Realistic Poker Odds
If you've read the original poker odds page, you may find it rather difficult to wade through, as the material is somewhat math intensive. This page will be a bit easier, as it gives a more general, realistic and pragmatic approach on how to properly use odds in poker; specifically, texas hold'em. If you have not read the original poker odds page, I still highly recommend you do so, as I will be going over concepts here that assume you have an understanding of how pot odds and hand odds work. (Update: Ok, I lied, there's a lot more math that goes into this page than I anticipated. However, understanding the calculation is not as important as realizing the conclusion. If you can do both, great, if not, you can still benefit.)
| # | Poker Room | USA | Key Points and Bonus | Play Now |
|---|---|---|---|---|
 |
us yes |
|
||
 |
us yes |
|
||
 |
us yes |
|
||
 |
us yes |
|
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:
- Calculating the odds for two cards at a time, instead of one card at a time
- Miscounting outs, either by not counting enough or not taking into account counterfeit outs
- 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.
Example: A lot of players tend to draw their open-ended straights thinking they only need 2:1 pot odds. This is sorely wrong. What is true is that an open ended straight draw sits at a 4.7:1 chance of completing when calculated one card at a time. This is a very far cry from a 2:1 odd draw and still nearly one whole big bet off compared to the 4:1 mentality.
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.
Example: Players will often draw to a straight with a flush draw possibility on the table, because they haven't taken into account that two of their straight outs actually complete someone elses' flush draw. On the other hand, a play might have AK with a paired Ace and face some heavy raising from the BB, who he suspects of having two pair. The AK player may think that he must hit another Ace or King (5 outs) in order to win the hand, where the reality is that he has 3 more outs for the board to pair (and not give his opponent a full house), which gives the player 8 outs. Another common mistake is to not recognize the Ace counterfeit, where you make mid-pair on the flop let's say and have the pot odds to draw for a two pair. While you may make the best hand, an Ace on the board may also mean that the top pair also makes two pair as well in the process, thus nullifying your Ace out. Not always the case, but something to be mindful of.
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).
Example #1: It's a $3/6 game and you are dealt T7o in the BB. Two limpers come in and the SB folds (pot $10). You check and the flop comes T-8-6 rainbow. You check, first limper bets, other two fold and it's now up to you. The pot is now at $13 with $3 to call, giving you 4.3:1 odds. Your total outs on this hand are 7 (3 outs to hit two pair and 4 outs to hit your inside straight, assuming your opponent has top pair/better kicker or overpair). At 7 outs, this puts your draw at 5.6:1, which compared to your 4.3:1 pot, means with conventional odds theory, that you should fold this hand. However, if you take into account implied value and the fact that the implied value is doubling on the turn, this actually makes your draw a 3.6:1 proposition. This may be hard for you to wrap your head around, so let's do some actual number crunching:
Pot: $13 ($10 preflop + $3 flop bet)
Cost to call: $3
Odds to make hand: 5.6 to 1 (15%)
Turn Pot: $22 ($10 preflop + $3 flop bet + $3 flop call + $6 turn bet)
Now let's run this scenario through 100 times to see where we fall:
Total Cost = 85 of 100 losses = 85 * $3 = $255
Total Win = 15 of 100 winners = 15 * $22 = $330
Average EV = ($330 - $255) / 100 = 75/100 = $0.75/hand = 0.1BB/hand
Hourly EV significance = (Hands/hour) * Average EV = (45 hands/hour) * (0.1BB/hand) = 4.5BB/hr
Note: If you are very observant, you should even be able to realize here that you have even more implied value on this hand, because if you make your hand, you will almost certainly raise on the turn and bet the river, which may add one or two additional BB. For the sake of clean theory, we will not add it in here, but realistically, you can probably add an entire BB on top of your implied value for this kind of hand.
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.
Example #2: You are in a $3/6 game and dealt AKo in middle position. One limper in EP, you raise up to $6, all folded to the big blind, who calls as well as the original limper. Pot is $18, flop comes triple rags. Big blind bets out, limper in EP folds and you see a pot of 21:3 - or 7:1 pot odds. You figure the big blind has a pair, most likely giving you 6 outs to make a better pair. Your odds of hitting an Ace or King one card at a time is 6.7:1.
On the very surface, this is a profitable play, since you are getting better pot odds than drawing odds, but you also have to take into account that your opponent may have better than one pair or may have a King or Ace to counterfeit your outs. This may make it a break even play on paper. However, given that the majority of the time he has a pair here, your implied value makes this more like a 8.7:1 draw, which easily nullifies any counterfeit threat.
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.
If you're advanced enough to apply your odds and outs, try playing at PokerStars.com, which has the best VIP program in the industry comparable to rakeback as well as bi-monthly reloads that reward regular players.
