by Richard Burke

First published in Poker Player

Hakim was taking a break from his Omaha/8 game on a cloudy Monday afternoon in midwinter. He looked glum so I went over to lend him some cheer. After some pleasantries, he asked me about suited starts in Omaha. It seemed to him that his suited starting hands weren’t standing up. When there were three or more trumps on the table, there was often a pair on the table, making someone else a Full House; when there wasn’t a pair, then his Flush would lose to a higher one.

He said he had played [As]-[2h]-[9h]-[Tc], figuring the two hearts added value to his marginal, bare Ace-Deuce. He was pleased with the Flop, [Kh]-[3h]-[8s], which gave him a draw to the nut Low and a Flush draw. The Aa on the Turn made his Flush and counterfeited his Low. The River was the [5c]. At the showdown, Hakim’s Flush lost to a higher one. “Those darn hearts cost me $36,” he groused.

I asked Hakim about how often he would have a suited start in Omaha. About half the time, he thought. I told him he wasn’t even close, it’s about 90%.

The chance that your four cards will be rainbow is 52*39*26*13/4!/C(52,4) = .105. The probability that your hand WON’T be rainbow is (1 – .105), or .895. More than 89% of the time you’ll have a single- or double-suited hand, I told him. The chart shows the distribution.

Hakim thought that even the smallest Flush would win often enough to show a profit. When the tableau is unpaired, I told him, in ten-handed Hold’Em the smallest Flush wins 76% of the time, but not in Omaha. Because four cards are dealt in Omaha, I told him, it’s quite likely that someone else also has two trumps. Only if no one else had two trumps would the smallest Flush prevail. In a ten-handed Omaha game, there are eight other trumps that could have been dealt among your nine opponents, so your only hope is that they’re all singletons: that chance is .1221, about 1 in 8.

In spite of that bad news, Hakim became even more excited about having suited starts: with a suited Honor and fortuitous tableau, he would have much better than 12.2% chance for High; plus, he might occasionally win an “emergency High” with low-ranking trumps, I warned Hakim not to go wild. With a single-suited starting hand, it’s only one chance in 104 that he’d flop a Flush, and even then he’d have to worry about the tableau pairing on the Turn or River. He’d flop a Flush draw about 1 time in 9, I told him, and not only must another trump appear, but also the board mustn’t pair. His chances for three or more trumps on an unpaired tableau are about 4.5%. A double-suited hand would double his Flush chances, still less than 10% after all the cards were out.

I told him he should think of suited starting hands just as having some extra values. He thanked me for the information and hustled back to his Omaha/8 game with a smile on his face and a spring in his step.

“De nada.”

by Sam Mudaro

Today we will look at the results of 10,000,000 hands dealt at an average table. Will the numbers be an average of the result attained from the loose table and the tight table?

Before I begin I will address a concept that is pretty widespread in most high/low games. It is tied somewhat to the concept of four cards working together which I have previously addressed. Ask any Omaha High/Low player what is the most important concept of the game. Inevitably you will be told to play for scoopers. A scooper is a hand that wins both the low and high halves of the pot without having to split either the high or low. It may occur when you have the best high hand and there is no qualifying low, either because no low can be made or your opponent was counterfeited on his low. The other way to scoop is to have the best high and best low with no one else having a similar or better hand. Lets take a look at who won the money at our average table.

The results here are ranked by the percentage of pots scooped by the players. Note that the results would have been the same had I ranked them by the number of pots scooped. I chose the percentage method because not all the players chose to play the same number of hands. Thus a player who scooped 2 hands out of 10 (20%) is properly weighted against a player who scooped 10 out of a 100 (10%). Clearly the loose player who scooped more then twice as much as the top money winning tight player was the biggest loser at the table!

Is conventional wisdom wrong? Should we not play to scoop? Why does a player who scoops more then twice as many hands develop into such a titanic underdog? Many factors come into play here. Clearly it is advantageous to scoop and play four cards working together than not to. When you scoop you win more money. When you play four cards working together you have a better chance of scooping. These are general guidelines and not meant to be the sole criteria for selecting starting hands. Playing four cards working together or hands that scoop does not, in and of itself, guarantee a winning session.

Our loose player above who happened to scoop the most pots is first and foremost a loose player. He/she will therefore play more hands and hence will scoop more and win more pots. We already know that the key to success is not winning more pots but winning more money. Our more conservative tighter players will play fewer hands, not chase as much and scoop less. They will however win a larger percentage the pots they enter with the stronger hands they play.

