Part I (May, 2008) involved a discussion of low aspects on the river. Part 2 (June, 2008) focused on
- I. top two pairs,
- II. three of a kind, and
- III. straights.
This month we’ll conclude the river series with consideration of
- IV. full houses and quads,
- V. flushes, and
- VI. straight flushes.
IV. Full houses and quads on the river
When you flop a set or trips, although you will win more often with the unimproved three of a kind than when you improve to quads or a full house, you are drawing for quads or a full house, and perhaps also a straight, flush and/or low. When you improve, it will be to a full house more often than quads, but sometimes it will be to quads.
The same is true of flopped two or three pairs.
Hero, sitting UTG, holds
A
, T, T
, 3
,
The board on the river is
7, 2
, K, T,7, with the cards dealt in that order.
Five players saw the flop for one bet each. (Hero limped before the flop, along with two players behind him and both blinds). Both blinds checked the flop, Hero bet, SmallBlind folded and the other three opponents called. Hero also bet the turn, BigBlind folded, but the two players behind Hero both called. Thus on the river, after the rake, there are seven big bets in the pot, low is not possible, and two opponents are still in the pot.
When the board has one pair, from Hero’s perspective, there are generally six possible full houses. If Hero does not have a card the same rank as the pair, quads are also a possibility.
In this particular case, since Hero does not have a card the same rank as the pair, the possibilities for high hands, arranged in descending order of strength starting with the nuts, are:
77XY,
KKXY,
TTXY, * Hero is here.
K7XY,
T7XY,
72XY,
22XY,
nut heart flush.
Hero thus holds the third nuts and can only be beaten by 77XY and KKXY.
Let’s suppose Hero would normally check and fold without a flop fit. Thus when Hero bets the flop, his astute opponents recognize that he has some sort of fit with the flop.
But what can the fit be when the flop is
7, 2, K?
Assuming Hero normally bets low draws, flush draws, flopped sets, flopped two pairs, and combinations of these - Hero’s astute opponents cannot tell which of these his flop bet represents.
In this particular case, by the time the river is reached, Hero’s opponents cannot tell for sure if Hero has been betting a high hand, a low hand, or a two-way hand.
Hero’s opponents cannot know Hero had the nut low draw after the flop and then picked up a set of tens (trip tens) on the turn.
Notice that it is important for Hero to bet this flop, both for this deal and for future deals - and that it was important for Hero to also have bet various other flops (where he continued) before this deal. Otherwise, if Hero suddenly started betting on the turn, Hero’s opponents would more strongly suspect Hero had turned a set of tens.
This article is about play on the river, but you set up play on the river with your actions on earlier betting rounds, especially the flop. Also of importance in setting up play on the river is the way you have played previous hands.
Although there are two possible better hands on the river (quads and kings full), because of the lack of action on the flop and turn, Hero suspects neither of his opponents actually has a better hand. However, there are no guarantees. One of Hero’s opponents could have flopped a set of kings or sevens and be slow playing them - and if so, Hero is going to get burned.
Occasionally getting burned by quads goes with the territory when you make a full house, as does occasionally getting burned by a slow played higher full house. You have to learn to take it in stride when it happens to you or you’ll hate this game.
Considering the cards Hero can see on the river, an opponent would only have been dealt the missing pair of sevens about one time in 150 (from 820/123,410). Four opponents who would see the flop with a hand containing a pair of sevens would increase that probability to about one time in 38. However, the probability is really much less than one time in 38 because most astute players would tend to fold most hands containing a pair of sevens before the flop. In addition, most opponents would tend to play a flopped set of sevens more aggressively, raising on either the flop or the turn. Thus quad sevens seem unlikely here.
A pair of kings is a greater threat, both because opponents are more likely to play starting hands with a pair of kings than sevens, and also because, considering the cards Hero can see on the river, it’s about three times more likely an opponent would have been dealt a pair of kings than a pair of sevens. But someone flopping a set of kings would probably play more aggressively after the flop and/or after the turn.
