Monday, October 19, 2009

Reasons to Limp-in on Third Street

In the previous post, I concluded that you gain an edge from attacking players who limp-in on Third Street with three low-cards, and fold immediately if hit with a high-card on Fourth Street. That raises the question: Are there situations where it is correct to limp-in on Third Street? As a general rule, open-limping is a weak play. If you intend to play the hand, and have the first opportunity to complete the bet, you should complete and force the players acting later to define their hands. It is also risky to allow the bring-in a free card. However, there are situations when limping has advantages. The situations I will analyze are when you act after multiple limpers, and you (1) hold a live-pair other than Aces (2) hold the lowest hand.

These situations occur frequently in low-limit Seven-Card Stud High-Low (Stud-Eight) games, when it is common for several players to limp-in holding just about anything. These players are hoping for a cheap card on Fourth Street that will somehow improve their mediocre starting cards. As a general rule, completing the bet after these players have limped-in, will not drive them out. Even though they would have folded, if a bet were placed before they had a chance to act, they now feel committed to the hand, and will call, if you bet.

(1) Pairs other than Aces. In Stud-Eight, pairs can present problems because they are a poor start for a low-hand, and in many cases, a poor start for high-hand. Mid-pairs, such as 9s and 10s are almost unplayable against a large field. The hand is unlikely to make low, and stands a good chance of being dominated by for high. A low-pair with a low-kicker, has a better chance of making a low-hand, but a greater chance of being dominated for high-hand. However, rolled-trips are powerful holdings, and in cases when the trips are low, an extremely deceptive holding. Rolled low-trips often look like the best low-hand, when in reality it might be the best high-hand.

Consider a $1-2 Stud-Eight game with a $0.20 ante and a $0.25 bring-in. Eight hands are dealt, and three players limp after the bring-in. You hold a low-pair with a low-kicker and your cards are completely live. Therefore, when it is your turn, the pot has $2.60. If by limping, you end the action, the pot is offering 10 to 1 on your $0.25 payment. What are the odds of making trips? You have seen 10 cards--the three in your hand, plus the other seven door cards. Only two of the remaining 42 unseen cards make trips, so the odds against trips are 20 to 1. However, the implied pots odds are much greater than the current 10 to 1 the pot is paying. If you make trips, a strong possibility exists for you to scoop what could be a $20 to $30 pot. You will have to contribute a minimum of $7 to reach a showdown, but with trips after Fourth Street, you are a heavy favorite.

However, if you complete the bet, instead of limping, your initial pot odds are greatly reduced. If you complete, and the other three players call, you have contributed $1, while the others contributed $4.85. The pot is now paying about 5 to 1, while the possibility of making trips on Fourth Street remains 20 to 1. You need much greater implied pot odds to have an edge compared to the case of limping. And remember, rolled-trips is not a lock, the hand will be outdrawn at times.

This analysis assumes that you will fold on Fourth Street, if your hand does not improve to trips. Against a large field this will often be the case. Limping, followed by a quick fold in the case of no improvement, is a viable strategy in circumstances when aggression will not drive players out. You will almost always need to have strong cards against a large field of limpers, because, in most cases, at least one person will improve, and stay until the end.

(2) Holding the lowest hand. Low-cards, that are unsuited and unconnected, are generally weak starting cards in Stud-Eight. These cards usually compete for just one half of the pot, so the pot odds are greatly reduced in comparison to a hand that can scoop. However, if you are the lowest hand on the board, against a number of players who have limped-in with high cards, it can be worth limping to pick up a cheap Fourth Street card. In this case you are looking to pick up a low-draw, not to make a low-pair. If your low-draw is completely live, there are 20 unknown cards that can help  (the 9 other low cards will pair your hand). In an eight-handed game with seven other door cards, 42 cards remain unseen. You are looking at "coin-flip" chances of picking up a low-draw on Fourth Street--20 out of 42, or 47.6%. However, a low-draw is not yet a qualified low, so you will be investing money on the later streets before you know if the hand has any value. But on later streets, a low-hand against multiple highs, can be a profitable holding because it can freeroll and jam the high hands.

However, limping with low-cards, after multiple players with low cards have also limped, is a questionable play. Even if your hand is the lowest of the lows on Third Street, the numbers of outs that you have to make a "viable" low-draw on Fourth Street is greatly reduced. By "viable," I mean a card that will allow your hand to remain the lowest on the board. Being second-best low is a dangerous position in Stud-Eight. Suppose you limp-in with a 6-high, such as 2, 3, 6. There are only 12 cards that can maintain a 6-high low-draw after Fourth Street (As, 4s, 5s). Even if none of those cards are on the board, chances are that some of the limpers with low door cards, have some of your outs for hole cards. The realistic chances of having a 6-high low-draw after Fourth Street are only about 25%.

In summary, I think there are some situations where late limping is a viable strategy. But, those situations are ones when a questionable holding after Third Street, has a small chance to improve to a powerful holding on Fourth Street. Because the improvement chance is small, the Fourth Street Card should be seen cheaply.

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