Seven Card Stud Eight-Or-Better: Chasing The Low

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In Seven Card Stud Eight-or-Better (Stud 8), as in all split pot games, the object of the game is to scoop! Our initial focus should be on seeking out situations where we hold the advantage, and avoiding those where we don’t.

However, occasionally things don’t work out exactly as hoped and we can get stuck with only a low draw against what appears to be a strong high hand.

When this occurs, do we have the odds to chase the low even when it appears as if we have very little or non-existent scooping chances? While there are many issues to consider, this is primarily a math problem. Let’s begin by taking a look at some numbers.

Suppose we are in a six-handed $40-$80 game with a high $10 ante, and on fifth street, two players hold the following hands:

(K K) K 9 K
(A 7) 4 3 10

Only one bet went in on both third and fourth street, so there is $220 in the middle after the first two streets. If the player holding quads bets, exposes his hand (assuming this in a card room where this is allowed), and then tells us we need to fold as we are only drawing to half, is this a correct statement? Is he being nice, or he is trying to coerce us to do something that benefits him?

The money that’s currently in the pot is no longer ours, therefore the expectation of folding is simply zero. If we call both fifth and sixth street, we are risking $160 to win $110, half of the $220 in the middle at our fifth street decision point. Theoretically, if the expectation of calling is positive by a penny, then that is what we should do.

Assuming no knowledge of the other up-cards, there are 16 cards out of the 42 left that will complete our low, and this draw will come in around 62% of the time. So is this a large enough probability where calling has a positive expectation?

A simple equation will provide the answer:

Expectation of Calling = (62%)($110) + (100-62%)(-$160) = $8.08

Under the assumptions above, calling does approximately $8.08 better than folding, so in theory we should call. However there are certain situations where we may want to fold anyway. After all, we are putting two big bets at risk where the net gain is only around one-tenth of a big bet.

In tournaments, we should tend to fold, as the chips that you lose are worth more than you win. And in some bubble situations, the chips that you could potentially lose may be very damaging to your stack position.

You may also want to fold in a cash game if you are taking a shot at a higher limit and don’t want to take the variance.

Exposed cards can make a difference and should always be taken into account. For example, if in the above example you have seen five other cards and three of them were low cards that you need, the probability of hitting drops to 59%. Calling down would then have a negative expectation and it would be incorrect to chase the low. It may also be wrong to chase if there was less dead money in the middle, which would be the case with a lower ante and/or with fewer players initially dealt into the hand.

This example is unique in that we know we are drawing dead for the high side. That, however, is not always the case and even a small probability of winning the high will greatly add to our expected value.

Having the ability to hit runner-runner for a low straight is nice because even if the straight isn’t good for the high, we will almost always at least take the low. Other sources of high equity, such as making two small pair or trips that we may feel compelled to call with on seventh street can add a dose of reverse implied odds. However, in general we would welcome these extra possibilities, especially if we have a good read on our opponent and can make good river laydowns.

One situation that we must be very particularly wary of is when our opponent has a high hand that will be very difficult to overcome, and may also end up with a better low than us.

For example, suppose the following hands are out on fifth street:

(X X) A A 6
(2 3) 5 8 Q

This spot is bad news and our hand should hit the muck. Our opponent is a big favorite on the high side and often also has the ability to beat us out for low. If we continue and on the river we can beat what we can see for high or make any low, we have to showdown on seventh street, and this has some reverse implied odds.

Assuming our opponent has any two low cards in the hole, we only have around 27% equity, which is less than the 31% equity (half of the 62% low probability) we had in the first example where we were completely locked out of the high side of the pot. And in the first example, we also had perfect clarity that any low we made would be good for one half of the pot.

Chasing the low will often work out slightly better than folding against a pure high hand, but we must tread very carefully in ambiguous situations where our opponent often has a two-way hand. We must be selective and only draw to the low when there is sufficient dead money in the middle, the exposed cards are either neutral or advantageous to us, and reverse implied odds are not a big concern. ♠

Kevin Haney is a former actuary of MetLife but left the corporate job to focus on his passions for poker and fitness. He is co-owner of Elite Fitness Club in Oceanport, NJ and is a certified personal trainer. With regards to poker he got his start way back in 2003 and particularly enjoys taking new players interested in mixed games under his wing and quickly making them proficient in all variants. If interested in learning more, playing mixed games online, or just saying hello he can be reached at [email protected].