Tagged: implied odds

Poker is essentially a game of betting and probabilities.

If the chance that you will win is better than the odds you are given on the bet – you should decide to take (or make) the bet.

A deep understanding of odds and probabilities is hugely helpful in becoming a better poker player.

Read this article and use the poker training exercises to practice and you will soon get the hang of it.

As an example imagine someone proposing you a bet were you will win $4 each time a 6 comes up on a dice and lose $1 every time anything between 1 and 5 comes up. Would you take this bet?

This bet is a bad proposition for you, because you are guaranteed to lose money in the long run (how long depends on something called variance, but that’s another topic).

You can see that this is a bad bet by calculating odds and probabilities.

The money odds you are getting on a 6 coming up is 4:1. You win $4 if it comes up and you lose $1 if it does not come up. This is written as 4:1.

The chance that there will be a 6 on each roll of the dice is 1 in 6. This means that it is 5 times as likely that there will a number other than a 6 on each roll. This can be written as 5:1.

To determine if a bet is good or bad you compare the money odds that you are getting with the probability that you will win.

In this example you compare the money odds of 4:1 with the odds that you win which is 5:1. The money odds are smaller in this example which means it is a bad bet. If you were getting $5 for the 6 instead the money odds would be the same as the win odds an the bet would be neutral. In the long run you would neither lose nor win money on such a bet. And if you were offered more the $5 for each 6 it would be a good bet and you should take it.

All casino games (except Black Jack where card counting can be used), lotteries and such are based on giving worse odds to the players than to the bank. And the players will always lose in the long run.

But fortunately poker isn’t played against the bank. And in poker you can use better understanding of odds to give yourself an advantage over your opponents.

Odds

Usually two concepts are used for odds in poker, pot odds and implied odds (negative implied odds are sometimes called reverse implied odds).

Pot odds are the odds you are getting from the money in the pot right now and the money you need to pay to call.

Implied odds take into account money that you can win or loose later in the hand.

Pot odds are calculated  and Implied odds are an estimation based on things like probabilities for cards to come, opponent tendencies and such.

Example with Pot Odds

The pot is $12. Opponent bets $6. Your pot odds are calculated by looking at the money you can win ($18) and the money you will put in the pot ($6). The ratio is 3:1. You get this by dividing 18 with 6.

Example with Implied Odds

The pot is $12. Opponent bets $6. You have a fairly disguised open-ended straight draw. Your opponent is aggressive and by considering his tendencies you and likely hand range you estimate that you will win in average $30 more if you hit your draw on the turn (he will often bet and sometimes call a raise).

Your Implied Odds are calculated by dividing the money you expect to win when hitting with the money you are betting (12 + 6 + 30 / 6 = 8:1).

Outs

If you believe your opponent may have a better hand than you, but that some cards will improve your hand to become the best you call each of these cards an “out”.

Example using Outs

You believe you opponent has a top-pair (one of his hole cards make a pair with the highest card on the board) or an overpair (he has a pocket pair as hole cards and it is higher than the highest card on the board) and you have 4 cards in the same suit with your hole cards combined with the board.

In this case all cards that complete your flush draw are likely to give you the best hand. 4 cards are already out in the suit and 9 remains. The 9 remaining cards are called outs.

If you instead have an open-ended straight draw (can be completed upwards or downwards) you have 8 outs (if you believe the straight will give you the best hand).

Other examples:

  • 2 overcards – 6 outs
  • Gutshot straight draw (need a card in the middle to complete) – 4 outs
  • Gutshot straight draw + a flush draw – 12 outs
  • Backdoor draw (same for flush and open-ended straight) – 1 out (only relevant on flop looking to river)

There is a simple rule of thumb to estimate how likely it is that your hand will improve with the help of the outs.

It is called the rule of 4 and 2 and gives a good approximation.

With one card to come the probability that you will hit your hand is number of outs * 2

With two cards to come the probability that you will hit your hand is number of outs * 4

Example with Outs

The pot is $12. Opponent bets $6. You have a fairly disguised open-ended straight draw. Your opponent is aggressive and by considering his tendencies you and likely hand range you estimate that you will win in average $30 more if you hit your draw on the turn (he will often bet and sometimes call a raise).