Lets take a look at the combined results:

The hands that win at an average table do indeed fall somewhere in-between those at a tight table and a loose table. It is not the arithmetic mean of both tables though. The best winning hand at the average table is the same as the tight table, 2 Pair. If we eliminate some of the rare hands, four of a kind and above, the least winning hand for both the tight and average player is the Bust. While there is a substantial drop from tight to average there is still a huge difference when compared to the loose table.

At the average table we find pretty much what we would expect. Each hand type shows a lesser loss percentage then those at the loose table. Each hand type shows a higher loss percentage then those at the tight table.

Turning our attention to dollars won and the percentage of hands played we again see that it is unhealthy for our bankroll to play more then 22% of the hands we are dealt. Selectiveness does count. Notice that even a tight player who strays and plays more than 22% runs into trouble.

Remember it is not just about being selective but being selectively aggressive. So what have we learned? The player who scoops the most is not necessarily the player who wins the most.

Scooping is great when it happens. It should not be used as the sole criteria for selecting starting hands.

The hands that win at an average table fall somewhere in-between those of a tight table and a loose table.

Next time we will take a look at which hands win a showdown. A showdown being a game in which each player keeps his or her hand to the river and the best hand wins.

by Sam Mudaro

First published in Poker Player

In my last article we compared two different loose tables to see what kind of player would dominate and what hands would win. Unquestionably the tighter players outperform the looser players. Before you continue reading, jot down how many hands per hundred dealt, you play. If that number is too high for you to work with, count the number of hands you play in a single round with ten seated players at the table. If all else fails just jot down how many hands you play per hour. If the dealer is good you may get 20 to 25 hands per hour. The number for Hold-Em is around 30 and maybe as high as 35/40 per hour with a shuffle machine. Honesty counts. Go write it down. Ok let’s continue. Do not take into account tournament play.

One measure of how tight a player is counts the number of hands played with respect to the number dealt. The lower the percentage the tighter the player. Someone who plays 20% of the hand dealt, (2 hands per round at a full table) is tighter then someone who plays 3 hands per round or 30%. If you play 2 hands per round, or 5 or more hands per hour you are not a tight player.

As in my previous article I dealt 10,000,0000 hands to a tight table consisting of 7 various tight players and 3 average players. Presented below are the dollars won, (loss) for each player. Please note that not all tight players are the same. They all are selective to varying degrees with respect to their starting hand requirements.

Tight is good. Tight is less then 4 hands per hour. You definitely should be playing less then 2 hands per round at a full table. Remember you are the big blind and small blind twice each round. If your dealer is dealing 20 hands per hour, and you play both blinds that is 4 hands per hour or 20%.

In the chart on the right it is clear that the ratio of money won or lost is directly related to the percentage of hands played. This is conclusive proof that it is not the number of pots you win but the amount of money you win that counts.

As a former blackjack player I can tell you the winning strategy is to “win the majority of your large bets, while loosing the majority of your small bets”. Translated to poker you want to win the majority of the few pots you enter while avoiding the majority of hands dealt to you. The advice I usually offer people is to look for reasons “not to play a hand” as opposed to looking for reasons to “play a hand”.

In the chart above we can view the difference between winning hands at a tight table and those of the loose tables from last time. Note that a large disparity occurs in the lower end hands between the tight and loose table. At the tight table almost 43% of the hands are won with a Bust, Pair or 2 Pair. Only about 18% win at the loose table. One logical explanation is that at a loose table more people are staying around after the flop and hence you need a much better hand to win with. On average 4.1 people fold before the flop at the loose tables while 6.8 fold at the tight tables. The more people in the pot and the longer they stay in the greater the chance to draw out to a better hand.

One may also infer from the above chart, in a looser game there are generally weaker players who tend to play far too many drawing hands. They will chase a low with only one low card on the flop and back into something more on the river. Let’s take a look at the other side of the coin.

Here we see a different pattern. The loss percentages are less for all categories at the tight table. You will loose half as less on a tight table with 2-Pair and almost one third as less with Trips, Straights, Flushes and Full house. With fewer people in the pot all your hands have a greater propensity to hold up. Ok I think you have the point by now. Your hands are worth more in a game with tight players. Does this apply to low hand? Will there be more low winners in a tight game or less? In our loose game the low hands won on average 56.4%. At our tight table the low only won 46.9%, some 17% less often. The answer here is quite simple.

There is always a high winner! When the low does not get there on the flop a player must draw to it. In a tight game there is less drawing. Less back door lows are chassed.

So what have we learned? It is better to play tight then loose. Most pros will advise to play just a little tighter the tightest player at the table. In Omaha H/L if we are playing 20% or more of the hands we are dealt we a probably playing too loose. Hand values go down in a loose game. In a loose game you will probably need to show down the best hand to win. There are less low winners at a tight table. Next time we will look at what happens at an average table.

by Sam Mudaro

First published in Poker Player

Today we will end our discussion of straight draws by looking at hands containing double connectors with no gaps, one gap and two gaps. We will look at all combinations of how the hand may be suited and include the non-suited variety.

