This is the second in a two-part series aimed at the numerically challenged, statistically phobic, or players otherwise unaware of the degree to which poker dwells within mathematical and statistical parameters. While there's much more to this subject than two articles can cover, it's a start -- an introduction of sorts -- to a topic many players are prone to avoid, even when they know better.

In Part 1 we talked about why the number of opponents in any given hand is important. You learned that there is a gaggle of plays that stand a good chance of succeeding against one or two opponents, but generally fail against four opponents or more. There are also hands and tactics that work better against a full complement of opponents than they do against one or two.

We also discussed the importance of knowing how many times the flop has to hit you when considering how to play your hand. With A-K, one hit will frequently suffice. With a hand like 7-6, you probably need the flop to hit you twice, particularly if someone has raised.

Quick Count Number 3: How Many Times Outs Do You Have?

This concept is analogous to counting the number of times the flop has to hit you. But when you're counting outs, you've already seen the flop and are trying to determine how many good cards are left in that deck. Knowing how many chances you have is vital information when trying to decide whether to continue with a drawing hand.

One of the nice things about Hold'em, as compared to 7-card stud, is that the number of discernable outs is always the same for any given situation. If you're playing stud, you may hold four hearts on your first four cards, but the number of hearts remaining in the deck has to be determined by counting your opponents' exposed cards as well as those you're holding.

But in Hold'em, if you begin with two hearts and two more pop up on the flop, you have nine outs -- two in your hand and the two that flopped subtracted from a total of 13 hearts in the deck. It's that simple. Unless an opponent has inadvertently exposed a heart, any time you flop a four-flush you have nine outs -- no more, no less.

If you flop an open ended straight, you have eight outs. With two pair you might have the best hand right now, along with four additional outs to a full house. If you flop a set, there are seven cards that will help you on the turn. One gives you four of a kind. Three cards will pair one of the board cards and three will pair the other, giving you a full house in either case, and ameliorating any concerns about an opponent catching a card to make a straight or flush.

Even if the turn card is no help, it still provides three additional outs on the river. Now there are nine cards that will pair the board, giving you a full house, along with that elusive case-card that will give you quads.

Quick Count Number 4: What Are the Odds You Need to Know?

It's not difficult to learn how to figure the odds for common Hold'em situations, but there's not enough room in this column to teach that to you. Instead, a chart is provided that you can commit to memory.

Outs	Chance of Success	Odds Against Success
15	54.1%	0.8:1	Draw for a straight or a flush
14	51.2%	1.0:1
13	48.1%	1.1:1
12	45.0%	1.2:1
11	41.7%	1.4:1
10	38.4%	1.6:1
9	35.0%	1.9:1	Flush Draw
8	31.5%	2.2:1	Open-ended Straight Draw
7	27.8%	2.6:1
6	24.1%	3.1:1
5	20.3%	3.9:1
4	16.5%	5.1:1	Draw to Improve Two Pair
3	12.5%	7.0:1
2	8.4%	10.9:1
1	4.3%	22.3:1

 

The odds against an event occurring are shown in the right-hand column. The chances of success, expressed as a percentage, are shown in the middle column, and the number of outs is shown on the left. Is there a relationship between them? Of course. Whenever you flop a flush draw, there's a 35 percent chance of succeeding. That means you have a 65 percent chance of failure, which converts to 1.9-to-1 odds against making a flush.

You can learn to do the math without any special computational ability. It's comforting to be able to do it -- trust me -- and nice to know that you don't have to rely on anyone but yourself to calc the odds. Doing, as opposed to memorizing, also facilitates learning.

Quick Count Number 5: Pot Odds versus Implied Odds

There's no cheap, easy trick here. To figure pot odds, you need to keep track of the amount of money in the pot. The easiest way is to count the number of players active on each round, account for the blinds if they've folded, and be sure to adjust for higher betting limits on the turn and river.

This is half of poker's basic equation: Does the money offered by the pot exceed the odds against making your hand? If you have a flush draw, and the odds against making your hand are 1.9-to-1, you need to know that the pot will more than offset those odds before deciding whether to play or fold. If the pot promises a return of two-to-one on your investment, it certainly pays to call when the odds against your ultimate success are only 1.9-to-1.

But how do you know whether the pot will grow large or stay small? That's where implied odds come in. Implied odds are your best estimate of the money likely to be in the pot once all the betting is complete. This estimate, when compared to the odds against making your hand, is frequently the linchpin in your play-or-pass decision.

There's no formula to follow in making these estimates, but these four guidelines will help:

· Know your opponent.

· Count the pot.

· Estimate the amount of money likely to be wagered in subsequent betting rounds.

· Know your own chances of success.

Otherwise you are navigating without moon, stars, or sextant -- and likely to be lost at sea.