Bluffing against one opponent
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Lets examine the less complex situation of bluffing on the river against one opponent. You are in last position and your opponent has checked to you. Here are the scenarios that you will be facing:
A. You have a good to strong hand
B. You have a mediocre hand
C. You have a below average hand
D. You have a very poor hand
Situation A is a simple situation. You should be betting and hoping your opponent calls and loses more chips to you. This is not a bluff.
Situation B is a little more complex. This is the type of situation that comes up where you have to think if it is worthwhile to make what is called a “value bet”. This is defined as a bet when your cards are not that great, but you still think there is value in making a bet because you believe your hand is stronger than your opponents with a decent degree of certainty.
Situation C & D are the situations where the decision of whether or not to bluff comes into play.
In each Situations B, C and D, the size of the pot needs to be considered as well as the opponent’s thoughts on the size of the pot. In Situation B, if the pot size is large, you should be more inclined
to make a wager, because your opponent will be more inclined to call with a worse hand since he believes he is getting relatively large pot odds in case you were bluffing. In Situation C & D, a bigger pot will reward you more handsomely for a successful bluff than a smaller pot would. But keep in mind that your opponent may be aware of the relative pot size as well, and thus may be
more inclined to call your bet when the pot is bigger. Here are some examples of Situation C&D
Example of Situation C
Assumptions:
1. You have a 25% chance of having the best hand
2. If you bet and your opponent has a better hand than yours, he will fold 40% of the time and call
60% of the time.
3. If you bet and your opponent has a worse hand than yours, he will fold 100% of the time.
4. The pot size is 5 big bets
5. Your lone opponent has checked on the River and you are last to act.
Expected Value of checking:
The pot size is 5 big bets. If you do not bet, you have a 25% chance of winning the hand and a 75%
chance of losing the hand. The expected value of checking in this hand is:
Expected Value of checking = (25% x 5 big bets) + (75% x 0 big bets) = +1.25 big bets
It is important to forget about the chips that you have put in the pot yourself in previous rounds. Those chips are now a sunk cost, it is no longer your chips as it currently belongs to the pot.
Expected Value of betting:
In the assumptions, it states that if you bet and your opponent has a better hand, he will fold 40%
of the time and call 60% of the time, but if he has a worse hand, he will fold 100% of the time.
In the assumptions, it was stated that when you have the best hand (25% of the time in this example), your opponent will not call a bet. When you have the worst hand (75% of the time in this example), your opponent will fold 40% of the time and call 60% of the time.
The expected values individual situations are: You have the best hand = 25% x 5 = 1.25
He has the best hand and he folds when you bet = 75% x 40% x 5 = 1.50
He has the best hand and he calls when you bet = 75% x 60% x -1 = -0.45
Since there is no increased value to betting when you have the best hand (since we have assumed
he will fold 100% of the time when he has a worse hand), the only possible extra value that is
gained by a bet is due to bluffing, when you bluff him out of a better hand. In this example, we are not sure if we have the best hand or not, so it is unclear if we are actually bluffing.
Expected Value of betting/bluffing = (25% x 5 big bets) + (75% x 40% x 5 big bets) + (75% x 60%
x -1 big bet) = +2.3 big bets
When we bet, we have an expected value of +2.30 big bets. In this example, it is clear that betting
is better than checking, as an expected value of +2.30 big bets is better than an expected value of
+1.25 big bets in checking.
If the numbers were slightly changed, then it could make the bluff an incorrect move. Lets change the assumptions and assume that instead of folding 40% of the time when he has the best hand,
your opponent is only going to fold 10% of the time when he has the best hand, and call 90% of the time. Then the expected value equation becomes:
Expected Value of betting/bluffing with adjusted numbers = (25% x 5 big bets) + (75% x 10% x
5 big bets) + (75% x 90% x -1 big bet) = +0.95 big bets
In this case, the expected value of bluffing is +0.95 big bets, which is worse than the expected
value of checking +1.25 big bets. So your decision to bluff or not is dependent on how likely your opponent is going to call.