By playing passively, even though they have position, Hero’s opponents are now (on the river) at a disadvantage because Hero feels fairly certain neither opponent had a set on the flop or turn. Thus Hero feels rather certain his hand is the best hand on the river, even though he neither has the nuts nor even the second nuts.
And now the question is, “What should Hero do on the river, with two opponents yet to act behind him”? Should he check, trying for a check/raise, or should he bet directly?
The answer depends on Hero’s opponents and their perception of Hero.
1. If neither will bet after Hero checks, then Hero should value bet, hoping to collect from an opponent who calls with a weaker hand (possibly a weaker full house, a flush, or even two pairs).
2. But if both will fold to a bet but might bet after Hero checks, then Hero should check, hoping to induce a bluff or a value bet with an inferior full house.
If Hero is not sure of what to do, his best move is probably to bet directly.
A slightly different full house scenario: Now let’s just change the river card a bit. Hero, sitting UTG, holds the exact same hand as in the last scenario,
A, T, T, 3,
But let’s make the board on the river
7, 2, K, T,K, with the cards dealt in that order.
From Hero’s perspective, again quads plus six full houses are possible.
In this particular case, the pertinent hands are:
KKXY,
KTXY
K7XY,
K2XY,
TTXY, *Hero is here
77XY,
22XY,
nut heart flush.
Notice Hero’s hand has dropped a couple of notches. Instead of being able to beat four full houses, Hero’s hand only beats two full houses, and loses to any kings full.
With this hand on the river, from first position Hero’s best course of action is probably to check/call. (It’s terrible for Hero’s table image to bet/fold).
V. Flushes on the river
Va. Flushes on the river when the board is paired:
Hero is in the big blind holding
A, T, 5, 4,
The board on the river is:
5, 4, Q, 2, Q, with the cards dealt in that order.
Five players saw the flop, four saw the turn, and three (including Hero) continued after the turn. After the rake, there are 9.5 big bets in the pot.
After the turn (2) and third betting round, all three players who have continued (including Hero) should more or less be suspected of holding at least one of the following:
- six-high straight,
- wheel
- flush draw,
- set,
- two pairs.
However, nobody who continues past the turn can know which of these anybody else who continues holds. In addition, there are no guarantees that players continuing actually do have one of these hands.
And now on the river Hero, holding the nut flush (but the board is paired) is first to act. Should he check/fold, check/call, hope to check/raise, or bet?
Now (on the river) the possibilities for high are:
- quad queens,
- six different full houses,
- a flush, *Hero is here.
- a six-high straight,
- a wheel,
- trip queens,
- two pairs.
In addition low is possible, but not for Hero.
Hero has rivered an ace high flush, but the river card (Q) also pairs the board, enabling a possible full house or quads for an opponent. Notice Hero’s hand also contains two blockers, cards the same rank as board cards - thus reducing the probability an opponent will make a full house.
As simulated for Hero’s hand against four non-folding hands with random cards on the river, approximately three times out of five (60.4%) nobody actually has a full house with this board.
But that’s not realistic for Hero’s two opponents because they do not have random hands. Instead they each probably have one of the hands listed above. Let’s somewhat conservatively view the possibilities for high as:
- quad queens,
- six different full houses,
- 2nd nut flush,
- a six-high straight,
- a wheel.
Considering the statistical likelihood of the hands opponents might be realistically playing after the turn, perhaps surprisingly, an opponent makes a full house on this river even less than simulated, probably closer to one time out of three.
However, keep in mind that Hero probably only wins half the pot when he wins.
Comparison of fixed-limit with pot-limit: In a pot-limit game with two opponents, when one opponent makes a pot sized bet, this amounts to an even money wager for Hero.
In a fixed-limit game with two opponents, when the pot size before the final betting round is 9.5 big bets and one opponent makes a big bet, assuming no raises, this amounts to an enormously favorable (5.25 to 1) wager for Hero!
