Either low is or it isn’t possible.
Without regard for the cards in your own hand, low will be possible on the river 60.1%, approximately three hands out of five.
The range of low, if you do consider the four cards in your own hand is from 68.6% to 44.7% When you have a hand with four high cards, such as KKQQ, low is possible on the river 68.6%. When you start with four low cards of different ranks, such as A-2-3-4, low would only be possible 54.5%. Starting with A234, low would only be possible 50.9% for you as the holder of A234. (If you started with a hand with low four cards of the same rank, such as AAAA, then low would only be possible 44.7% of the time).
Although low will be enabled by 60.1% of the possible five card boards, someone will actually qualify for low somewhat less often. How much less depends on the number of players who were dealt hands and the tightness of the players. To give you a rough idea, when Omaha-8 is played in a typical brick and mortar casino as a full nine or ten player game, someone will actually make a low about half the time.
Thus, assuming you play a balanced game, you might expect to win for high roughly twice as often as you win for low. And about half of those wins for high should be scoops. Of course if you only play for low, you’ll probably win less often for high than twice as often as you win for low.
When ace-deuce-x-y is the nut low, it gets fractionated in a full nine or ten player game roughly two times out of five. Most of the fractionations are for a quarter of the pot, but sixths for low are not unusual and eighths for low occur occasionally (about one time in a thousand).
A bare ace-deuce starting hand, a hand such as A2QK or A2KK, will end up as the nut low on the river less than one time out of four. In a full, nine or ten handed, non-tight game, another player (or two) will also have the nut low (with an ace plus a deuce) approximately two hands out of five.
Ironically, despite the fact that winning high is very clearly worth more than twice as much as winning low, many individuals concentrate on winning for low. There are several reasons for this.
1. Back in the old seven-stud-high-low split-with-a-declare days, when players declared with chips for high, low, or “pig,” low was just as valuable as high.
2. Low cards can win for high too. When there is no eight or better qualifier for low, you scoop more often with low cards than high cards.
3. It is very difficult before the flop to determine whether your hand will win for high or not. It’s much easier to pick a winner for low.
Hand reading hint on the river.
Most of your opponents in fixed-limit Omaha-8 will tend to voluntarily play starting hands with one or two aces plus one or two deuces or treys.
If anyone includes hands with a pair of aces plus any wheel card, then hands in these four categories:
- A2YZ,
- A3YZ,
- AA4Z,
- AA5Z
make up ~33424/270725=~12.3%, or very close to one eighth of the hands dealt to anyone.
Thus there is a very good chance (roughly 50%) an opponent (Villain) who voluntarily plays between one hand out of four and one hand out of three is seeing the flop with A2YZ, A3YZ, AA4Z, or AA5Z.
Depending on the flop and subsequent actions of Villain, this information might often help you to arrive at a reasonable estimate of a tight Villain’s hand on the river.
You start before the flop, estimating the range of hands with which Villain would voluntarily see the flop. Then you narrow that range, depending on the cards on the flop and how Villain bets. Then you further narrow the range on the turn, and finally you often can come to a good estimate on the river.
When an opponent plays for low and misses on the river.
After the turn, low will either be enabled or not. In other words, the board will either have three or four low ranks or not.
After the turn without regard for the cards in Hero’s hand:
- one fifth of the time low will be impossible. (~19%)
- two fifths of the time low will already be possible. (~39 %%)
- two fifths of the time the board will have two low ranks. (~42%)
On the two times out of five when there are only two low ranks on the board after the turn, there is a very good chance an opponent is drawing for low, perhaps without much of a draw for high. For example, when the flop is:
7
, 8
, K
and the turn is Q
,
there is a good chance an opponent, or perhaps all your opponents had starting hands with a good two-card low component such as ace-deuce, ace-trey, or deuce-trey, continued after the flop drawing for low and maybe little else, and then continued drawing for low and maybe little else after the turn.
Particularly if the river is an ace, but also if the river is a deuce or a trey, an opponent, who was drawing for low with a two-card low component may be counterfeited.
Or an opponent who already had the nut low when the flop is:
7, 8, 4 and the turn is Q,
will be counterfeited if the river is an ace or deuce. Although a hand with ace-deuce will still qualify for low, the ace-deuce will no longer be the nuts for low.