Example of Situation D
In cases like Situation D, where we have a very poor hand, with almost no chance of winning the pot outright, the calculations would be similar. We could assume we had 0% of winning if we
checked, but a 20% chance of our opponent folding if we bet. If we also assumed the pot contained
5 big bets, then the expected value formula is:
Expected Value of checking in Situation D = 0% x 5 big bets = +0.00 big bets
Expected Value of bluffing in Situation D = (20% x 5 big bets) + (80% x -1 big bet) = +0.20 big bets
With these numbers, it is clear that a bluff bet is the best option as we gain +0.20 big bets compared
to 0, but if we changed the percentage of your opponent folding down to 10%, then bluffing would
be a worse option than just giving up the pot without a fight. The expected value formula is:
Expected Value of bluffing in Situation D with adjusted numbers = (10% x 5 big bets) + (90% x
-1 big bet) = -0.40 big bets
Now we have the math, but we still need to learn the skill of pinpointing the percentage that our opponents will fold. If we were able to obtain their folding frequency number, then poker would
be very easy for those who are adept at math, we could just plug the numbers into an expected
value formula like the ones above and it will tell us the right move to make. Alas, in real life, it is difficult to make these assessments. Putting a percentage on whether a player will call or fold is not the easiest skill in the world to learn. You need to be paying attention to the players and see how they play to try to pick up on their tendencies. Whether they call with mediocre hands or if it seems they are calling a lot even though there are not any draws available. The reason why that is important is because it will show that they are calling with a low pair instead of just folding on a missed draw. The main way to gain this skill is through experience, observing your opponents and
thinking about the game.
Another example of a bluff attempt against one opponent
You are in the big blind holding Ad8c. Everybody folds to a player one to the right of the cutoff seat who raises. Everybody else folds and you call, there are two players and 2.25 big bets in the pot.
Flop: 8s-7s-6c
You check, the pre-Flop raiser bets and you check-raise. He re-raises and you decide to call. Going into the turn, there is 5.25 big bets.
Turn: 2c
You check hoping that your opponent was only on a spade draw and checks as well. However he does not, he bets. You are afraid that he has an overpair and has you down to just 5 outs (if he has KK you have 5 outs, 3 A’s and 2 8’s) or 2 outs (if he has AA, you only have 2 outs, the 2 8’s). There
is also the distinct possibility that he holds a hand like AsKs or AsQs which may seem to him like
he has many outs, thus raising on the flop and betting on the turn as a semi-bluff may seem reasonable to him. With two overcards and a flush draw, you can see that maybe he thinks he has
as many as 15 outs, so he did not mind re-raising on the flop. Many times these players will also continue to bet on the turn too with the hopes that you fold, and if you do not fold, at least they still have outs. It is unclear exactly what hand he has, you may be the favorite or you could be the underdog. You decide to call his bet.
But that is not the important decision. The important decision is wondering what to do on the
River. There is an opportunity to bet out if a T, 9 or 5 hits the board, whether or not it is a spade.
In fact, if it is a spade, it actually helps your bluff attempt even more. That is because if he is on spades, he will raise you and you can fold knowing that you are beat, thus losing the same amount
as a check and call. If he is not on spades and has an overpair, the 9s is going to look like a very
dangerous card to him. You may have been in the hand with a spade draw, a straight draw or hit two pairs. If he views you as a good player, he may be afraid that a bet on the river by you is a bet that is trying to save the hand from being checked down on the river. It will look like you got there with a draw. Whether a bluff is correct or not will depend on your thoughts about the chances that
your opponent can fold with an overpair.
There are two important points to take here. One is that you do not have to succeed all the time
with your bluff to make it profitable. All you need is to win it the same percentage of the time that the pot odds reflect that you need to win it by. So if you get called once or twice making a bluff
like this, it does not necessarily make it a bad bluff. On the other hand, if you are bluffing into players who are incapable of folding a big pocket pair even into a scary board of 8s-7s-6c-2c-9s, then you are just throwing your money away. Bluffing depends heavily on the ability of your opponent to fold a better hand. If they are incapable of that, then it is a foolhardy experiment.
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