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Checking & Calling

This essay is about a subject that is admittedly not that important as far as yoiur daily poker winnings are concerned.  However, it concerns a question that is frequently raised among good lowball players in California and elsewhere. 

The question is whether it can ever be the correct play to check and then call after-the-draw with a seven low. As far as I know there has never been a definite answer given in print. I am now about to give that definite answer.

First, I should explain why this question even comes up.  It is because of the sevens rule that is used in almost all limit lowball games.

The rule says that if you check a seven low or better after you draw and then call a player who has bet behind you, you must return his last bet if you beat him. 

You will still win the pot but not the last bet. Of course, if he has the better poker hand you still lose that last bet. In other words, once you check a seven after-the-draw, you can only lose bets, not win any

Now there is no doubt that the situation might arise where you should check a seven with the intention of folding if someone bets. This should also be done if you are sure that you will only be called if you are beaten, as well as only bet into if your are beaten. 

The tougher question is whether it can be right to check and then call with a seven, especially in a heads-up situation. To examine this further, let’s take a situation from a $ 10 “blind” game.

You are dealt:

You  raise it to $ 20. A tight poker player makes it $ 30, and you make it $ 40. He calls, you stand pat, and he unhesitatingly draws one card.  At this point you can put him on something like to draw to.

For the sake of analysis, let’s say that you know that he has this exact hand. Taking into account the cards in your hand, this gives him twelve cards to beat you as well as four cards to make him an eight low and four cards to make him a nine low. Should you now check your pat seven after-the-draw?

If you do, you must certainly call if he bets, since he will bet an eight low as well as his better hands. If the bet is $ 20 you will be getting almost 5-to-1 odds from the pot, even though you must refund his bet if he is betting the eight. 

You, however, are only a 3-to-1 underdog, since you will still beat him if he catches four of the sixteen cards that will make him bet.  (I’m assuming he will show down a nine low.)

How you play this hand depends on how you think he will play.  Let us take three cases.

Case No.1: If you bet he will call with an eight low and raise with a seven or better.
Case No.2: If you bet he will raise with an eight or better and fold otherwise.
Case No.3: If you bet he will call with a nine low and raise with an eight or better.

(In all three cases, It is assume that he will bet an eight or better if you check.)

Case No.1 is not only the simplest but is also how the typical player would play poker play. Against him you should bet but then fold if you are raised. If he does make an eight low, you win a bet from him. 

If you check you have to call in case he made an eight but if you do, you have to return that $ 20. As long as the threat of a raise doesn’t really hurt you (because you don’t have to pay it off), you do better by betting than calling.

Let us work out Case No.2 according to mathematics of poker. First, let’s see how you do betting. To do this we really must only consider the sixteen times he make his hand.

Since he will raise with an eight or better, pot odds force you to call his raise.  Therefore, four times you win a double bet ($ 40) and twelve times you lose $ 40.

This works out to a total $ 320 lost in sixteen trials.

-320 = (4)(40) –(2) (40)
or an average of $ 20.

20 = 320

However, if you check and call, you lose $ 20 twelve times and break even four times, (since you have to give him his money back) for a net loss of $ 240 in sixteen tries.

-240 = (12)(-20) + (4) (0)

or $ 15 per trial.

15 = 240

This is a case where it is correct to check and call.

What about Case No.3? Once again, we will work is out mathematically. If you bet, you once again must call his raise. However, we said that he will now call your bet with a nine low and raise with an eight or better. 

After twenty trials, on average you will win $ 20 four times (when he makes a nine); win $ 40 four times (when he raises with an eight); and lose $ 40 twelve times (when he makes a seven or better). This is a net loss of $ 240 after twenty decisions.

240 = (4)(20) + (4) (40)-  (12) (40)

Checking results in a $ 20 loss twelve times and a refund to him the other eight times, which is also a $ 240 loss

-240 = (12) (20) + (8) (0)

or an average of $ 12

Now the decision is a toss-up. If there is any chance at all that he will call with a ten low (or that he won’t raise with a seven low), the right play is once again to bet.

Without going into complicated poker mathematical formulas, we see that situations can occasionally arise in which it is correct to check and call with a seven low. 

They occur when :

1.The pot is large.

2. Your opponent will not call with many hands worse than yours.

3. Your opponent is a tricky player who occasionally raises (if you bet ) with a hand that you can beat.

(In practice this situation can really only occur when you have a pat hand.)

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