The next two articles deal with the middle rounds and are divided into two sections; “ABC Play” and “Making Moves”. This article is on “ABC Play” and deals with situations that you decide to play in a straightforward manner when you believe that you have the best hand or when you are pretty sure that you don’t but just call in an attempt to outdraw your opponent.
If you think you are behind it is important to evaluate all options; folding, calling, or making a move at the pot. Before deciding on a plan the first determination you should always make is to determine whether or not you can make a profit by simply calling. You can still make a move either way but if you can make a clear profit by calling it usually makes sense to go that route if you feel your opponent is sticky. However, if you can make a profit by calling that means you do not require a large an amount of fold equity when you do make a move at the pot.
When You Have the Best Hand
When you are a card (or two) ahead of your opponent you have to make what is an automatic bet for both value and protection. If you and your opponent are both drawing one you need to bet if you believe your three card badugi is best. The better tri hand has a huge equity advantage. For example, with two draws left A23 is a 69% favorite over 256. With one draw left the A23 is an 81% favorite.
Even if you do not improve on particular draw it is mandatory that you continue to bet. There is only around a 20% chance that your opponent will drawn a badugi so on average your equity advantage in this situation is high. For example, you have A23 and bet it after the second draw against an opponent who drew one. 80% of the time you will be around an 80% favorite. If your opponent made a badugi, on average you have around 5 outs or 10% equity. So against the range of hands your opponent can have your estimated equity is around (.8)(.8) + (.2)(.1) = 66%. Even if your opponent did make a badugi he might not choose to raise thus it is a clear bet after the second draw in this situation whether you improved or not.
When You Don’t Have the Best Hand
When you probably don’t have the best hand you need to first estimate your equity and compare it to the odds the pot is offering. Don’t forget to consider if reducing your incomplete will possibly put you ahead in the hand. In addition, there are also possible reverse or implied odds to consider. In limit Badugi, reverse and implied odds do not play as large of a role as it does in other games but in some situations it can tip the scales towards folding or calling.
Also consider whether or not you will need to fold if you do not improve your hand on this draw and thus relinquish your equity in the pot. This is especially important to consider when you hold a two card draw as they need to show improvement to stay in the hand. If there is a good chance you will have to “abandon your children” then you require a somewhat significant overlay from the pot to proceed.
Lastly, is your opponent possibly snowing? If this play is in your opponent’s repertoire then you must be willing to occasionally call down with hands that can beat his bluffing range.
Pot Odds Charts
The charts below display the pot odds and target equity for a heads-up situation depending on whether or not one of the players started in one of the blinds. Pot odds are slightly greater when none of the players were in the blinds due to the effect of dead money. The odds displayed after the first draw are what a player will have if his opponent bets and the calculations after the second draw assume that there was a bet and a call after the first draw.
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After the second draw a commonly used approximation to estimate your equity is to multiply your estimated outs by two. For example, if you estimate that on average you have six outs this means that your equity is approximately 12%.
The target equity is just a guide. If you have implied odds and position you can call a turn bet with less than your target equity. If you have reverse implied odds or may have trouble realizing your equity you require an overlay on the target equity.
Chasing Down a Badugi
When your opponent stays pat you must be able to determine on average how high the badugi is that you are chasing. You do this based upon the aggressiveness of the player and how the hand has been played. As we already learned, the average badugi strength obtained through the initial deal is weaker than one obtained through drawing.
If a tight player open-raised from early position we would expect them to have a jack or better. In this situation their median badugi is around a ten thus with any reasonable tri you would rate to have around 6-7 outs. Clearly you have odds to call the small bet after the first draw but the decision after the second draw is much closer. With only around 12-14% equity it appears to be a marginal/neutral call if the pot was 3 bet pre-draw but a call if the pot was capped pre draw. Of course if you know your opponent will only cap with extremely strong badugis this changes the entire calculus of the situation and the estimation of your outs. As always implied odds and position can turn a slightly negative or neutral call into one with positive expectation.
If your opponent obtained a badugi from drawing it will tend to be stronger and on average you may only have 4-5 outs. In this situation if you believe your opponent has a badugi you should tend to fold after the second draw as the pot is simply not big enough to chase. Only in a capped pot pre-draw can a call be considered.
