Part #2 Of Our Beginners Poker Tournament Guide
Poker Odds, Outs and Expectation All Clearly And Concisely Explained!
. For example, using the Good approximation, if you have 9 Outs, then you have a 19% chance on the turn, a 19% chance on the river, and a 38% minus 19% of 19% (close to 20% of 20%, which is 4%) equals a 34% chance on the turn and river combined. From David Solomon, mentioned in Harrington on Hold 'em: Volume 2. View THETA Poker Pro in App Store Return to THETA Poker. Online Poker » Poker Strategy » Math » Poker Outs and Odds. Most new poker players tend to start out playing poker the same way. They play too many starting hands, which only gets them into trouble because these hands turn into lucrative drawing.
Poker odds are a critical factor in success in online poker tournament strategy. While alone information on odds and outs will not make a player an instant winner, this knowledge will certainly give them an instantly profitable advantage over those players who do not understand these simple poker concepts correctly.
A good way to begin looking at poker odds and outs is in terms of expectation. During any game of poker we will be faced with a number of ‘bets’ at various prices. When you bet with the odds in your favor then you have a positive expectation. That is to say that regardless of the outcome of any particular hand you will show a profit over time. If you bet or call when the odds are against you then your wagers have a negative expectation, that is you will lose money over time.
The most commonly referenced form of poker odds are known as ‘Pot Odds’. This describes the price you are getting when calling a bet from an opponent compared to the current amount of money already in the pot.
For example, if the total pot - including your opponent’s last bet - was $100 and you had to call a $20 bet then your current pot-odds are exactly 5/1. Pot odds are useful when working out whether your call has a positive expectation. In this example, assuming this was the final bet of the hand, then you simply need to work out whether you have a greater than 20% (1 in 5) chance of winning the hand. If you think this is the case then calling will show a profit over time if you think your chances are lower then calling will lose money over time and your hand should be folded.
Pot-Odds can also be used before the last card is dealt. Imagine you have King-Jack of spades and by the time the turn card is dealt there are 2 other spades showing. With 1 card to come you are sure that hitting a spade will win the hand for you. In this situation you need to compare the pot-odds being offered to your chances of winning the hand. In this case you are approximately 4.5/1 against hitting that last spade (see ‘outs chart’ below for more information on this).
Thus if you are getting better than 4.5/1 odds from the pot then calling will show a profit over time. If you are getting less than this price then calling will lose money over time and you should not usually call the bet.
Looking at the current odds that you are getting by calling a bet leaves out one very important factor. You may be able to win one or more additional bets after the last card has been dealt. This is especially significant in No-Limit Holdem Tournaments where you can bet any amount you like. The additional bets you might win if you make your flush (for example) are known as the Implied-Odds and need to be factored into your expectation.
To return to the King-Jack of spades example, the pot-odds after the turn has been dealt there is $30 in the pot and your opponent bets $10 more. Here you are getting odds of 4/1 with a 4.5/1 of completing your flush, pot-odds alone indicate a negative expectation from this bet. However after the river, if you do make your flush by hitting that last spade then you estimate that your opponent will call an additional $20 bet. Your implied odds are now the $30 in the pot + $10 bet from your opponent + $20 on the river for a total of $60. This means that the real odds of your $10 call on the turn were 6/1. If you take 6/1 odds on a 4.5/1 chance then you will show a profit each time – you will have a positive expectation for the bet.
Planet Mark's Tool Tip! Did you know that poker software tools are available which automatically calculate the math, leaving you to outplay your opponents? I strongly recommend Tournament Indicator, which watches your opponents while you play then uses a unique algo based on Dan Harrington's famous 'M' to recommend the best action. This tool not only stops you from making mathematical mistakes, you can actually start profiting from poker tournaments while you are learning. Find out more and take a free trial at the Tournament Indicator Website now!
What are Poker ‘Outs’ and how are they calculated?
During the play of any hand there are a number of the unseen cards left in play that will improve your hand, and a number that will not. Any card that will improve your current holding is known as an ‘out’. Any hand that is not yet complete, for example 4 cards to a flush or 4 cards to a straight, is known as a ‘drawing hand’ or just ‘draw’. Poker odds can be used to assess whether your play has a positive expectation if you know the basic chart of ‘outs’ that will improve your hand.
