The Flop

The flop was 983. The first player bet and two online poker players called. What should our hero do?
The conventional wisdom says to fold. The reason for a fold is simply that we only called based on the chances of flopping a set. We missed the flop and discard your hand and just go for the next hand. On the contrary we have good-sized pot here.

Let's analyze what kinds of poker odds that we are getting for a call. Eight players called two bets each before the flop. Now there are sixteen bets which went into the pot before the flop. We have one bet and two callers, adding three bets to the pot. We are getting at least 19-1 to call if no one raises.

What are the chances that the next card will be a 4? We have seen five of the fifty-two cards. Forty-seven cards still left in the deck. Two of them are 4s. Two out of forty-seven cards will make our set and forty-five out of the forty-seven will not help us. The odds are 22.5-1. The pot odds are not much big enough but if we do make a set of 4s on the turn we will win a few extra bets on the last two betting rounds in holdem poker. Generally we look for odds of about 20-1 to call a bet on the flop with a small pair with the intention of making a set. We don't have that, but with at least three other players active, we can be almost sure that we can gain more than one or two extra bets on the also betting rounds and they are double-sized bets. Thus depending purely on the pot odds our hero should probably call. The combination of the large pot and our implied odds from future bets is big enough.

When thinking about calling on the flop to draw to a small pocket pair, we not only need to think about the pot odds we are getting on the call, but we also need to be sure that we really will get those pot odds, that no one is going to raise. Further we need to consider the probability that our three-of-a-kind will be the best hand should we get lucky and spike the third of our rank on the turn card. In this situation we have one player left to act, and that player had raised before the flop. The risk to of him raise holdem poker hand might be large. This is a situation where tells come into the view of the play. The main thing to do is to distinguish between when they are acting and when they are behaving naturally. A player who is not paying attention to the action and is behaving naturally probably doesn't really care what's happening and is going to fold but a player who is acting in such a manner that he wants you to think that he's not paying attention is very interested in what's happening and is very likely to raise.

What about the probability that a 4 on the flop will make someone else a better hand at the same time it makes your hand? With a flop of 983 a 4 won't make anyone a straight, and one of our 4s is a Diamond, matching the suit of the potential flush draw. That means that a 4 can't make anyone a flush. This consideration is very significant. No matter how large your pot odds, if there is a potential flush draw on the flop, it is almost never right to take one more card off in the hope of turning your pocket pair into a set unless you have a card in the flush suit. That's because making three of a kind with the same card that makes someone else a flush can be dangerous. It is dangerous that is best avoided.

There are some other reasons against calling. It is possible that someone else has a pocket pair of 8s or a pocket pair of 9s, meaning that you would be drawing dead, but that's very unlikely. It is not worth worrying about someone having a larger set unless there is some clear-cut reason to think they do, and there's no reason here to think that. Our hero bet called the bet. The button called but didn't raise.

The Turn

The card on the turn was 3. Now the board looks 9833. To our surprise, the first three players checked.

Until now it was safe to assume that someone had an 8 or a 9 and that our pocket 4s were not the best hand, but with every-one checking it starts to look as if everyone has some kind of a draw. Maybe flush draws, straight draws, or overcards draws. With the 9 and 8 on the board, a lot of players would call a bet on the flop with a hand like KJ and then check on the turn. If that's the case, it is important to bet.

Betting requires some change in thinking at this point. Until now we were playing passively, assuming we didn't have the best hand and would have to passively play catch-up in order to end up with the best hand. It also seems that no one else has much of a draw, but a lot of cards can still beat us. The other players don't realize it. A bet may likely cause players who have nothing except cards larger than a 4 to fold; they won't realize that they are getting the pot odds to beat our miserable pair of 4s.

Our hero bet. This bet was very crucial play in this hand. A couple of players folded and a couple of them called.

The River

The card on the river was a Queen and it didn't make a flush. At last the board looks like 9833Q. Everyone checked. Our hero showed his pocket 4s; everyone folded. Our hero won the pot with the pair of 4s.

Without knowing more about the players, checking was really the fair option our hero had. If we know about the other players though, there are times when it would be correct to bet in this situation. There are players who don't call enough on the river and would certainly fold an 8. There are also players who were calling may be with an Ace for high. If two remaining poker players have those kinds of habits, a bet might be considered. Checking is also automatic under normal circumstances.


This was an unusual hand ending with an unusual result. Our hero was fortunate enough but it is not all luck. His quick wittedness on the turn by taking advantage of an unexpected turn of events probably saved a day for him. One of the players who had folded on the turn gave a wince when the Queen fell on the river. It is clear that the player had folded a hand with a Queen in it.

The key of this hand is both that you need to consider the pot odds when calling as our hero did calling before flop and on the flop and you need to be careful to the changes in this situation, taking the benefit of information as the hand unfolds

Continue: Mathematics of Poker