I am beginning to wonder if I remember anything about stat at all. :smack:
I’m just doing some probability exercises with respect to simple five-card draw poker hands. I’m not having any trouble with the more complex draws (e.g. 2 cards to three of a kind). But the one-card draws have me flummoxed.
Starting hand is a four-flush. If I draw one card to try and fill the flush, the odds are (13-4)/(52-5) or 9 (remaining hearts) out of 47 (remaining cards)… right? That comes up 1:5.2, but the stated odds are 1:4.2
Ditto for filling a closed straight. There are four cards that will fill the straight, so the odds should be 4/47 or 1:11.75. Stated odds are 1:11.
Open straight, while we’re at it, should be eight cards from 47, or 8/47 or 1:5.9. Stated odds are 1:5.5.
What the HELL am I doing wrong?
(Insert lament about “poker” on the web meaning 99.99% community-hand games; I couldn’t even make a standard draw poker chart come up. Jesus the Mechanic wept.)
For the drawing to a flush, the PROBABILITY you get the flush is 9/47. The probability you don’t is 38/47. The ODDS are the ratio of the probability you get the flush to the probability you don’t. In other words, 9/47 : 38/47, or just 9:38, which is 1:4.222.
My assumption is that when you did the “odds,” you found the probability of success and used that as the odds, i.e., 9:47 would give you 1:5.2.
Probability and odds aren’t the same thing.
Likewise, for a closed straight, the probability you get the card you need is 4:47. The ODDS, then, are 4:43 --> 1:10.75.
Open straight, probability is 8:47. Odds are 8:39 --> 1:4.875.
Obviously, the last two don’t agree with what you posted as the “stated odds.” Not sure why, but maybe the probability v odds discussion will help enough.
EDITED TO ADD: For the “open straight,” it’s possible that maybe the “stated odds” are looking at completing a 4-card straight which could include, say, A-2-3-4, in which case there aren’t as many outs because you can only complete one end of it. I’m not sure if that counts as an “open straight.” And rounding could be the other error (10.75 vs. 11.)
I’m sure someone will be along shortly to answer, but does the discrepancy lie in the fact that there are other players at the table and there is a probability some of their cards will be the ones you need but unavailable for you to draw?
No. Since you don’t know what cards they have, you’re still equally likely to draw any of the remaining cards. There are still 47 cards that you could draw. Of course, if they revealed their hands, the probability / odds would change dramatically.
That’s because everybody plays Texas Hold’em, or Omaha.
OK. A the chance of drawing one of 9 hearts out of 48 (you’ve got 4 cards in your hand, not five) deck are 9/48 or a little worse than one out of five (17.5%). The odds - the chance you’ll make it, are therefore approximately 1:4, or 82.5:17.5%) One chance you’ll make it, 4 chances you won’t. So if you’re trying for the flush, and the flush is the only way to win, you need to make back you’re original investment. If the pot is $45, and it costs you $10 to play. You will average, on average, make $5 ( You"ll lose $1O 4 times (-40) and win $45 once, four out of very time you make a mistake.
So,the 1:4.2 number correct. You just forgot that you have 4 cards in your hand, not five.
You made the same mistake with the second and third examples. It’s one card out of 48, not 47.
Why can I hear my Stat 101 teacher saying that so clearly… now? :smack:
Thanks. Stat: it’s all in the setup.
Correct. Unless you see dealt cards, the remaining deck is ALL cards you aren’t holding.
Thanks for letting me know. :dubious:
I really miss traditional poker. When it’s so out of fashion that it doesn’t exist in a Google search (or at least is swamped thousands to one by community game hits) you know you’re a dinosaur. Oh, well. Rahr.
Nope, sorry. Calculations for draw assume five cards dealt and in the hand; since discards aren’t part of bettering the hand (unless you’re really stupid, really crafty or really drunk), they are nulls and excluded from the calculation of odds. All draw odds are calculated starting with the unknown 47 cards in the deck.
But it all boils down to (and I can hear Mr. Shapiro saying this clearly) “Inverting probabilities does not give you the odds.” Oops.