Badeucey: Realization Of Equity With Premium Three-Card Badugis

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In this issue we switch back to Badeucey. For those readers that are unfamiliar with this variant, it is a split-pot game where the object is the make the best deuce-to-seven (27TD) low along with the best badugi. Aces are high, and straights count against you, so the best possible deuce to seven low is 2-3-4-5-7 that is not a flush. On the badugi side, aces are also considered high, thus the best possible badugi is 2-3-4-5 with all different suits such as 2 3 4 5.

In a previous issue, we discussed the type of hands we should play when we are the first to enter the pot. When someone else opens before us, we must tighten up, and with our really good hands we have a decision between re-raising for value and attempting to isolate, or smooth-calling to try and pull other players into the pot.

With premium three-card badugis such as 2-3-4, 2-4-5, and 2-3-6 we are highly incentivized to three-bet an opener as our hand is likely best and it increases the odds that we end up scooping. However, hands such as these can make very strong holdings on both sides, and this is an argument for smooth-calling and inviting in others in the hopes of winning a massive pot.

This decision is relatively close, so we should consider the ability to effectively realize our equity relative to our opponent when we do choose to re-raise and are successful in getting the pot heads-up. When we escalate the betting early on in a hand, it’s important to know that we can often get to a showdown profitably even if we don’t improve dramatically.

Consider a hand where the hijack open-raises, and we three-bet from the button with 2 3 4 X X, everyone else folds, and both players draw two. After the first draw, the hijack leads out and we just call after failing to improve. On the second draw, the hijack now draws one. While you may be up against a badugi, it could still just be a tri hand that picked up a low draw. Against a very loose player we may even be up against a holding such as 2 3 5 8 X, which would give you a freeroll.

Unfortunately, we fail to improve on the second draw, in any fashion, meaning we have not made a badugi or a low draw to at least a nine or a ten. After the villain bets the turn, we are getting pot odds of 5.75:1 and need around 15% equity to continue.
So how much equity on average do we have in this situation? This is not easy to nail down precisely, however, the low side is a little easier to estimate so we will start with that.

On the second draw your opponent will have completed his one-card draw to a hand he will pat around 40% of the time and against this pat range you have approximately 10% equity. Since we were drawing two on the second draw, the villain should tend to pat anything up to a 10 low, and depending on his holdings, sometimes jacks as well.

When our opponent is still drawing one, we have around a 35% chance of ending up with the best low. Therefore, a simplified average equity calculation for the low side is as follows: (40%)(10%) x (60%)(35%) = 25%. Since it is a split-pot game, the chance of making the best low gives us approximately 12.5% (25%/2) equity towards the 15% that we require.

Estimating our equity on the badugi side is much more complicated, but as you can see, we don’t need that much of a contribution from it to make our call profitable. When our opponent does not have a badugi we are the favorite, and when he does, we still have a chance with our premium draw. It appears as if we have a clear continue, but the hand does not end on the turn and we must also consider the river betting round.

If our opponent was drawing one on the second draw, we are going to be calling the river a large amount of the time. On the river, we will be getting 7.75:1 to call and getting these odds only require 11% equity. Even when we end up with ace high, we are going to have the best low against a one-card draw around 20% of the time, and that fact alone is almost enough to call the river bet.

There is still a chance that our three-card badugi is best and on our good days we will even scoop the pot when villain was betting a worse three-card tri with a low draw on the turn and paired up on the last draw.

On the turn, we should clearly continue on with 2-3-4 and also with other good three card hands such as 2-4-5, 2-3-6, and 2-3-7. With these hands we will have the best current badugi hand with some frequency and when we don’t there is the opportunity to improve.

Given that we have such a high chance of realizing our equity with premium three-card badugis, this makes an aggressive three-betting strategy before the first draw with them fundamentally sound. Even when we fail to improve on the first two draws, we can usually continue on profitably and thus not often abandon the chips we have invested in the pot.

It’s important to note that had the draws gone differently and we were fortunate enough to improve while our opponent did not, he won’t be able to profitably realize his equity as often as we do. Our re-raise before the first draw represents a premium three-card badugi, he is out-of-position, and his overall range is wider since he was the first to enter the pot.

When we expect to win the realization of equity battle, isolating an opponent becomes more enticing. In the next issue we will use some of what we discussed here as we formulate our strategies on how to play against a raise before the first draw. ♠

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. His new mixed-games website Counting Outs is a great starting resource for a plethora of games ranging from the traditional to the exotic. He can be reached at [email protected].