In general, in a full game, Hero should probably not draw to a flush when the board is already paired, either in a fixed-limit game or a pot-limit game - but if Hero already has the flush and then the board pairs, or if Hero makes the flush at the same time the board pairs, Hero should generally see the showdown in a fixed-limit game.
Pot-limit considerations are somewhat different – but even in a pot limit game, Hero should probably generally call a pot sized (or less) river bet if low, especially a low straight, is possible.
Without blockers which reduce the probability an opponent with random cards will make a full house, and without any other cards that block a full house, the ace-high flush, as simulated, wins about half of the time. (Each blocker adds about 5% simulation value to the flush).
Ironically, although AT22 makes a full house with this board, as simulated against four non-folding hands with random cards, AT22 wins slightly less often than an ace-high flush with two blockers.
Calling on the river considerations are quite different in fixed-limit than pot-limit. In fixed-limit, assuming at least one bet each round and no raise on the river, Hero is getting at least five to one pot odds to call. In pot-limit, if Villain makes a pot sized bet, Hero is only getting two to one pot odds to call.
Vb. Nut flushes on the river when the board is not paired:
Hero is in the big blind holding
A, T, 5, 4,
The board on the river is:
5, 4, Q, 2, 9, with the cards dealt in that order.
Five players saw the flop, four saw the turn, and three (including Hero) continued after the turn. After the rake, there are 9.5 big bets in the pot. Note that this contrived example is the same as the previous one, except no full house becomes possible on the river. Instead, Hero makes his flush draw and has ended up with the stone cold nuts for high. Obviously Hero wants to optimize the money going into the pot.
How best to do this from the big blind depends on Hero’s opponents and their impression of Hero. In general it’s probably best to bet, hoping for a raise, and then re-raise. But against some opponents a check-raise may work better.
Vc. Non-nut flushes on the river when the board is not paired:
In a fixed-limit game if Hero gets this far with any flush, it’s probably best to call one last bet (which could be coming from a low hand or some non-flush high hand).
VI. Straight flushes on the river
VIa. Straight flushes on the river by Hero:
Of course you’d like to make a straight flush. But it’s not worth playing a trashy hand that happens to have a possibility of making a straight flush. Consider, for example,
K,8,7,2.
As simulated, the hand makes 210 straight flushes in 100,000 deals. That’s roughly two straight flushes per each thousand deals. The hand makes quads more often than that (234/100000) and full houses much more often (4854/100000).
Bottom line: hands are not worth playing merely on the basis of having two cards that might make a straight flush.
VIb. Straight flushes on the river by a villain:
Of more concern to you will be the possibility of an opponent having a straight flush when you have a flush or better.
Consider, for example:
K,A,3,2.
That’s a hand you’ll actually be playing. As simulated (200000 deals against 8 random hands), when the board on the river is
K,T,9,6,2 (one possible straight flush),
the ace-high heart flush loses to a straight flush 5.170%. But that’s for a non-folding simulation. In order to lose to a straight flush in real play here, someone would have to be playing 8,7,Y,Z. That’s a hand that probably gets folded before the flop.
When the board on the river is
K,T,9,7,2. (two possible straight flushes),
the ace-high heart flush loses to a straight flush 10.213%.
When the board on the river is:
K,T,9,8,2 (three possible straight flushes),
the ace-high heart flush loses to a straight flush 15.009%. But that’s for a non-folding simulation. In real play someone would have to be playing a heart combination that would lead to a straight flush. Q,J,Y,Z is more of a possibility of cards not folded before the flop than J,7,Y,Z or 7,6,Y,Z, but none of those heart combinations is particularly appealing.
Bottom line: When Hero holds the ace-high flush, even though a straight flush may be possible, an opponent is not likely to have it. Only when an opponent raises or re-raises should Hero seriously consider the possibility (and probably simply call the raise or re-raise).
This concludes the three part river series.