Flops II

Coding system.
The 22100 (without consideration for the cards in Hero’s hand) possible three-card flops, have been subdivided into 27 flop types of interest in Omaha-8, The 27 chosen flop groups are identified in the September article.

All flops are identified by a letter or letters followed by a number.
• The letter “R” stands for “rainbow” or three different suits.
• The number (3, 2, 1, or 0) following the letter or letters represents the number of different ranks of low cards on the flop.

Last month (September 2012) there was a discussion of flop type R3. (rainbow with three low ranks).

Flop Type R2
• “R2” means three different suits (rainbow) and two different ranks of low cards without a pair. 2520 (11.4%) flops belong to this category, not considering the cards in Hero’s hand, are in the R2 category. Examples follow:
• 9,6,5 is an “R2” flop where a straight is possible. But only back-door flushes are possible. And there is a low draw.
• 9,6,2 is an “R2” flop with a straight draw. Only back-door flushes are possible. And there is a low draw.
• K,7,2 is an “R2” flop, with no straight draw. Only back-door flushes are possible. And there is a low draw.

If a straight is not possible on the flop
When the flop is
• 9,6,2 no straight is immediately possible.
But any 3, 4, 5, 7, 8, or 10 on the turn will enable a straight on the turn. And every other card in the deck that doesn’t pair the board on the turn will enable a straight draw on the turn.

If a straight is possible on the flop: Flopped middle card straights
When the flop is
• 9,6,5, a nine-high straight is possible.
Anyone who happened to have been playing an 87** starting hand, flopped a nine-high straight.

Flopped middle card straights are notoriously poor at holding up. In other words, on the turn or river, the board is likely to either (1) pair (enabling a full house or quads), (2) enable a higher straight, or (3) enable a flush.

Without consideration for Hero’s hand,
• there are 9 possible cards (fives, sixes, and nines) that pair the board. The probability of the board pairing with a five, six, or nine on the turn or river is
P=1-40*39/49/48=0.3367 or about 34%
In addition, any of the unseen ten ranks may form a pair on the turn and river. The probability of this is:
49*48/2=1176
P=10*6/1176=0.0510 or about 5%.
Thus, without consideration of Hero’s cards, the flopped straight has about a 39% chance of being up against a possible full house or quads by the showdown.

• a different 12 possible cards (sevens, eights, and tens) enable a higher straight.
P=1-37*36/49/48=0.4337 or about 43%
In addition, a king plus a queen, a king plus a jack, or a queen plus a jack on the turn and river also enables a higher straight.
P=3*4*4/1176=0.0408 or about 4%.
Thus, without consideration of Hero’s cards, the flopped straight has about a 47% chance of being up against a better straight by the showdown.

• For a flush to become enabled, the turn and river would have to be a running pair of hearts, diamonds, or clubs.
P=3*12*11/2/1176=0.1684 or 17%.

The percents add up to more than 100% (39+47+17=103) because there can be some overlap. (Both a higher straight and a flush or a higher straight and the board pairing are possible. And it’s also possible to have the board pair and also enable a flush.)

But even if we subtract the overlap, there’s a better than 90% chance the flopped middle card straight, which is the nuts on the flop, will not be the nuts on the river.

If you flop the nut straight yourself
If you flop the nut straight yourself, you’d like to protect it if possible. You protect it by betting or raising so as to induce opponents to fold. The idea is to cut down on the possibility an opponent who would fold to a bet or double bet continuing and outdrawing you.

But if betting or raising won’t induce anyone to fold, then don’t try that tactic. Only do what works for you against the opponents who are in the hand with you.

If you don’t flop the nut straight
87 is not a particularly favored two-card combination. But that’s not to say one of your opponent will not be playing 87**. Tight opponents, unless with another great two-card combination, will probably not be voluntarily playing 87**, but non-tight opponents might. And in unraised blinds, anyone, even tight opponents, can have anything. Try to get a read on your opponents. Try to figure out why someone bets, raises or calls. (There are a variety of reasons, not all dependent on a particular card holding).

Playable Hands for R2 type flops.
For any R2 type flops, whether a straight is possible or not, you want to have a nice low draw and something decent for high. You want a nice low draw because roughly three times out of four, low will become possible after an R2 type flop.
• 9,6,5 “R2” flop, flopped straight possible.
• 9,6,2 “R2” flop, straight draw.
• K,7,2 “R2” flop, no straight draw.

Flopped Sets: To flop a set, you need a pair in your hand. Except for aces, kings, and perhaps queens, pairs in Omaha-8 starting hands tend to be more of a liability than asset. You only will get a flop with a card the same rank as your set one time in eight. In other words, seven times out of eight, your set will miss on the flop.

When you do make a set, you’re more or less drawing for the board to pair so that you will make a full house or quads. When the board pairs, there are always six possible full houses. When the board pairs and you make a full house, you want it to be one of the better full houses rather than one of the poorer full houses. When the pair in your hand is lower than the pair on the board, you have one of the poorer full houses. You don’t want to get there. A way to tend to avoid the dilemma of what to do if an opponent is betting as though he has a better full house is to avoid making a poorer full house. The simplest way to do this is to tend to shun starting hands with low pairs.

Folding starting hands with low pairs probably goes contrary to the grain, especially if you’re used to playing Texas hold ‘em. But in Omaha-8, although it’s always possible for you to make a poor play and then get lucky, low pairs in starting hands are more of a liability than an asset.

If someone flops top set, it’s the best hand after the flop. Even if someone flops middle set or bottom set, it’s still probably the best hand after the flop. In general, the lower the flopped set, the more protection it needs. You protect your flopped set by betting or raising so as to knock out opponents where possible. A general problem with betting after a flop with two low ranks is your opponents may have good low draws. Depending on the particular individual opponents, it may be difficult or impossible to “protect” your flopped set after a flop with two low ranks.