Your Implied Odds are calculated by dividing the money you expect to win when hitting with the money you are betting (12 + 6 + 30 / 6 = 8:1).

Should you call (not considering raising now as this is an example of Implied Odds and Outs)?

You have an open-ended straight draw. This means 8 outs. 8 outs gives you 16 % chance with one card to come. 16 % chance is the same as 5:1 odds. Your Implied Odds are 8:1 and your odds for improving is 5:1. This is a clear call.

Discounted Outs

To complicate things a bit there is something called discounted outs. This is used for situations where you are uncertain if your hand will improve to be the best if these cards hit. For example if you two overcards but you believe that hitting either of them will only improve your hand to be best half of the time (for example if you believe your opponent will have a higher overpair half of the time). Then you compensate for that by changing the probability that you will hit a winning hand. If you estimate that the cards will help you to the best hand 50 % of the time, you have to half the probability. In this case you have 6 outs, but you discount half of them (the discounted outs) so your “real” outs are 3 and you have 6 % probability to get a winning hand on one card, and 12 % with two cards.

When you are thinking about calling a raise with a hand that is not likely to be ahead of your opponents in average you need to think about your implied odds. This means that you should think about how much you will likely win in average when you hit a good hand.

You can of course sometimes also win with these hands without hitting a monster. Most of the time either by having a pair when your opponent has nothing or by bluffing. More on that in Preflop Strategy – Someone has raised where we look at scenarios were you have addition equity on top of the Implied Odds.

There is an old rule-of-thumb for this situation called the rule of 5-10. This might have worked in the less competent poker games a couple of years ago, but that needs an update.

The rule of 5-10 say that if the effective stack sizes are less than 10 times the amount for the call you should fold. If it is more than 20 times the amount for the call you should call. If it is somewhere in between you should think. Simple enough, but not good enough unfortunately, as people are getting better and better at poker – and few players nowadays will stack off with an overpair or a TPTK (top-pair, top kicker).

So here are my suggestions:

Rule-of-thumb: Calling with pocket pair against one likely opponent based on implied odds:

  • call if opponent is a TAG on a very narrow range (max 5 %) and is likely to be willing to stack off with overpair or top-pair and effective stack size is at least 20 times the call amount or
  • call if opponent is a maniac and effective stack size is at least 20 times the call amount.

Rule-of-thumb: Calling with pocket pair against several likely opponents based on implied odds:

  • call if raiser is TAG on narrow range (max 10 %) and at least one person has called before you and effective stack size between raiser and you is at least 20 times the call amount and risk of squeeze is max 10% or
  • call if at least one of the other callers is a fish willing to commit a lot with a weak holding or
  • call if at least two persons has called before you and risk of squeeze is max 10 %

Rule-of-thumb: Calling with suited connectors against one likely opponent based on implied odds:

  • don’t

Rule-of-thumb: Calling with suited connectors or suited aces against several opponents based on implied odds:

  • call if raiser is TAG on narrow range (max 10 %) and at least two persons has called before you and effective stack size between raiser and you is at least 20 times the call amount and risk of squeeze is max 10%

Important note: here I talk about calls made more or less only based on Implied Odds. The decision might be different when you consider winning by bluffing or by hitting a mediocre hand. See Preflop Strategy – Someone has raised for more discussion about that.

Examples with Implied Odds Preflop

You hold a pocket pair – Set Mining. Your chance of hitting a set on the flop is 7,5 – 1.

This means that you need to be able to win 7,5 times the amount called in average when you hit a set (for the moment simplifying by assuming you don’t win unless you hit the set and you always win when you hit, see below).

Let’s take a deeper look at what that means with an example.

