The reader may feel confusion about the many different kinds of odds. “Odds” is a general term having to do with the likelihood of a particular event. “Hand odds” are the odds against making a winning hand. “Implied pot odds” are how much will be in the pot at the showdown (estimated) divided by how much Hero will henceforth contribute to the pot (also estimated).
One has “favorable odds” in poker when one expects to show a profit playing or drawing to a particular hand (+e.v.). One has “unfavorable odds” in poker when one expects to show a loss playing or drawing to a particular hand (-e.v.).
In a high only game, the easiest way to determine whether you have “favorable odds” or “unfavorable odds” is to compare “implied pot odds” with “hand odds.”
- When your “implied pot odds” are greater than your “hand odds,” then you have “favorable odds.”
- When your “implied pot odds” are less than your “hand odds,” then you have “unfavorable odds.”
The same is true in a split pot game such as Omaha-8, but the odds calculations are greatly complicated by the possibility of split pots.
Typically, when you’re drawing in an Omaha-8 game, some of your outs will be for the whole pot while others will be for some fraction of the pot. In addition, even when all of your outs are for either high or low, (when you’re playing a one way hand), your opponents may have some outs for high only, other outs for low only, and still other outs for scooping.
(Implied pot odds were discussed in greater detail in my August article).
Whole Pot Outs
When Hero holds KK32 and the board is KQJT, Hero has trip kings and is drawing for the board to pair. Thus all of his outs are whole pot outs. Hero has 10 of these whole pot outs. Hero won’t have the nuts if the board pairs with jacks, tens, or nines, but he’ll have kings full and should expect to win unless an opponent makes quads. Whether or not an opponent will make quads depends on whether that opponent sees the flop and continues with the appropriate pair or not. With kings full in this situation, Hero should expect to win the whole pot in the neighborhood of 95% of the time. And with KQJT on the board, Hero should expect an opponent to already have a straight.
Thus Hero expects to make a full house on the river and win 9.5/44,
make a full house on the river, but lose to quads 0.5/44,
and miss a full house on the river 34/44.
In a fixed-limit game if it will cost Hero one big bet to see the river and two more big bets if he loses to quads (a conservative estimate), Hero figures to lose 3 big bets 0.5/44 times when he loses to quads. In addition, if Hero folds on the river when he doesn’t make a full house, he figures to lose 1 big bet 34/44 times when the board doesn’t pair on the river.
-3*0.5-1*34=-35.5. That’s how much Hero expects to lose in the 44 tries.
Then in order to have “favorable odds,” Hero has to win at least that much, 35.5 big bets, on the 9.5 out of 44 times Hero wins the whole pot. Hero has to win 35.5/9.5=3.74 big bets when he wins in order to justify drawing for 10 outs. Thus, if the amount already in the pot plus what Hero’s opponents re will henceforth contribute will be 4 big bets, Hero has “favorable odds” to draw for the board to pair.
Since Hero will be putting two big bets into the pot, one on the turn and the other (implied) on the river, with only one active opponent, there only have to be two big bets already in the pot for Hero to have “favorable odds” to draw.
There almost always will be that much already in the pot, even with just one opponent. More opponents, perhaps all of them with the nut straight, are just gravy.
Hero needs four opponents who will contribute in order to have “favorable odds” to initiate fresh money into the pot. That’s because Hero needs to win four bets per bet he initiates in order to get better than the 3.74 to 1 “pot odds” he needs to draw.
There are, of course, some other considerations (mainly intimidation) besides having “favorable odds” involved in initiating fresh money into the pot. However, the current article is about having “favorable odds” or not.
Half Pot Outs for high (full house or flush draws)
When Hero holds KKQJ and the board is K876, Hero again has trip kings and is drawing for the board to pair. As above, Hero won’t have the nuts if the board pairs with eights, sevens, or sixes, but he’ll have kings full and should expect to probably win about 95% of the time (or even more if his opponents are not likely to be seeing the flop with 88**, 77**, or 66**, hands that would possibly make quads for an opponent.
But with three different ranks of low cards already on the board, in a full, loose, game Hero should expect all ten of his outs to be half pot (high only) outs. Hero should like to improve those half-pot outs to scoop outs by betting the turn and river so as to scare anyone without the nut low out of the pot. However, in thinking about having “favorable odds” or not, with three different low ranks already on the board, especially when none of the low ranks showing are wheel cards, Hero should (slightly conservatively) consider all his outs as half pot outs.
-3*0.5-1*34=-35.5 is still how much Hero expects to lose in the 44 tries.
In order to have “favorable odds,” Hero has to win at least that much, 35.5 big bets, on the 9.5 out of 44 times Hero wins half of the pot. Hero has to win 35.5/9.5=3.74 big bets when he wins in order to justify drawing for 10 outs.
Hero still needs to win 4 big bets when he wins. But now he’s only winning half of the pot.
