Common Errors in Calculating Odds

If you're like most somewhat read poker players, you'll think that your chances of drawing to a straight or a flush is 2:1, because you've read it and seen in in poker books high and low. I want to tell you right now, that this can be a very wrong statement to apply to your game at face value. Here are a list of common errors for drawing:

1. Calculating the odds for two cards at a time, instead of one card at a time
2. Miscounting outs, either by not counting enough or not taking into account counterfeit outs
3. Not taking into account implied value - what your opponents will put into the pot if you make your hand

Regarding the points above, I will go into more detail regarding each one and explain why they are common mistakes for many poker players and how to correct your thinking.

Figuring odds one hand at a time

I believe one of the major reasons that I've seen players make this mistake in calculating odds, is that poker odds tables universally show the odds of making a hand by the river first, then the odds of making a hand by the turn. In reality, unless you are playing in no-limit tournaments or playing in a crazy no-limit cash game, you will rarely ever have to perform a two-card calculation for your hand. The huge majority of the time, you will need to figure out your odds on your immediate hand to the next card, so it's pointless to calculate any more than that. You can do yourself a big favor by forgetting the odds of making your hand by the river and instead, memorize the odds of making hands one card at a time.

Miscounting Outs

Out counting is an important skill that is often overlooked or too easily assumed. Every time you are on a draw, you need to know exactly how many true outs you have. True outs are cards that will help your hand while not helping your opponents' hand in the process. An out that hurts you is considered a counterfeit out. Often times, your true outs may be in a gray area, because you don't for certain whether or not a certain out is counterfeit or not. Thus, your ability to read your opponents and put them on a hand is going to be very critical in figuring out what your true outs are.

The mistake of not factoring Implied Value

Not factoring in implied value is a huge error that a lot of players make, because they drop out of a draw when the are actually break-even or better on making their hand. For those who need a quick refresher on implied value - IV is considered the extra bet in the pot that occurs when your opponent calls you or bets on the river after you've made your hand. Implied value assumes that your opponent will indeed pay an extra bet on the river, which a number of old or weak-tight books have said they wouldn't. Realistically, this is mostly untrue.

Internet poker players, especially in the low limit games, will often pay you out quite handsomely at the river if they have gone that far, so it is almost an automatic assumption that you will get an extra bet on the river. What this means in application, is that all of your odds of drawing should be effectively reduced by one when calculating your odds. In fact, your flop to turn draw can also be decreased by 2 points, as the implied odds double when considering a turn bet vs a flop bet (assuming we are playing limit poker here).

IMPORTANT CONCEPT: Many of you reading this will probably nod your head, look at the odds and say that implied value makes this draw ok, but only by a marginal amount, as it's only 0.1BB after all. For that reason, you think that you don't need to focus very hard on the odds or implied odds when counting your draw. That line of thinking will absolutely destroy your bankroll.

This is not to say that playing this hand incorrectly will cause you to lose 4.5BB/hr, but if you made the constant mistake of misplaying hand such as these, it would cost you that much over the long term. This is why a complete and critical understanding of odds is necessary to win at poker - especially low limit. Knowing when to draw marginal hands can turn you from a losing player to a winning player if you are consistently able to spot profitable situations.

Advanced Applications of Odds

It doesn't stop here however. For the regular player, they will look only at this one decision and figure that they want to draw because they're getting 8.7:1 realistic odds. Think what happens on the turn however? Say you call the flop bet and your opponent bets the turn on another rag. The pot is now $30, giving you 5:1 drawing odds on the turn. Even with implied value on the turn, you cannot continue to draw and must dump at this point unless you are planning on bluffing your opponent out. Your hand is now over.

On the other hand, let's take an offensive approach to implied value. It's to you again on the flop. Instead of calling, you raise instead. By raising, you're making your pot odds 24:6 or 4:1. On the turn, if your opponent bets again, the pot is 36:6 or 6:1, which gives you at least 7:1 realistic odds when factored with implied value.

Pot: $30 ($21 flop + $6 raise + $3 call)
Cost to raise: $6
Chance to make hand: 6.7 to 1 (13%)

Total Cost (to get to turn) = 87 of 100 losses = 87 * $6 = $522
Total Win = 13 of 100 wins = 13 * $36 ($30 pot + $6 implied turn bet) = $468
Net Gain = -$55

These are all the on paper stats. One thing that isn't taken into account but easily dealt with, is what happens if the big blind reraises you on the flop? Easy, you drop your hand, because he most likely has better than top pair or likely has an Ace to counterfeit your outs, giving you an unprofitable draw.

What has not been taken into effect is the Bluff EV and the free card factor. With a raise, you can expect to make your opponent fold 5% to 15% of the time here on this hand. Taking the low end of the estimate, even if your opponent folds 5 out of the 100 times on this hand, that means an extra $105 ($21 flop pot * 5 successful bluffs) in your pocket, which turns this from a unprofitable play to a profitable one instead. And we're just getting started.

Now you also have to factor in the free card effect. We can estimate that if your opponent calls, he will probably check to you 30% to 70% of the time. We will again take the conservative estimate of 30% and recalculate what our real cost is playing this hand if we miss on the turn.

Turn opportunities: 87 of 100 hands
Opponent bets on turn: 70% of 87 = 61 hands
Opponent checks on turn: 30% of 87 = 26 hands

--Opponent bets--
Pot: $36 ($30 + $6 bet)
Cost to call: $6
Chance to make hand: 6.7 to 1 (13%)

Total hands lost = 87% * 61 hands = 53 hands
Total hands won = 13% * 61 hands = 8 hands

Total Cost = 53 hands * 6 = $318
Total Win = 8 hands * $42 ($36 pot + $6 implied bet/call) = $336
Net Gain if opponent bets turn = $18

--Opponent checks--
Pot $30
Cost to call: None
Chance to make hand: 6.7 to 1 (13%)

Total hands lost = 87% * 26 hands = 23 hands
Total hands won = 13% * 26 hands = 3 hands

Total Cost = $0
Total Win = $30 * 3 hands = $90
Net Gain if opponent checks turn = $90

--Overall--
Total Net Gain from turn to river = $118

Now, we will combine the turn stats with the stats from the overall hand:

Total Cost (to get to turn) = 87 of 100 losses = 87 * $6 = $522
Total win from playing past turn = $118
Total Win = 13 of 100 wins = 13 * $36 ($30 pot + $6 implied turn bet) = $468
Total Bluff EV = (5% * 100 hands) * $21 flop pot = $105

Net Gain = -$522 + $118 + $468 + $105 = $169
Average EV = ($169 net / 100 hands) = $1.69/hand = ~0.3BB/hand.
Hourly EV significance = 13.5BB/hr

Remember, all of this assumes that your opponent will only fold 5% of the time to a bluff and only give you a free card 30% of the time. The implications of what you can win even still with these types of figures, is to show that implied odds and bluff EV can and should be used as a tool to aggressively attack your opponents - especially if you can selectively pick on those who will fold and check to you the most, as they will offer substantially higher EV to these actions.

Realistic Odds Conclusion

As a conclusion to this example of realistic odds, think about how you normally play AK when you miss the flop and the big blind bets out. Most tight people fold and get rid of their hand without a second thought. Hopefully if you've read through all of the above so far and have understood it, you can benefit by applying this information to not simply play a defensive draw game, but an offensive game as well. This is where the concepts of aggression, folding equity and free cards become much more significant, as they open many more doors that a simple drawing game does not.