From all that I’ve read, it seems the difference between great poker players and the rest of us is the fact that, by the time the river card is dealt; great players pretty much know what hand their opponent has while we mere mortals are basically guessing. That’s not necessarily what I see in many of the televised poker tournaments; great players make mistakes all the time – it’s generally labeled “a bad read”, rather than a mistake, but it all amounts to the same thing – the player, great or not, misplays the hand by folding a winner or calling with a loser.

Ideally, you will know exactly what you’re facing after the river card is dealt. Should your opponent bet, you’ll know if it’s a bluff or if s/he has a better hand than yours; if your opponent checks, you’ll know if s/he is trapping or not. That’s the ideal situation – something we can aspire to, but in reality we’ll never know with 100% certainty – great player or not. But suppose we can determine the situation with 75 or 80% accuracy, which would still be an improvement over guessing and should put some $$$ in our pocket, right? Even if we can’t determine exactly what our opponent’s holding, there are certain mathematical aspects to river bets that can help us in the decision-making process. Perhaps more importantly, if we can win some extra bets on the river (primarily through bluffing or “value” betting), then calling our opponents more often can still be a positive expectation for us in the long run. River bets are a two-sided coin and we’ll examine both as we go along.

In Limit games – primarily Hold’em, because that’s mostly what we talk about here – whether or not to call on the river is, to a large degree, a function of pot odds. If the pot is big enough, I’ll call with almost any hand. Give me 20 to 1 odds and I have to win only 5% of the time in order to break even. Remember now, we’re talking about a bet on the river, so all of the cards we’re going to see for this hand are out – a drawing hand isn’t going to do us much good. Of course, that’s not to say your missed Straight or Flush draw isn’t the best hand, but with no more cards to come, it isn’t going to get any better, so if you call you better have some chance of winning. If your opponent is bluffing with his bet on the river, you certainly have some chance of winning, but you might still lose to a card higher than yours, assuming a kicker will apply in the hand. Obviously, if the board (the five community cards) form a Full House, Straight Flush or other similar hand, nether you nor your opponent may be able to break a tie with one of your pocket cards, but you still want to be in on the “chop.”

My advice to Limit Hold’em players is to remember that river bets are pretty much cut-and-dried; players know their bet will likely be called, so bluffing is not as strong a tactic. That’s not to say bluffing doesn’t happen – particularly in higher limit games like $100/$200 – but the pot odds almost always justify a call. On the other hand, a player who feels she or he likely has the best hand should almost always bet on the river because even a raise by their opponent will usually offer the proper odds for a call. A place where you can go wrong here is when playing one of those hands that saw a lot of checking on both sides. If your opponent finally bets after the river card is dealt and the pot is offering, say, only 4 to 1 odds, it could be a mistake to call if you think your hand will be good less than 25% of the time. For example, let’s say the pot is $60 in a $10/$20 game and your opponent bets $20 into you. The pot is now $80 and it’ll cost you $20 to call, which is a 4 to 1 return, should you win. If you do this four times, you’ll call 4 times $20 = $80, lose 3 times and win once, if you have a 25% probability of winning. You can see that’s the break even point. But if you can beat only a bluff (let’s say you have Ace high and your opponent has absolutely nothing) and your opponent bluffs only about 10% of the time (actually a fairly good number for Limit Hold’em river bets), then you’d call 10 times, which costs $200 and win $80 only once, for a net loss of $120.

We can gather from this the fact that we have to assign some sort of probability to the success of our hand when facing a bet on the river. That seems to inject a random element here (what’s called a “guess”) and, while we can’t get completely away from guessing, we can minimize its impact through deductive reasoning. Bluffs work against good players only if they’re believable. That may seem obvious (“Wow, GM…how profound!”), but even inexperienced players have some of that old “IJDLR” in them: It Just Doesn’t Look Right. A bluffing bet on the river is the final chapter to a story that’s been told since the cards for the hand were first dealt. Did the player raise pre-flop? If so, an Ace on the river may signal that s/he has paired an Ace in the hole. If that player did not raise pre-flop, s/he may still have a pair of Aces, but a bet now seems more like a bluff, so if the Ace improved your hand, a raise on your part might be in order. Certainly, if the river card is one that that may have made a Straight or Flush for your opponent, a bet on the river is going to be tough to call. But before you fold, piece together the story this hand is telling.

The way I “read” the story of a hand is pretty simple and I find that taking the optimist’s point of view works best for me. One of my all-time favorite sayings goes like this: “The pessimist may be right in the long run, but the optimist has more fun on the trip.” As an optimist, I naturally think my opponent does not have me beat, but the mathematician in me says I have to prove that to one degree or another before I can place a wager on my hand. It’s a process I covered somewhat in Lesson 21, “Sniffing Out a Set”, which you should review, because you may well be up against a set on the river. But more likely, an opponent who’s bluffing will have a busted Straight or Flush draw and they’re 90% sure the only way they can win the pot is by leading into it on the river. Are they bluffing if they have top pair with a lousy kicker, 2nd pair, 3rd pair or just Ace high? Well, of course that all depends upon what you’re holding. If you have top pair, top kicker, then they are bluffing and you’ll hopefully pick them off by calling. If they have a set and you haven’t gotten away from the hand yet, you’re probably going to lose, because they’re not bluffing unless you made a Straight or Flush.

