limit O8 - betting top two pair or a set on the turn (or not)

[Buzz]

I hadn’t thought about this before reading a recent post by Tex.

Suppose Hero’s hand is A[img]/images/graemlins/diamond.gif[/img], Q[img]/images/graemlins/diamond.gif[/img], T[img]/images/graemlins/club.gif[/img], 8[img]/images/graemlins/heart.gif[/img], and the board after the turn is Q[img]/images/graemlins/club.gif[/img], T[img]/images/graemlins/diamond.gif[/img], 6[img]/images/graemlins/diamond.gif[/img], 3[img]/images/graemlins/club.gif[/img].

Notice that every single card possible river card in the deck either pairs the board or enables a straight. I don't think it's an unusual situation for most or all river cards to pair the board or enable a straight.

Four of Hero’s opponents see the flop for one small bet each. SB bets the flop, BB calls, and Hero raises. Button calls the double bet and both blinds also call. Thus three opponents stay to see the turn, (3[img]/images/graemlins/club.gif[/img]).

Should Hero bet this turn or not?

(Peeking ahead to the showdown, Hero has only one opponent, Button, who is putting money into the pot. The other two opponents, presumably having missed their draws, fold to a bet on the fourth betting round. Hero needs this sort of information to estimate how much to expect to be able to collect on the river if he makes his draw.)

Because of the money already in the pot, there is no question about whether Hero should call a bet on the third betting round. Hero clearly has favorable odds to call a bet.

But should Hero initiate fresh money into the pot or not? <font color="white">_</font>That is the question. With three people calling, at first glance Hero would seem to have favorable fresh money odds to initiate a bet on the turn.

However, if Hero misses (fails to make the nut flush or a full house on the river), he’s still going to have top two pair and he’s going to wonder if he should pay off a bet on the river or not.

That’s going to be the situation almost every time Hero either has top two pair or a set after the turn and then fails to improve on the river.

When no straight or flush is yet possible after the turn, top two pair or a set is almost surely the top high hand. That is, if there was no river and if the game stopped after the third betting round, Hero’s top two pair would be a likely winner.

However, there’s that pesky river card yet to be known - and then one more betting round.

Looking ahead, if Hero is going to be stuck in the hand and pay off an additional large bet because of the size of the pot, he’s going to be putting in a big bet on the fourth betting round when he misses on the river.

In other words, if Hero intends to call a bet when he misses on the river, in terms of fresh money going into the pot on the third betting round, Hero is really only getting two to one fresh money odds, instead of the three to one Hero is getting if he folds to a bet when he misses on the river.

Immediately after the turn, when no straight or better is yet possible, probably nobody would be able to beat top two pair (or any set) for high. Sensing that, with either top two pair or any set, it seems natural to want to get as much money into the pot as possible.

Like Tex, I would have been inclined to bet the turn, but let’s think about it.

Realistically, is there any way a single big bet by Hero will take the pot (with everyone folding to the bet)? Is there any way a bet will induce anybody who doesn’t hold pure garbage to fold?

I don't think so. This is a $15/$30 limit game, not a pot limit game. Because of the size of the pot already, after a trey on the turn, Hero simply cannot make a bet large enough to knock out anybody except perhaps someone holding A3XY or 23XY who was stupidly drawing purely for a non-nut back-door low (or something of the sort). What I mean is Hero cannot make a bet large enough to knock out a valid draw after this flop and turn and the betting up to this point.

Meanwhile, of the forty four unknown cards, seven (the high diamonds plus the tens and queens) are scoopers for Hero while five more (all the low diamonds except the trey) win the high half of the pot for Hero.

With a queen on the river, Hero could get tied by an opponent also holding QTXY. With a ten on the river, Hero could get beaten by an opponent holding QQXY or tied by an opponent also holding QTXY. Neither of these is likely.

With a queen on the river, I think Hero gets tied by another QTXY about one time out of twenty.

With a ten on the river, I think Hero gets tied by another QTXY about one time out of twenty, and loses to QQXY about one time out of forty.

I ran the sims for a ten or queen on the river on the basis of four opponents seeing the flop and assuming anyone holding QQXY or QTXY would continue after a QT6 flop. (That’s the only way Hero could get tied or beaten when he made a full house on the river). At any rate, the queens and tens are not quite as good outs as high diamonds - but for the sake of keeping it simple let’s not quibble about the 5% ties or the 2.5% beats.

The trey of diamonds is enigmatic. Hero would certainly rather see any high diamond on the river, and next he’d rather see a queen or ten, but the trey of diamonds doesn't enable low, and probably no opponent will make a full house with it so that Hero’s diamond flush, although not the nuts with a pair of runner-runner treys on the board, is <font color="white">_</font>probably a scooper. For the sake of simplicity, let’s group the 3[img]/images/graemlins/diamond.gif[/img] with the scoopers.

Since a low diamond on the river probably only gets Hero half the pot and (more to the point) only half of any fresh money Hero initiates into the pot on the turn, a low diamond is not equivalent to a whole out.

When Hero scoops, because of the size of the pot, let's assume Hero will collect one big bet from an opponent on the river. (Notice that in the actual hand two of Tex’s three opponents folded to a bet on the river).

Just considering the fresh money going into the pot on the turn plus the one (implied) pay-off bet from an opponent, Hero seems to be getting 4 to 1 fresh money odds (implied) for the whole pot and 1 to 1 fresh money odds (implied) for half the pot. But looking ahead - if Hero misses his draw on the river, does Hero plan to call a bet by an opponent because of the size of the pot?

Yes, or no?

Look ahead. You can see it coming. If Hero misses his draw on the river Hero should fully expect a bet from somebody. If nobody ahead of Hero bets, then Hero should fully expect a bet from Button (assuming Hero doesn’t bet himself).

And then what?

If Hero does not plan to call a bet on the river when he misses his draw, then
• 8/44, Hero scoops and wins 4 big bets fresh money,
• 5/44, Hero splits and wins 1 big bet fresh money, and
• 31/44, Hero loses 1 big bet fresh money.

However, if Hero does plan to call a bet on the river when he misses his draw, then
• 8/44, Hero scoops and wins 4 big bets fresh money
• 5/44, Hero splits and wins 1 big bet fresh money, and
• 31/44, Hero loses 2 big bets fresh money.

That’s not quite it because we’re ignoring some ties and losses of some of the 8/44 river scoops, but it’s good enough to see an important difference. In terms of fresh money Hero initiates into the pot on the third betting round,
• if Hero plans to call the (expected) bet when he misses his draw on the river, then Hero does better by checking the turn.
• However, if Hero plans to fold to a bet on the river when he misses his draw, then he does better by betting the turn.

I’m not criticizing the way Tex played the hand. Not at all. Tex played the hand just as I would have played it.

But maybe we should re-think betting top two pairs or a set after the turn in a typical limit Omaha-8 game if by doing so we're going to make the pot large enough that we'll probably be stuck paying off when we miss our draw on the river.

(With the added nut diamond draw, I realize Hero actually has better than just top two pairs - but usually when we have top two pairs on the turn, we’ll also probably have better than just top two pairs).

Anyhow, this is just an idea I haven’t completely thought through - but that seems to make preliminary sense. In a limit Omaha-8 game, if we’re going to call a bet on the river even when we don’t improve, maybe we generally do better by not betting top two pair or top set on the turn. On the other hand, if we’re not going to call a bet from an opponent on the river when we miss, looks like we do better by betting (or raising) with top pair or top set on the turn.

Seems odd, kind of the opposite of what it should be. I’ll give it some more thought.

Just an idea.

Buzz