Each of these simulations was run a minimum of 100,000 times with many run a million or more. As usual they were run at a full tight table with the same tight players playing each hand from all positions.

By examining the charts below it is apparent that the best hands, those producing the highest net return or lowest loss, are those of the double suited variety. On the other hand it should come as no surprise that the non-suited variety offer the poorest net return. This observation serves as additional reinforcement that a suited hand is always preferable to a non-suited hand

Another fact easily discernable from the three charts is that as in all other forms of poker, the greater the gap the less likely it is to complete the straight. The no gap straight draws are approximately twice as profitable as the single gap straight draws. The two gapers overall produce a negative return. When you reach the two-gap level or higher you should only concentrate on those hands containing the A-2.

All the hands containing an A-2 are profitable regardless of how they are suited and even if they are not suited. Again, what makes these hands profitable is their excellent low potential even when they miss the straight. Of course when they are double suited with the Ace in particular you have a powerful hand capable of sweeping the entire pot. You will usually win a larger pot and make out like a bandit even if you get quartered on the low when you hit that flush. When you do get lucky and flop the nut flush you should always raise or re-raise. You may still get plenty of action from the other lows and any king or queen high flushes who may unknowingly put you on nothing more than a low.

The 2-3-4-5 and 2-3-5-6 are mostly profitable in the no gap and one gap variety but again this has more to do with their low potential. Although not shown one should avoid playing any three gap straight drawing unless they contains an A-2. This concludes my series of articles on straight draws. Next time I will begin a series of what kind of hands win and how table personality affects the outcome as well as that of the individual player. Each of those simulations will be run 10,000,000 times to insure randomness.

So what have we learned? Having two connectors does not improve our straight draw chances unless it is combined with a flush draw and also contains a nut low or possibly nut low draw. One should not look at a straight draw as a reason to play a hand. It should be viewed as an additional benefit to a hand that would otherwise be playable.

by Sam Mudaro

First published in Poker Player

You’re in the big blind. You look at the flop and then down at your cards and voila, you have an open ended straight draw. Should you continue with the hand? How about if there is any kind of action?

Today I will give you a test. Look at the first chart below and decide how many of the starting hands combined with the given flops you would play. Would you play them for a single bet? Write down answers before you continue and look at the second chart.

Let me advise you as to how I set this simulation up and explain the chart. I dealt this flop 1,000,000 times to a tight player sitting at a tight full table, holding the indicated hands. None of the cards held by our tight player were suited thereby eliminating any flush possibilities.

The flop was rainbow. I chose these particular cards so that there would only be one straight draw. Except for the first line, the straight draws are all open ended. Additionally only the first hand would have the nut low draw.

The “Made” column indicates how often a straight was completed and the “% Won” indicates how often the straight won. I should mention the our tight player for all but the A-4-T-K only saw the flop, turn and river about 5% of the time. This would indicate that once committed passed the flop, the hand was played to the river. The hands are arranged in no special order of relevance except that the first hand was not open ended. The T-K-3-4 while second in frequency completed maintained the highest win percent of 82.5%. The A-4- T-K with the nut low draw while completed the most could only manage a win percentage of 67.6%. The second worst! The least completed 6-9-2-Q had the sixth highest win percent. So which hands would you play? Can you rank the hands in terms of profitability?

If you have read my article you should know that profitability and win percent are not correlated. A high win percent is not indicative of a winning hand. A low win percent is not indicative of a loosing hand and visa versa. The only true measure of profitability is net win. In Omaha H/L or any split pot high/low game, you may experience a 100% win percentage and loss money every time you play the hand. This occurs when the high hand collects half the pot and you must split the low with the high or all the remaining callers. You will receive one quarter of the pot or less.

Before we look at the second chart let me clarify one more point. Our tight player only played the 4-7-T-K, 5% of the time. That is approximately 50,000 times out of 1,000,000. Let me further point out that our tight player would have started with this hand from the big blind 100,000 times. It is logical that with this hand he only saw the flop when he could get in cheaply. Now lets take a look at the second chart.

The difference between these two charts is that here we are looking at the net win. This is how much money we earned or lost when playing this hand. The “W %” is now the win percent as compared to the total number of hands played. As I have stated many times before, win percent, in and of itself is irrelevant in determining whether a hand is profitable or not.

