Posted: Wed Jun 22, 2005 10:59 am Post subject: Confused about # of cards
I have always played poker by my reads and feel for others at the table. I am starting to dive into the Odds and Probabilities and have a "newbie" question I am hoping someone can explain to me.
Scenario:
I hold K9 off against one opponent. . Flop is K94 rainbow. What are my odds of hitting the full house?
47 cards unaccounted for. 4/47 is around .085 or an 8.5% chance of me hitting, correct?
Here is where I am confused. The number of cards left in the deck says 47. But if there are say 10 other players at my table that's 20 cards that are dealt out to begin the hand. 52-20=32 left "in the deck". Take out the flop and burn card, 32-4=28 cards left "in the deck".
Why are the cards that are out of play and not able to affect the outcome of the hand factored in to the math?
Joined: 10 Sep 2004 Posts: 4781 Location: Alpharetta, GA
Posted: Thu Feb 21, 2008 1:45 pm Post subject:
Your first post, and no one even bothered to answer it? Shameful of us, really. Better late than never, and for those who might stumble on this post and not have already figured out the answer on their own...
You use 47 cards (for the turn draw only) because you only know 5 cards (your 2 and the flop 3), so you can't assume anything about the 18 other cards dealt out to the table. So the 4 cards you need are equally likely to have been dealt already or still be in the deck and the chance that any of given card you haven't seen being one of them is 4/47, or 8.5%. Note that while there's an 8.5% chance the turn card is one of your 4, there's an 8.5% chance that any single card your opponents hold (or folded) is a K or a 9 as well.
Joined: 10 Sep 2004 Posts: 4781 Location: Alpharetta, GA
Posted: Wed Feb 27, 2008 12:06 pm Post subject:
doubleup wrote:
So pre-flop with K9 you have a 12% chance of pairing up? 6/50 = 12%?
No, it's not that simple. To figure the chances of hitting at least one of your hole cards on the flop, you need to know the chances of not hitting either of them for three cards. That's:
44/50*43/49*42/48 = 67.57%
So you'll at least pair at least one of your hole cards (this calculation includes other things like flopping trips/quads/FH) 32.43% of the time. The same would apply for any hand where you have two different hole cards.
Holding any two unpaired cards, you will pair one of them 33% of the time.
In other words, when you raise with AK, the flop will miss you, on average, 2 out of 3 times.
When calculating the % of hitting your outs after the flop, a nice shortcut to know is the rule of 2 and the rule of 4.
Your % of hitting on the next card is the number of outs times 2 = 4 outs x 2 = 8%.
With two cards to come (for example, you're all-in on the flop), your % is the number of outs times 4 = 4 outs x 4 = 16%.
These numbers aren't the exact %, but they're good enough in the heat of the battle.
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