Half of the amount that is already in the pot plus half of what his opponents will henceforth contribute minus half of what Hero will henceforth contribute has to equal 4 big bets.
When Hero has only one opponent (who presumably has the straight plus a qualifying low), and if there are already 8 big bets in the pot, and if Hero’s one opponent bets, then Hero doesn’t have “favorable odds” to initiate fresh money into the pot (raise), but Hero does have “favorable odds” to call the bet drawing for the board to pair.
When Hero has two opponents, if there are already 6 big bets in the pot, and if Hero acts last, then Hero has “favorable odds” to draw for the board to pair. (Hero will win 4 big bets when the board pairs and neither opponent makes quads).
When Hero has three opponents, if there are already 4 big bets in the pot, and if Hero acts last, then Hero has “favorable odds” to draw for the board to pair. (Hero will win 4 big bets when the board pairs and neither opponent makes quads). With three opponents it’s almost inconceivable that there won’t be at least 4 bets in the pot.
Hero needs nine bets from opponents going into the pot for every bet Hero makes in order to win four of the bets when he wins half of the pot. Thus Hero cannot have “favorable odds” to bet or raise when drawing for half of the pot unless at least nine opponents will call. (There are considerations other than having “favorable odds” involved in initiating fresh money into the pot, but the current article is about having “favorable odds” or not).
Fractional Pot Outs for low (or for high straight)
When Hero holds AKQ2 and the board is T987, Hero has the nut low draw without counterfeit protection, plus Hero has four outs (the jacks) for high.
Because of the distinct danger of being tied by one or more opponents also drawing for the same low or the same straight, fractional outs for low or straights are not worth quite as much a fractional outs for high flushes or full houses.
Since Hero’s opponents will tend to like starting hands with aces and wheel cards, Hero should expect to occasionally be tied for low by an opponent with the same nut low.
- When Hero is tied by one opponent, Hero is “quartered.”
- When Hero is tied by two opponents, Hero is “sixthed.”
- And roughly one time in a thousand in a full, loose, game Hero will be eighthed.
When Hero makes a straight he also will be occasionally fractionated. Occasionally getting fractionated in Omaha-8 goes with the territory.
We counted half pot outs for flushes and full houses as worth half the pot. But because of the fractionating effect (getting quartered, sixthed, or eighthed), half pot outs for lows and straights, especially lows, are worth less, probably closer to a third (on average) of the pot, but depending.
When Hero holds AKQ2 and the board is T987, Hero needs a six, five, four, or three on the river to make a qualifying low, which in this case will be the nuts. Hero needs any one of 16 missing low cards on the river to make the nut low or Hero needs a jack to end up with the winning or tying high.
But because of the danger of getting quartered at a full or nearly full table, Hero is more realistically only drawing for one third of the pot for the low outs and four fifths of the pot for the high straight outs. Hero expects to fold to a bet if the river is not a jack, six, five, four, or three.
When Hero, acting last, is faced with one bet to see the river, Hero expects to fold and lose the one bet 24 times out of 44. But 16 times out of 44, Hero will make the nut low and 4 times out of 44, Hero will make the nut high with no low possible. When Hero makes the nut low, he expects to win an average of about one third of the pot. (Mostly Hero will win half the pot but roughly two times in five, Hero will win a quarter or a sixth of the pot. It’s close enough for our purposes to think of this as averaging to about one third of the pot).
When Hero wins high, Hero be be tied roughly (also) two times in five. This averages to about four fifths of the pot.
Four outs for 80% plus 16 outs for 33% averages to 20 outs for 0.424P
(the math: 0.8P*4/20+0.33P*16/20=8.48P/20=0.424P)
When Hero, acting last, is faced with one bet to see the river, Hero expects to fold and lose the one bet 24 times out of 44. But 20 times out of 44, Hero will make either the nut low or the nut high straight.
To simplify, think of each one big bet as one chip
If we lose 24 times, and if we only win some or all of the pot 20 times, then to recoup the 24 chip expected loss, we have to average winning 24/20=1.2 chips on each occasion when we win.
If we make the nut low on the river, sometimes our opponents will fold to a bet. And then, although it didn’t seem as though we could scoop when we were figuring the odds, we’ll scoop after all. We’ll just have a one-way hand, but when we bet we’ll scoop. Even though we won’t have favorable odds to bet, by betting we may promote our hand from a half pot winner to a scooper.
Thus even though you risk getting quartered or sixthed for low it behooves you, in general, to bet the nut low on the river. But don’t bet the nut low with no high on the river if you’re absolutely certain at least one of your opponents will call (because of the danger of getting quartered or sixthed).
You see this tactic more coming from low-only hands because one has less to possibly lose when one does this with the nuts, and one is more likely to have the low nuts than the high nuts... but the same is true of a high only hand when low is possible. Consider betting the river to coerce opponents with non-nut lows to fold, thus converting a half pot hand into a scooper.