A non-tenacious opponent who was counterfeited on the river may fold if pressured. If you think that may be the case, even if you got counterfeited yourself, betting to steal the pot should be a consideration.
When you are not counterfeited for low and you end up with a low on the river, it should usually be the first nut low or the second nut low. And when you have one of these, roughly half the time, an opponent in a full game will have been dealt the other.
Ten handed nut low
As simulated for a ten handed game, when you end up with ace deuce making the nut low on the river, at least one of your nine opponents will also have been dealt the nut low (ace-deuce) 43% of the time.
2nd nut low
As simulated for a ten handed game, when you end up with an ace-trey in your hand making the second nut low on the river, at least one of your nine opponents will have been dealt the nut low (ace-deuce) 53% of the time. And another opponent will end up with the second nut low 20% of the time. Thus in a game where nine opponents are dealt cards, assuming they all will continue with ace-deuce or ace-trey, when you have the 2nd nut low, you will only have sole possession of the winning low 27% of the time.
Nine handed nut low
As simulated for a nine handed game, when you end up with ace deuce making the nut low on the river, at least one of your eight opponents will also have been dealt the nut low (ace-deuce) 39.1% of the time. Another opponent will end up with the second nut low more often than that, almost half of the time.
2nd nut low
As simulated for a nine handed game, when you end up with ace three making the second nut low on the river, at least one of your eight opponents will have been dealt the nut low (ace-deuce) 48.3% of the time. Another opponent will end up with the second nut low 19.8% of the time. Thus in a game where eight opponents are dealt cards, assuming they all will continue with ace-deuce or ace-trey, you will have sole possession of the winning low only 31.8% of the time. Whether that alone is good enough to continue or not depends on the action and how much is in the pot.
On the river when you have the 2nd nut low, you will win half the pot with the second nut low all to yourself only three times in ten.
Six handed nut low
As simulated for a six handed game, when you end up with ace deuce making the nut low on the river, at least one of your five opponents will also have been dealt the nut low (ace-deuce) 26% of the time.
2nd nut low
As simulated for a six handed game, when you end up with ace three making the second nut low on the river, at least one of your five opponents will have been dealt the nut low (ace-deuce) 32% of the time. And another opponent will end up with the second nut low 16% of the time. Thus in a game where five opponents are dealt cards, assuming they all will continue with ace-deuce or ace-trey, you will only have sole possession of the winning low 52% of the time.
Heads up nut low
As simulated for a one-on-one game, when you end up with ace deuce making the nut low on the river, your one opponent will also have been dealt the nut low (ace-deuce) 5.4% of the time.
2nd nut low
As simulated for a one-on-one game, when you end up with ace three making the second nut low on the river, your one opponent will have been dealt the nut low (ace-deuce) 7.0% of the time. And your opponent will also end up with the second nut low 4.4% of the time. Thus in a game where only one opponent is dealt cards, assuming he will continue with ace-deuce or ace-trey, you will only have sole possession of the winning low 88.6% of the time.
Getting quartered, a comparison of pot-limit to fixed-limit.
The easiest way to make the comparison is for heads-up play.
When your one opponent bets the pot on the river in a pot-limit game, getting quartered costs you one fourth of the amount you put into the pot on the fourth betting round. (If your opponent only bets half the pot on the river, then when you get quartered, you break even on the call of the half pot river bet).
When your opponent makes a bet equal to 2 small bets on the river in a fixed-limit heads-up play, assuming there has been at least one bet each betting round, there are already the equivalent of at least 8 small bets in the pot. If you get quartered under these conditions, you gain at least 1 small bet.
You obviously never like to get quartered because you lose 3/4 of the investment you make in the last betting round. But, when you get quartered in a fixed-limit game, because you gain 1/4 of the amount that was in the pot from the first three betting rounds plus 1/4 of your opponent’s investment in the last betting round, you come away with more than you would come away with by folding.
That’s not true in a pot-limit game when your opponent makes a pot sized bet. By calling you come away with less money than you would come away with by folding.
Next month we finish the two part “on the river” series with a consideration of various high hands on the river.