Calculating favourites
 

I was reading Lee Jones' "Winning Low-Limit Hold'em" on the weekend, and got stumped by one of the statements.

He says, paraphrased, "consider the situation where you have AKs and your opponent has 78o. You are a 2:1 favourite before the flop".

I buy that AKs is a far better hand than 78o, but how does he calculate the 2:1? He doesn't give any justification or explanation of how the odds are calculated. I have a math degree, so I should be able to figure out a way to quantify this, but I'm not sure how he's getting that exact ratio.

I'd like to understand the general rule for figuring out which hand is a favourite over another. Is it the number of outs you each have? The number of flops or boards that give you a hand?

MathBabe

you are roughly a 3 to 2 with AK vs 78 (60%, 40%...if they are both unsuited)....the reason for this is even though AK is a dominant hand over 78 you still have nothing but high card. If a 7 or 8 hits the hand wins as long as a A or King doesnt hit... when you are all in and cant be bet out (if the flop is 7,J,Q, youd probably fold to a bet with 78, but all in u get to see all the cards) the chances of AK are only a little better than 7 8. There is roughly a 40% chance that you will hit a 7 or 8 and he will miss his king or ace.

If your AK is suited, and the 7 8 is not, you have to figure in the flush potential even if he hits and u miss, so your odds go up to roughly 65/35

hope this helps

sorry i didnt realize you wanted to know how it was calculated... you do this by knowing the amount of unseen cards and your number of outs. AK vs 78 assume you hold 78.... Preflop there are 50 unseen cards and you have 6 outs (3 sevens and 3 eights....keep in mind if he hits a king or ace you know have to recalulate bc you now need 2 cards to make an out, not just one). On the flop there are 47 unseen cards and you have 6 outs (your % would drop to about 25 if you miss the flop, and much lower if u missed and he hit), after the turn there are 46 unseen cards and 6 outs. So you get your % of hitting a card in each instance (ur 6 outer would be 12.5% if you also missed the turn)

Hope that clears it up

This should be right up your alley, MathBabe. It's just math.

For fun, deal out two cards to you (AsKs) and two cards to me (7h8d)... Now deal out a 5 card board and see who wins. Now deal out another 5 card board and see who wins. And then another. And another. And another. Repeat untl you've dealt out EVERY possible combination, keep track of who wins along the way, and you'll have your answer.

You may want to use a computer to help out with this task ;)

Alternatively, you could understand that this sort of thing has been done before, these numbers are proven, and you can just commit them to memory.

sorry i realized i was off by 2 each time...since you know your opponent holds an AK you can take those cards out of the unseen ones.... there are now 48 unseen cards preflop, 45 post flop, and 44 on the turn.

A pretty shitty book with a great section with odds tables is Ken Warren Teaches Texas Hold 'em. He's got more charts than the bible's got psalms.

Exactly!

That sounds a lot like computer science, not math! I know you know there are 205 million combinations on the board possible. I'm wondering if I can come up with the simple, elegant way to calculate the ratio.

Well, that's a lot less fun. I'll fiddle around with my own calculations and spare you folks the pain, unless someone else is actively interested. I realize it's of limited use!

MathBabe

Remember, the order the cards come up doesn't matter in this calculation... and to make your life easier, you can forget about suits... that will dramatically reduce the permutations as well.

The point is, that's where the numbers come from. And the bigger point is once you believe that, there's no need to recreate it.

Favorite...
 

I just notice you spelled "favorite" wrong,. What is with all the freaking Canadians around here??? :D

Better:

What do you mean, flush?
 

I'm actively interested. I'm having a hard time with suits, though, and it's not a lot of use if I have to pretend that flushes don't exist...

babe do u play on stars? i recognize ur picture from somewhere

Yup, I played in the last TPF invitational - you probably saw me there!

MathBabe