When you flop a set of kings and no straight draw is possible, you want to charge the low draws, back-door flush draws, back-door straight draws, lower sets, two pairs, and various other hands that might want to continue. When you flop a set of kings and the flop also enables a straight draw, then in addition to a low draw, you have to be wary of an opponent making a low and a straight or back-door flush.

But some of your opponents may play starting hands with low pairs and may think they have strong hands when they flop a low set.

Flopped Two Pairs: In Omaha-8, when you flop two pairs after a flop with two low cards, in general you don’t your flopped two pairs to be bottom two pairs, especially if your low draw is counterfeited.

But some of your opponents may think they have strong hands when they flop any two pairs, even bottom two pairs. Then if the board pairs on the turn or the river, these opponents may have made a full house or quads.

Flopped One Pair: After an R2 flop In Omaha-8, without also the nut-low draw, one flopped pair is not a good hand.

Draws and “back-door” draws:
When you need two cards to make your hand after the flop, one on the turn and the other on the river, you have a “back-door” draw.

For a rough comparison of low draws to back-door low draws, if one rank (of four) is needed on either the turn or river, the probability of making low is good,
P=1-29*28/45/44=59.0%.
But when two ranks (of four) are needed, one on the turn and the other on the river, the probability of making low is poor,
P=16*12/2/990=9.7%.
The probability of making a back-door low is thus about one sixth of the probability of making low when either the turn or river is needed, not both.

“back-door” flush draws:
For a rough comparison of flush draws to back-door flush draws, when only one heart of nine is needed to make a flush, the probability of making the flush is good, about 36%.
1-36*35/45/44=0.3636
But when two cards of ten are needed to make a flush, one on the turn and the other on the river, the probability of making the flush is poor,
45/990 or about 4.5%.
In other words, the probability of making a back-door flush is about one eighth of the probability of making a flush when either the turn or river is needed, not both.
After a rainbow flop, there are only back-door flush draws. You don’t generally want to be drawing for back door flushes.

Low Draws:
You don’t usually need the nuts to win for high even at a full (nine or ten player) table. Indeed two pairs, never the nuts, is the most common type winning hand at tables where fewer than five opponents usually see the flop. But since many of your opponents will tend to include hands with at least one good two-card low combination within their voluntarily playable range, you do want the nuts for low at a full table. Therefore, when drawing for low, unless you have a strong high draw, only be drawing for the nut low.

At a full nine player table, when the nuts for low on the river is ace-deuce, assuming nobody would fold a hand containing and ace and a deuce before at least seeing the flop, as simulated (100,000 runs, Wilson), at least one player will have been dealt a hand with an ace and a deuce 56.2%. And at least one opponent wins low with the 2nd nut low 24.4%. The combination of those two is 80.6%, more than four times out of five.

At a full ten player table, someone will be dealt a hand that would make either the nut low or the second nut low, as simulated, 84.5%.

At a full six player table, someone will be dealt a hand that would make either the nut low or the second nut low, as simulated, 63.7%.

Since one cannot make the nut low without two wheel cards, “good” two card low combination means at least two wheel cards. But all two-card combinations of two wheel cards are not equal. Ace-deuce is clearly the best and ace-trey is clearly the second best two-wheel-card combination.

Some tighter opponents may need a hand with at least three wheel cards to voluntarily see the flop. Your opponents do not all play the same and to do well, you should remember who plays how.

At any rate, after a flop with two low cards, some, if not all, of your opponents may be drawing primarily for low.

R2 flops only represent only 11.4% of possible flops (without consideration of Hero’s hand) but what is written about low draws for R2 flops is generally applicable to other flops with two card ranks as well.

Without consideration of Hero’s cards, there are
• 3584 possible flops with three low ranks,
• 10304 possible flops with two low ranks,
• 7072 possible flops with one low rank, and
• 1140 possible flops with no low ranks,
(the total is 22,100)

As you can see, flops with two low ranks are most common.

After a flop with two low ranks, without consideration for Hero’s cards, low will become possible on the turn or river almost three times out of four (74.5%).

There’s no telling for certain if anyone will qualify for low if low does become enabled, but there’s a fair chance an opponent who continues to play after an R2 flop has a good low draw (and possibly a decent high draw as well).

Best hands to hold after R2 flop:
• nut low draw plus any set,
• nut low draw plus top two pairs, or
• nut low draw plus top and bottom two pairs.

Know your opponents:
Will anyone have one of those three hand types listed? Will anyone have been dealt cards that would make one of those three hand types?

Probably not.

But at a six handed table (five opponents), after an R2 flop that contains neither an ace nor a deuce, someone will have the nut low draw (A2**) about 41.7% of the time. Without something very good for high, you don’t want to be playing for low without the nut low draw. (And when nobody has the nut low draw, someone will have the 2nd nut low draw another 22.6% of the time. That total is 64.3%.)

And at a ten handed table (nine opponents), after an R2 flop that contains neither an ace nor a deuce, someone will have the nut low draw (A2**) about 60.6% of the time. Without something very good for high, you don’t want to be playing for low without the nut low draw. (And when nobody has the nut low draw, someone will have the 2nd nut low draw another 23.9% of the time. That total is 84.5%.)

There’s no telling for certain if anyone will qualify for low if low does become enabled, but there’s a fair chance an opponent who continues to play after an R2 flop has a good low draw (and possibly a decent high draw as well).

Bluffing when there are two low cards on the flop is not generally effective. That’s not to say bluffing never works here. That’s also not to say your opponents will never try it. It’s just that bluffing after an R2 flop is a low percentage play - depending, of course, on your particular opponents.

by Frank Jerome