What's wrong w/ these odds

If I need a particular card, the odds are 1 in 13

If I need a particular suit, the odds are 1 in 4...

Of course these chances are modified by what is in your hand and the board......... and these odds are approximate - not accurate.....

So, if I have four suited cards at the flop, the odds are 1/4 plus 1/4 modified slightly downward because of the cards shown.....

If an Ace is shown on the flop, the chances of another player having a pair of As is 8/13 .....on a nine player table....if they stayed in...

I know this approach is not accurate but it does allow a simplistic approximation so that more energy can be put into competitive analysis and position play.........

Now, shoot me down....I have thick skin....

It modifies more than slightly down on flush cards to 1/5. Four card flush on flop is only 36% to hit. I think alot of flush chasing is due to people believing they have 1/2 chance of hitting it.
I'm not sure how you came up with 8/13, because there are 8 players and 13 diff cards?

FR A flop if all aces stay in and you don't have one 72% someone does. If you have one 57% someone else does. Is that right, Zach?

The way most people do it is calculate # of outs. Now technically this number would be divided by 47 on the flop and 46 on the turn, but most people just double the number and convert it to % (basically dividing by 50) and add ~1 for the difference. I've seen charts before with exact % and estimated % with the double+1 and they're within 1% I think unless you're calculating 1 or 2 outs or something.

You might think this with a totally, completely random deck.

Flush, flop you have 4. That means there are only 9 left of the 47 cards you don't know about. 9/47 is a bit less than 20%, so with 2 streets you have a bit less than 40%. Figure that there were likely a few of you suit mucked along the way, and conventional wisdom puts hitting the flush with 2 streets to go in the 25% range (+/- several % pts). Thats also the range to hit a OESD, and for the board to pair filling your set into a boat.

As fewer seats are occupied, the odds get purer, and in heads up, could approach absolute perfection. But with a limpish table, i.e. many lookyloo's, even though the odds say stay, reality might (like in a tourney) say, don't bother.

IMO. This is more how I deal with odds than factual.

Another good odds oddity is in the small blind when it is mucked to you. According to Harrington on Holdem, in the last chapter of Vol 2, he says it is always right to call in a heads up situation regardless of your cards. Logic being you only have to win 1 time in 3 to break even. That chapter is about HU, and the only difference is that at that point (actual HU) you have a ton of chips (probably), and the deck is closer to pure (thus more accurate odds prediction). In a sb/bb setting, there are all those mucked cards lurking, and you know they were cards that didn't get any interest, so one might figure that the suit distribution in the muck was flat, and it was likely loaded with raggy cards (no aces/kings ).

ok, but using the approach of 47 unknown cards, unless for some reason we know that our suit is more likely to be "mucked along the way" than other suits (ie someone would call with hearts but fold with clubs), this doesn't matter. Now if there are 2 hearts on the board and we get a few people call a flop bet, that may increase the odds that at least one other is also drawing to the flush, decreasing the # of outs.
The problem is that reality may actually say the odds are better. Over the long run when dealing with unknowns, they will cancel each other out. As I said with flops that favor more people with a certain suit calling you could use your logic, but most of the time we can't do this and the odds are pretty much 9/47 or 9/46 which is around 20% each.

This is actually interesting, and you're definitely right. Although I'm pretty sure in HOH he said it was right to call if we knew our opponent would check. Personally HU in the SB I'm raising most of the time. Another difference between HU and a bigger table when it's folded to you in the SB is that you have the button in a true HU game.

But that actually brings up a decent study, see what kind of distribution the big blind has if we assume a standard range for the 7 people who folded and it's to us on the SB. Of course folds would indicate less aces, but A2 in UTG won't be calling most of the time. See how different the distribution is from a true distribution with no folds.

excellent thread... excellent posts.

I just got the Harrington on Hold'em Vol 1 & 2. I cant wait to read both of them atleast a couple times. lol then i might be as smart as these fellows

If your game is based and leans toward an odds based game then where is it wrong to call with ATC in a SB/BB face off. We can never be sure if BB will raise until at least a few attempts. I have found that better players in the BB will seldom raise and are content to see a flop, even if they are sitting with good cards. In which case a better player figures he was looking at first to only pick up the sb, but there may be more coming. SO he will check to a completion, fold to a raise unless he is solid, and reraise any habitual play from the guy to his right.

Your right about essentially having to assume a flat distribution accross the muck. Early positions might muck QJ, where late position would not, same with suits. Pairs are always playable from any position, but with no way to tell, the flat distribution must be assumed.