I’m throwing out a lot of possibilities here, which – if taken too seriously – can easily let you talk yourself into folding. That must be avoided if you hope to become a winning player and to do that, you have to make a realistic evaluation of the probability your opponent actually made the hand s/he is betting. Notice that I said, “the hand”, not “a hand”. If a 9h hits the river and that’s the 3rd heart on the board with no Straight possibilities, a bet by your opponent is implying s/he made a Flush much more than it means s/he made a set of 9s or two-pair, although that certainly is possible – and would generate a bet just like a made Flush. (If your opponent thinks the card helped you make a Flush, I’m going to assume s/he would check, absent holding the Ace-high Flush.) If we take those three possibilities, two-pair, a set of 9s or a Flush, what are the probabilities of each? A third suit on the river means a player who was holding two cards of the same suit in the hole just hit a 9-outer, at best. (With me on this? With two suited cards in the hole and two more of the same suit on the board, there are 9 cards of that suit unseen, assuming you don’t have one yourself in which case there’d be only 8 – if you had two of them, it would be Flush vs. Flush and it’s back to a guessing game, unless you have the Ace.) Anyway, if you don’t have any cards of that suit, there’s a 21% chance your opponent made his Flush. There were 9 cards of the suit in question still to be played out of the remaining 44 cards (2 in your hand, 2 in your opponent’s hand, 4 on the board before the river card is dealt = 8. Subtract that from 52 and you get 44 cards remaining.) Divide 9 by 44 and you get 20.5% and it’s 8 of 44 if you have one of the suit in your hand, which makes it 18.2% s/he made a Flush. As I mentioned, perhaps the 9h made a set of 9s, which means your opponent just hit a 2-outer, which has a probability of 4.5%, assuming you don’t also have a 9, or may have hit a 6-outer to make two-pair, which has a probability of 6/44 or 13.6% (Got it? Three cards of each of your opponent’s two hole cards remain – that’s 6 outs, at best.)

What this all boils down to is this: If you have any kind of hand that will warrant calling a bluff (top card; any pair, etc.), there is about a 40% chance your opponent is NOT bluffing in this hand and has two-pair, a set or a Flush, which means you have a 60% chance of winning. If those are the only hands that can beat you (your estimation or guess), a quick examination of the pot odds will tell you whether or not you should call, assuming your stack of chips make the pot odds your primary consideration. In a cash Limit Hold’em game, that’s easy to do; we’ll discuss No-limit Hold’em next. For this to be a very profitable call in any type of game, the pot has to be paying you only 1 to 1, which requires just a 50% probability to break even – you should be in the 60+% range in this example.

The probabilities and odds for the situation discussed above do not change in No-Limit Hold’em, be it a cash game or a tournament, but factors other than the odds may influence your decision. In all frankness, if it’s a cash game and you have such odds available, you’d be crazy not to call your opponent’s bet. Of course, if your opponent overbets the pot, which puts your odds below 1 to 1, you’ve got a decision to make. To me, big (more than pot-sized) bets on the river in NLHE games are either black or white – s/he’s bluffing or has the nuts. In those cases, there’s still a story being told, like did the bettor raise pre-flop, bet or check the turn, etc., but in the final analysis, I know I have to call some of those bets or my opponents will try to run me out of hands like this by making big bets on the river. Depending upon how well I know the opponent, the size of my stack in relation to his, whether or not “It Just Doesn’t Look Right” and other factors I’ll keep to myself for now, I may call an overbet that has reduced my pot odds to below 1 to 1 fairly often. Don’t forget, because this is frequently an “all or nothing” bet, it’s usually fairly easy to make a decision. If I already believe my opponent only a 35% chance of having made the hand s/he’s betting, I would call a “loose” player and fold to a “tight” player when the pot odds are less than 1 to 1 in a situation like this.

The other consideration is, of course, NLHE tournaments where such a call might cripple you or knock you out of the event. In situations like that, pot odds are not my only criterion for calling. If I’m sort-stacked and need to gamble, I might call, but I’d much prefer to have pot odds of 1 to 1 or better, if my read is that I have a 65% chance of winning. If I have a big stack, I’ll definitely gamble with 50% of it in a situation like this (maybe even more) because I might be able to eliminate or at least cripple an opponent. Beyond that, I just try to remember I’m essentially playing my opponent’s hand, so I give thought to his or her situation: will a call by GM (moi) eliminate me? Am I (my opponent) so short that I have to gamble here? Have I bluffed recently and got caught? (Again, I’m thinking like my opponent.) Is my opponent (GM) a tight player who will fold to a bluff? Generally, if they “know” me, they’ll consider me a tight player, but in tournament situations that’s hard to determine at the beginning of the event or if I just joined the table, so I don’t give that thinking a lot of credibility. And so forth.

To sum this up, remember that this also works if I feel a need to bluff on the river, with the biggest question being, who did the river card help the most? I keep a 3 x 5 card handy that shows me the probabilities that my opponent may have made certain hands on the river and, of course, I already know my situation, so if the percentages make sense – and the “story” being told allows for a bluff – I usually make a bet where I try to reduce my opponent’s pot odds. You can’t always do that but if the pot contains, say, T1000 and I bet T500, my opponent is getting 3 to 1 odds to call me, whereas if I bet T1500, my opponent is getting 2500 to 1500 or less than 2 to 1 odds, which may or may not induce a fold. It’s usually easier for players to believe a “big” lie than a small one – which favors a pot-sized or larger bet – but against experienced tournament players, a small bet like T300 into a T1000 pot looks suspicious; it has “please call me” written all over it, along with the added benefit of being a smaller loss if my bluff fails. I use both methods and will continue to do so in the (relatively) few times I bluff on the river.

I’ll see you here next time.