Analysis in Practice

To demonstrate how this analysis works in practice, we will go through two of the examples.

Draw Poker

$5 - $10 Limit

You

Rival (Hidden Cards)

You start with $5 in early position. Each one folds except the player who normally checked to you and who now raises another $5. Suppose you know this player will never make such a play without three-of-a-kind or better. And also suppose that with the antes and your implied odds it would be incorrect to fold even if you knew your rival had a pat hand. Now, the question arises whether you should call the $5 raise or re-raise another $5.

Your rival's raise confirm you he has either trips which may be smaller than your three aces, or a pat hand. If he has trips, you have the best hand and are the favorite to win the pot; if he has a pat hand, you have the second-best hand and an underdog to win the pot. As per draw poker allocation, your rival will have three-of-a-kind about 65 percent of the time and a pat hand about 35 percent of the time. When he has a pat hand, you should of course not re-raise. However, it is almost 2-to-1 he has trips. Will you hence re-raise?

The answer to this would be no because when you only call and your rival draws cards, you can draw one card, as though you had two pair and check-raise after the draw. Supposing he calls your raise, which he will nearly always do, and overlook the little chance of your rival improving to a full house when you do not, you win $30 (plus the antes) by playing this manner - $10 before the draw and $20 when you check, your rival bets $10, and you raise to $20. On the contrary, by re-raising $5 before the draw, and then coming out betting $10 afterward, you win a sum of $25 - $ 15 before the draw and $10 afterward. Therefore, 65 percent of the time your rival has three-of-a-kind, you win more $5 by calling instead of re-raising. Subsequently, 35 percent of the time he has a pat hand (and you do not improve to a full house), you lose only $10 instead of $15, a saving of $5. Hence, under such circumstances, the correct play is to call as it is right most of the time - whether your rival has three-of-a-kind or a pat hand.

The second example is critical one taken from hold'em:

Hold'em

$10-$20 Limit (Small Pot)

(Hidden Cards)

Rival You

Board

Your rival being a good player checked and called your bet on the flop. When the deuce falls, your rival again checks. Will you check or bet your pair of kings?

In hold'em, whenever your rival bets, calls, or raises, good players almost question, "What would my rival have done with that?" After that they think of very possible hands the rival might have to do what he did. Thus, when your rival called your bet on the flop and then checked on fourth street , you try to ascertain what hands he might have that swift him to play the way he did.

Your rival would be slowplaying a better hand than your - say, K, 9 or 6, 6. You calculate there is a 25 percent chance he has such a hand. He may reasonably have a good hand like K, J or K, 10. You figure even those hands at 25 percent, as well. Your rival may have an average hand like K, 4 or A, 9 or 10, 10. The chances of those hands would be at 35 percent. And you figure there is a 15 percent chance your rival has 8, 7 and is drawing to a straight.

You are sure that if you bet on fourth street after his check, your rival will possibly call with his decent hands, with a straight draw and at least call with his big hands. But, this player will possibly fold his average hands because the pot is not big enough to justify calling with them. Hence, after your rival checks on fourth street , the correct play may be to check it right back. Your aim is to bet on the end if your rival checks and call if he bets.

The logic for this play is that, like most of the player, this rival will fold his average hands if you bet on fourth street to prevent having a call couple of times to see what you have. It is simpler for him to call on the end when you check on fourth street , not only because you have made it cheaper but also because you have revealed weakness. Of course, checking is also the better play that 25 percent of the time you have the worse hand. Ultimately, checking on fourth street persuades a bluff on the end.

The disadvantages to checking of fourth street are:

• It gives your rival a free card to outdraw you.

• There is a 25 percent chance your rival has a hand such as K, J or K, 10, with which he would possibly call twice.

It is significant that the pot must be small - say, below $60 in a $10-$20 game - to make checking correct because you gain only one bet by checking and betting on the end into your rival's average hands, but you lose the entire pot if the free card gives your rival the best hand.

Observe that the ratios support checking as the correct play on fourth street .

Rival's Probable Hands Approximate Chances Best Play
Decent hand (K, J or K, 10) 25 percent Bet
Better than Yours 25 percent Check
Average hand 35 percent Check
Straight Draw 15 percent Bet

As you hope your rival to fold his average hands if you bet on fourth street , and you want to win at least one more bet from those hands, the correct play 60 percent of the time is to check. It would be correct to bet only 40 percent of the time. You would normally select the play which is correct most of the time: Hence, you will check.