@SweetPlain]

​​@mathaha2922 shouldn't it be 9C1? A2345, 23456, 34567, 45678, 56789, 678910, 78910JQ, 8910JQ, 910JQK

[@nihalkumar6695]

Great video, well explained, a shame I had to spend so much time finding it.

[@mathaha2922]

Thanks! And sorry it took so long to find!

[@tonychopper3751]

I think I am misunderstanding. I am confused on the straight flush 10 choose 1. You explained that you cannot start a straight above a 10 with jack and queen because it does not go that far, but you can still have a Q, J, T, 9, 8 straight flush. Should it not just be 13 choose 1, 4 choose 1, and then subtract 4 to account for the royal flush possibilities? So 48 Possibilities of a Straight flush?

[@mathaha2922]

Good question! The answer is that we don't want to double count. 8,9,10,J,Q is the same hand as Q,J,10,9,8. So it's enough to just consider what the lowest card is. If we wanted, we could also just consider the highest card. Or just the middle card, etc. Hope that helps!

[@tonychopper3751]

@@mathaha2922 Ohh I see, thank you so much for the response. Very helpful.

[@DonMattoncino]

Wow! Interesting insight to the game of poker. I never looked at it like this. What’s the probability of the royal flush?

[@mathaha2922]

Good question! There are exactly four royal straight flushes (one for each of the four suits), so the probability would be exactly 4/2,598,960. In other words, you have a 0.000153908% chance of being dealt such a five-card hand.

[@johnwaugh8035]

This is a pretty interesting video and I like the way the maths behind the chosen combinations is explained intuitively. But the sound is terrible. You have evidently invested in a big microphone so please turn it up - exponentially. (m, v)! ^ (m, v)! = Microphone Volume! x Microphone Volume!.

[@mathaha2922]

Thanks for the tip!

[@nynthes]

hii, could you do a video on 7 card poker (texas holdem)? im struggling to figure out how to calculate the probabilities

[@mathaha2922]

Thanks for your comment and the suggestion. Do remember that even in Texas Hold 'em there are exactly 5 cards that make up your final hand.

[@patricksutton4662]

For straight flush, wouldn't it be 9 choose 1 because royal flush is its own hand?

[@mathaha2922]

A royal [straight] flash -- as I treat it here -- is simply the highest form of a straight flush.

[@patricksutton4662]

@@mathaha2922 Oh, okay. I see what you did.

[@sven9487]

How do i convert these probabilities to 8 hand poker?

[@mathaha2922]

Good question. I don't know the rules to that game. But the principles remain the same for computing the probabilities.

[@jeremyhannah283]

Good video, but shouldn't the number of conbinations for a straight be 9 choose 1? 10 choose 1 works for a 4 hand deck, but I think 9 is more appropriate with 5 cards. Unless you are treating ace as high and low?

[@mathaha2922]

Thanks for the question. I would say 10 choose 1 because there are 10 cards that can function as the bottom (or top, or middle, etc.) of a straight and we must choose one of them. (And yes, the Ace can be high or low.)

[@jungwisely8725]

Nice Video

[@mathaha2922]

Thanks!

[@bubuz60]

Why the 4 1 for 3K?

[@mathaha2922]

The 4 choose 1s are for the single cards, the ones not involved in the 3 of a kind. For each of these two cards there are 4 suits to choose from, and we choose 1 of them. I hope this helps.

[@prob_io7299]

You speak too silently, increase the volume of your videos after you make them please

[@mathaha2922]

Thanks for the feedback!