Having the Second Best Tri
In a raised heads-up pot, you should essentially never fold after the first draw getting such high pot odds against an automatic bet. However, you should often be folding after the second draw. Even if your opponent did not make a badugi he is typically an approximate 4 to 1 favorite with one draw left:
A25 (81%) vs 456 (19%)
In the above example you have no chance to win by reducing your incomplete. If however, your first two cards are smooth and thus can potentially win by reducing your incomplete you would be less of an underdog and can consider making calls in big pots. In the example below you have two extra outs that would give you the best tri hand:
A25 (77%) vs A37 (23%)
So here you have twelve outs at making an A23, an A34, or a badugi. Of course you can reduce your incomplete at the same time your opponent completes their badugi but it is a factor to consider in large pots and close decisions. Keep in mind that the equities above almost represent the best possible situation as you would be an even greater underdog the times your opponent made a badugi.
Sometimes the situation is close and you actually don’t know if you have the second best three card hand. If that is the case and you are in a big pot with an aggressive player you should error on the side of calling.
Playing Two Card Draws
Against a player who stood pat on the first draw, it is time to fold your hand if you started with a two card draw and did not improve. A few sample equities with two draws left:
A2 (21%) vs KQJT
A2 (15%) vs JT98
A2 (6%) vs 8765
You cannot even call the small flop bet in a big pot because 50% of the time you will not even improve to a three card eight on the next draw. This is another example of why A2 has trouble realizing its equity and also demonstrates that it can be highly susceptible to snows.
Now let’s take a look at a situation where your opponent draws one. You open from the cut-off and are re-raised by the button who holds 246. After you check and the button bets you are getting pot odds of 8.5 to 1. That indicates that your target equity is around [1/(1+8.5)] or around 11%. What is your estimated equity?
Since the button’s bet is automatic the estimation of your equity is based purely on mathematics. On the first draw the button had around a 21% chance of making a badugi. If he made it you are around a 92%/ 8% underdog under the assumption that he made a nine badugi. Sometimes he will make a stronger badugi, sometimes it will be weaker, but when he makes one on average it will be around a nine so that is why we choose to use that assumption for our calculations. If he didn’t make a badugi you are an approximately 65%/ 35% underdog with two draws to go.
Thus you can estimate your equity by performing a weighted average of the these two possibilities:
| 246 vs A2 with two draws left | ||
| 246 | 65% | |
| A2 | 35% | |
| 2469 vs A2 with two draws left | ||
| 246 | 92% | |
| A2 | 8% | |
| A2’s Weighted Avg Equity | ||
| 29% | ||
The weighted average equity works out to be approximately 29%. [ (79% * 35%) + (21%*8%) ] = 29%. You are a sizeable underdog to win the hand but given the tremendous overlay in pot odds you must call.
You make the call and your opponent draws one again. Unfortunately you don’t help on the second draw and after your opponent bets you are getting odds of 6.25 to 1 making your target equity around 14%. Going through the same analysis that we did after the first draw we arrive at an estimated weighted average equity of around 21%:
| 246 vs A2 with one draw left | |
| 246 | 74% |
| A2 | 26% |
| 2469 vs A2 with one draw left | |
| 246 | 97% |
| A2 | 3% |
| A2’s Weighted Avg Equity | |
| 21% | |
There is an overlay here but it doesn’t appear to be enough as you probably face reverse implied odds after the last draw. The decision is very easy considering that you fare much worse against stronger three card badugis. Against 234 your estimated equity would only be approximately 13%:
| 234 vs A2 with one draw left | |
| 234 | 84% |
| A2 | 16% |
| 2349 vs A2 with one draw left | |
| 2349 | 97% |
| A2 | 3% |
| A2’s Weighted Avg Equity | |
| 13% | |
In this particular matchup you couldn’t even call this bet if it put you all in thus all things considered this analysis shows that folding an unimproved two card after the second draw should be considered standard.
Multi-way Pots
Multi-way pots often play themselves as the most common scenario is when multiple players are trying to outdraw a badugi. Consider a hand where the cut-off raises, the button calls, and you defend in the big blind with 256. If the cut-off is pat, you and the button are subsidizing each other’s drawing hands thus it is usually correct to just play straightforward and hope to hit a good badugi. The button is not closing the action and thus has a riskier call than you but overlay and implied odds are just too good for either one of you to consider folding.
This month’s article focused on the times we have the best hand or if we don’t provided insight to how we can try and determine whether or not we can profit by simply calling and drawing to outdraw our opponent. Of course, the beauty of poker is that you can win without the best hand and various ways that we can attempt to that in Badugi will be the subject of the next article.