So were you able to pick the only profitable hand and the worst? The A-4-T-K is profitable but not because of it’s straight potential. Remember it had the second worse percentage for winning with a straight. There are no doubts about it. This hand is profitable because of its nut low potential. Only one of the four fives would complete the straight while any of the twelve other remaining low cards (6-8), would complete a low. The hand with the draw to the nut high straight, which had the best win percentage when making the straight, came in second best, but is still a losing hand. It will cost you on average 67 cents. Amazingly the 2-5-T-K, which is very similar to the A-4-T-K, except your low draw is to the second nut low, cannot show a profit. It will cost you $1.04 on average each time you play it. This once again reinforces the concept that in Omaha H/L you want to be drawing to the nuts.

It should be apparent that pursuing a straight draw, even an open ended straight draw is a losing proposition. Your straight draws need some help as in being coupled with a nut low draw. Also note the A-4-T-K is not open ended. Would two straight draws perform better? How about if our straight draws are coupled with a flush draw or pair on the flop? So what have we learned? Single straight draws in and of themselves are not worth pursuing whether they are high or low straight draws. They all need some additional redraw help as in being coupled with the nut low draw. Next time we will take a look at what to expect when we add some help as in the form of a flush draw and maybe flopping a pair.

by Sam Mudaro

First published in Poker Player

Today we will examine some of the factors to consider when formulating our decision to fold or muck. I outlined some of the factors last time as questions we should ask ourselves. Today we will look at why we ask these questions and what do the answers mean.

A tip before we get started. When your cards are being dealt, look at your opponents. Watch the expressions on their faces and what the do with their cards and hands. This is one of the easiest ways to pick up tells. You will always have time to look at your cards before you act.

Most of the factors discussed apply to Hold-Em as well as Omaha H/L. I will concentrate on Omaha though. Lets start at the top.

How many players saw the flop? This is important in both Omaha and Hold- Em. If for nothing else it is essential for calculating pot odds. If we are looking at a draw we want enough callers to render that draw profitable. We do not want to chase a 1 in 6 shot with only one caller. Especially if we are only shooting for half the pot, or there is a chance we could be quartered.

Certain hands play well against few callers while others demand more players. In Omaha when you flop the nut high with no chance of counterfeiting you want as many players in the pot as possible. Your decision to call, bet, raise or re-raise is driven by your desire to keep your opponents in the pot. With the nut low you must be mindful of counterfeiting and getting quartered or worse.

The more callers you have the higher the probability someone already has the nuts or is drawing to the nuts. With many callers you can be assured most of the aces and deuces are out there, especially if the pot is raised and re-raised. It is also very common for a player to have a wheel with a flop containing three low cards of 5 or less. If the flop contains two or three cards to a flush you are probably looking at the nut flush. On the other hand if you are last to act and have all high cards before the flop, you may be looking good.

Lets look at a chart (below) of how often the wheel will get there with 3 cards to the wheel on the flop. Contrary to what some players may think, the chance to scoop the low goes up when an ace does not hit the board. Look at the 3-4-5 it will scoop the low 41% of the time and there will be a low over 90% of the time. The A-2-3 scoops 28% of the time with a low occurring 80% of the time. The combined Nut low is almost double for the 3-4-5, 62.3% vs. the A-2-3, 34.7%. Remember, most people play A-2 rather than 3-4. There is much more sharing when the A-2 is not counterfeited.

How many players to act after you? This has a material effect as to whether you want to call with a marginal hand. The more players to act behind you the more likely the pot may be raised. If the flop brings a made low or low draw especially if it does not include an ace or deuce and you are sitting there with a high draw it may get pretty costly real fast. You must ask yourself why did all these players call to see the flop in the first place. Is it worth pursuing a high draw with two pair, a set, a straight draw or a flush draw?

The number of players to act after you will affect the pot odds you receive as well. The key is being able to estimate how many of them will call. The earlier offered tip should be very useful.

How many players to act in front of you? If you have a hand that warrants a check raise you want few people in front of you. The more that are behind you the more likely one of them will bet. This works especially well when you have a good high, (Ace high flush) combined with the nut low, (a wheel). Another opportunity arrives when you have flopped quads. You want as many people in front of you as possible so you can watch them bet and raise while you wait to cap it.

How many players were at the table at the start of the hand? This concept is valuable in both Hold-Em and Omaha. The greater the number of players that are dealt in the more likely you will run into superior hands. The fewer opponents dealt a hand, the easier it will be to steal the pot. In Omaha high/low the value of a high hand goes up as the number of players dealt in goes down. I have written an entire article on this subject. The reason behind this is that there is always a high hand winner. There is not always a low winner. One should always be cognizant of how many players were dealt in as well as who they are.

So what have we learned? There are factors other then our own 4 cards to consider before entering a pot or calling on the flop.