Let’s say you are playing $0,5 / 1 and someone has raised to 3. You call. The pot is now 7,5. Opponent bets 5 on the flop. You call. The pot is now 17,5. Opponent bets 13 on the turn and you call. The pot is now 43,5. On the river opponent checks and fold to your bet. In this example you win slightly less than 7,5 – 1. The situation will be similar if you raise on the flop instead of calling and opponent checks on the turn and folds to a bet. Sometimes opponent will call bet of half the pot on the river in which case it has netted you $43. But this will surely not happen the times they don’t even have a pair.

It is easy to see that it is rarely correct to call with a pocket pair against a single opponent unless he is particularly willing to put a lot of money in the pot with a semi-strong hand (based on implied odds for hitting a set alone).

Assume his 5 % range is AA-99, AK, AQ. Exactly what a 5 % range consists of varies from opponent to opponent, but this is a common top-5% range. This opponent will have an overpair or a strong pair by the turn about 40% of the time. But some boards will be so scary that he will not commit. Let’s assume he is willing to commit 30% of the time and the rest of the time will only bet one barrel and fold to resistance:

0,3*60 + 0,7*9,5) –  = 25

This is slightly more than the 7,5*3 which is needed for call to be profitable on implied odds alone. This scenario would be similar if he has 3-bet and you call. Let’s assume you bet 3 and he raises to 9. If he misses he is only willing to pay one barrel – let’s assume he bets 14 on the flop. In this scenario you consider calling 6 big blinds and you need to win in average $48 the times you hit your set.

0,3*120 + 0,7*26,5 = 54

Which makes it profitable to call. If the same opponent only has 100 big blinds (less than 20 times the call amount of 6) the call is 0 in EV – meaning it doesn’t matter if you fold or call.

Let’s assume the same opponent on a 10 % range consisting of AA-22, AK, AQ, AJ, KQs. Now he will have an overpair or a strong pair by the turn about 15 % of the time. Sometimes he will have a fairly strong pair and be willing to commit 2 bets. For simplicity let’s assume he commits about 15% of the time and only pays one barrel  85% of the time.

0,15*100 + 0,85*9,5 = 23

This is almost enough, but not quite – even assuming he will commit 100 big blinds. And you rarely know for sure what an opponents range will be in a certain situation AND that he really will be willing to commit with a semi-strong hand. So to compensate for this uncertainty the guidance recommends a 5 % range as max.

Let’s take a look at another opponent, a competent but aggressive TAG who is often willing to double-barrel bluff. But not willing to stack off with only a pair. Let’s assume he bets 3 preflop, 5 on the flop, 10 on the turn and calls 12 on the river with TPTK or overpair. Let’s assume he C-bets on the turn 75 % of the times when he has a weakish hand and folds to a bet the other 25 %.  Let’s assume he calls the river bet with TPTK or overpair 100% of the time (reasonable since the bet is only 1/3 of the pot).

5 % range:

0,3*31,5 + 0,7(0,75*19,5 + 0,25 * 9,5) = 9 + 10 + 2 = 21

This is not enough to make a call profitable. So advice is to not try set mining against a lone, competent TAG based on implied odds alone, even if he’s very aggressive. The scenario is even worse if he is on a wider range (which he normally is).

There are some exceptions when the stacks are shorter, if the raiser is willing to often stack off when missing the flop. For example if effective stack size is 30 big blinds and opponent will be stacking off most of the time with AK and AQ on missed flops it can be profitable to call if opponent is playing a 5 % range and is willing to stack off 80 % of the time.

The second scenario is much more complicated. There is a risk of losing to flushes and straights, there is a risk that opponent will not C-bet at all etc. But examine one scenario to support the rule-of-thumb:

Opponent is TAG and raise to 3, there is one caller ahead of you. In this scenario opponent has range of 10%, will fire 2 barrels after missing the flop 30% of the time and with TPTK or overpair will call a bet of slightly more than 1/3 of the pot on the river 100% of the time. The other opponent folds on the flop.

0,15*49,5 + 0,85(0,3*29,5 + 0,7*14,5) = 24,5

If we assume that there is a raise behind and you have to fold, it is still (barely) enough to make set mining profitable.