Hand Odds

 

Calculating Realistic Holdem Hand Odds

Anybody who has done any research at all into the subject of poker strategy knows that the game involves the usage of poker odds. And whether they be pot odds, implied odds, or reverse implied odds, quite a few players will make decisions based on what their calculations are in the end – especially in the game of Texas Hold’em. The problem with using these odds is most people already know about pot odds and hand odds (you should too for the purpose of understanding this article). Using common poker odds to make decisions will lead you into a defensive drawing game by; in order to get out of this trap you need to start using the realistic odds approach to the game. Here’s how.

You may need to reference our Poker Chart.

Errors made when Calculating Odds

Almost every poker book talks about different poker odds concepts; charts are usually given in these sections along with an explanation on how they work. But the truth is widely accepted poker odds don’t always work out when everything is taken into account in a drawing hand. Here are some of the problems that arise when people are drawing for a card.

1. Players will calculate their odds for making a hand two cards at a time instead of one card at a time like     they should.

2. Outs are miscounted either because people don’t count enough of them or they fail to include counterfeit     outs.

3. Players don’t include the concept of implied value or what a made hand will yield once opponents have put     more money into the pot.

Now you know what errors can arise from using common poker odds to draw for cards; the matter of why these errors occur and how a person can fix them still needs to be explained.

Making Two-Card Calculations instead of One

One of the biggest problems with calculating odds arises from the commonly accepted logic that people should focus on their chances of forming a hand by the river. The truth is though, you’ll be wasting bets by using two-card calculations to determine whether or not to stay past the flop; you’re far better off calculating odds for the very next card instead of two cards ahead. The best thing to do is to memorize odds one card at a time when trying to make a hand.

Example: Many players draw for an inside straight thinking they need better than 5:1 pot odds to stay past the flop – but 5:1 is a two-card calculation and only gives odds for making a hand by the river. In reality, you’ve only got 10:1 odds to hit a straight on the turn; so you’re going to be wasting a lot of bets by using odds of 5:1 to make a hand in this case.

Not Counting Outs Correctly

Most poker players know “outs” are how many potential cards are in the deck that could make your hand. Unfortunately, many players don’t know much about “true outs” – these help your hand but don’t help an opponent’s hand. An out that helps an opponent is called a “counterfeit out”. You may not always be able to figure which outs lie in the counterfeit area, but you should have an idea from looking at the board and by reading opponents.

Example: Sometimes people will stay past the flop or turn looking for a flush, not realizing that two of their outs could help someone else form a better flush. A reverse scenario exists where someone might be holding KQ with the king being paired; if the small blind makes a big raise then they assume the person has a two pair. This leads them to think they need to hit another king or queen – 5 outs – to take the pot when they really have 3 extra outs since the board could pair too.

Leaving Out Implied Value

Implied value – extra money opponents bet on the river after you make your made hand – is something many players mistakenly avoid factoring in when they make the decision to fold a hand. But realistically, you can assume extra bets will be made on the river the majority of the time so this needs to be taken into account when drawing.

Example #1: You’re holding KJo in a $5/10 cash game while sitting in the small blind position. One limper calls, you call the full blind, and the big blind checks (pot $15); the flop shows Ks-10h-9d. The original limper checks, you check, and the big blind bets making the limper fold. With $20 in the pot and $5 needed to bet you have 4:1 odds. You have 4 outs to make an inside straight and 3 outs to get a two pair giving you a total of 7 outs. The problem is that you’re only going to get a 5.6:1 draw – this means you should fold since the pot odds are 4:1. However, using implied value will yield that the money in the pot could be much greater and change the whole outlook of the hand. Using the math below, your pot odds would change to 7:1 which would make a 5.6:1 draw profitable in the long run using implied odds.

Pot: $20
Call: $5
Hand odds: 5.6 to 1 (15%)
Turn Pot: $35 ($20 pot + $5 flop call + $10 turn bet)

After figuring out your implied value, it’s always a good idea to go through and see how the scenario would play out over 100 hands (expected value):

Loses = 85 losses (out of 100) * $5 = $425
Wins = 15 wins (out of 100) * $35 = $525
Expected value = ($525 - $425) / 100 = 100/100 = $1/hand = 0.1BB/hand
Hourly expected value = (hands/hour) * Average EV which would be (45 hands/hour) * (0.1BB/hand) = 4.5BB/hr

Additional Concept: 0.1BB doesn’t seem like a huge amount to win every hand, but it actually is when you look at the long run; in fact, this number will end up costing you the same 4.5BB/hr amount you could have won if ignored. This is why you need to have a good handle on when drawing marginal hands will be profitable.

Example #2: Let’s say you’re in a $5/10 game once again and you receive the same KQo hand. One middle position person limps in, you raise in late position while the big blind calls and so does the limper making the pot $32 ($2SB). The flop is 4d-3s-9c which causes you and the limper to check while the big blind bets – the limper folds leaving the decision up to you with 7.4:1 pot odds (pot is $37).

Since there’s nothing in the community cards, you assume the BB might have a pair of jacks or lower since they did not re-raise you which rules out counterfeit outs. This leaves you with 6 outs to get a better pair or 6.7:1 odds of being dealt a king or queen.

Advanced Calculation of Odds

While the decision above looks like an easy one to make, there is plenty of stuff that could complicate things. Let’s say you do call the flop wager (pot is now $42) and the BB bets on the turn despite another poor card hitting the board (pot is now $52). Everything has changed now since your pot odds move to 5.2:1 and your chances of making your hand are only 6.7:1 – here’s how the math works out:

Pot: $52
Call : $10
Hand odds: 6.7 to 1 (13%)
Losses = 87 losses (out of 100) = 87 * $10 = $870
Wins = 13 wins (out of 100) = 13 * $52 = $676
Net Gain = -$194

It’s easy to see just how quickly things can change when looking at realistic odds; but one crucial element that hasn’t been discussed yet is what happens when an opponent folds due to an aggressive flop raise by you (called “Bluff EV”). It’s not unreasonable to think that your raise on a poor flop will knock an opponent out of the hand 10% of the time. Plugging in the flop numbers from example #2, you could net an extra $420 (10 X $42 flop pot).

Going even further with this concept, there is also the “free card” scenario where your opponent will call the flop raise and merely check after the turn. Let’s say this happens about 40% of the time when you miss the turn and take a look at the math:

Turn chances: 87 of 100 hands
Opponent turn wagers: 60% of 87 = 52 hands
Opponent turn checks: 40% of 87 = 35 hands

Opponent wagers:

Pot: $52 ($42 + $10)
Cost to call: $10
Chance to make hand: 6.7 to 1 (13%)

Hands lost = 87% * 52 hands = 45 hands
Hands won = 13% * 52 hands = 7 hands

Cost = 45 hands * $10 = $450
Won = 7 hands * $62 ($52 pot + $10 implied bet) = $434
Net Gain on opponent turn bets = -$16

Opponent checking:

Pot $42
Calling Cost: None
Hand odds: 6.7 to 1 (13%)

Total hands lost = 87% * 35 hands = 30 hands
Total hands won = 13% * 35 hands = 5 hands

Cost = $0
Won = $30 * 5 hands = $150
Net Gain if opponent checks turn = $150

Overall cash won or lost:

Total Net Gain from turn to river = $134 The idea of being aggressive on the flop in the above scenario looks favorable over the long run – this is assuming opponents fold 10% of the time and give free cards at a rate of 40%. The main thing to be taken away from this is that being aggressive with certain opponents while utilizing Bluff EV and implied odds can win you a lot of money over the long run.

Realistic Odds Conclusion

A good thing to take away from this discussion on realistic odds is that you want to avoid being the player who automatically folds when they have KQ (for example) and don’t make their hand on the flop. These defensive drawing players end up wasting lots of bets over the course of their playing career instead of using things like implied odds and Bluff EV to take advantage of situations. So next time you hit the tables, make sure to start using realistic odds because it could make you a lot of money in the long run.