A Full Outs Chart is Below - Here are the most common poker outs:
Odds Of Poker Hand
- 4 Cards to a Flush with 2 cards to come: Odds = 1.9/1 (35%)
- 4 Cards to a Flush with 1 card to come: Odds = 4.1/1 (19%)
- 4 Cards to a Straight with 2 cards to come: Odds = 2.2/1 (32%)
- 4 Cards to a Straight with 1 card to come: Odds = 4.7/1 (17%)
- Inside Straight Draw, 2-3-5-6, 2 cards to come: Odds = 4/1 (20%)
- Inside Straight Draw, 2-3-5-6, 1 card to come: Odds = 10/1 (10%)
As you gain experience in using poker odds and outs you will be able to quickly calculate your winning chances using simple math. After the flop in Holdem there are 5 cards which you have seen – and so 47 unseen cards. You calculate the number of cards that will help your hand out of those unseen cards and then divide this number by 47. For example if you calculate that 10 cards will improve your hand then (10/47) = 4.7/1 odds which is approximately 21% winning chance, with 2 cards to come then doubling the winning chances is close enough for most situations. Learning the most common outs from the chart below will help you make good decisions during a hand – remember that if you take positive expectation bets you will show a profit over time!
Number of Outs
You Have Trips, Make Quads
You have a pair, make trips
You hold 1 ace, make a pair of aces
You have 2-3-5-6, hit a 4 for inside straight
You have 3-4-5-6, hit 2 or 7 for straight
You have 4 to a flush, make flush
You have 4 to flush + an ace, make either flush or A-A
You have 4 to flush and open-ended straight, make either hand
You have open ended straight flush + 2 overcards
SNG Planet Tip: A quick way of calculating your chances of making a hand after the flop (with 2 cards to come) is the ‘Rule of 4’ – Simply Multiply the number of cards to make your hand by 4! For example if you have 4 to a flush on the flop then there are 9 unseen cards of your suit that will make your hand… 9*4 = 36% which is very close to the 34.97% shown on the outs chart above! With just one card to come you multiply by 2 instead.
One last thing, tournament pros tend to congregate at the bigger poker sites - you will find significantly easier games at mid-sized sites, especially those linked with sports-books and casino brands (since the 'gamblers' come over into the poker rooms!). I recommend 888 Poker as a fantastic place to profit from tournaments while you are learning. Check out the games for yourself, you will see the difference!
Poker Outs to Odds
5 Card Draw Poker OddsTo find your chance of improving a drawing hand based on the number of outs, use the following table:
|Outs||Turn Odds||River Odds||Turn+River Odds|
|1 Out||45.9-to-1 (2.13%)||45.1-to-1 (2.17%)||22.3-to-1 (4.26%)|
|2 Outs||22.5-to-1 (4.26%)||22.0-to-1 (4.35%)||10.9-to-1 (8.42%)|
|3 Outs||14.7-to-1 (6.38%)||14.3-to-1 (6.52%)||7.0-to-1 (12.49)%|
|4 Outs||10.8-to-1 (8.51%)||10.5-to-1 (8.70%)||5.1-to-1 (16.47%)|
|5 Outs||8.4-to-1 (10.64%)||8.2-to-1 (10.87%)||3.9-to-1 (20.35%)|
|6 Outs||6.8-to-1 (12.77%)||6.7-to-1 (13.04%)||3.2-to-1 (24.14%)|
|7 Outs||5.7-to-1 (14.89%)||5.6-to-1 (15.22%)||2.6-to-1 (27.84%)|
|8 Outs||4.9-to-1 (17.02%)||4.8-to-1 (17.39%)||2.2-to-1 (31.45%)|
|9 Outs||4.2-to-1 (19.15%)||4.1-to-1 (19.57%)||1.9-to-1 (34.97%)|
|10 Outs||3.7-to-1 (21.28%)||3.6-to-1 (21.74%)||1.6-to-1 (38.39%)|
|11 Outs||3.3-to-1 (23.40%)||3.2-to-1 (23.91%)||1.4-to-1 (41.72%)|
|12 Outs||2.9-to-1 (25.53%)||2.8-to-1 (26.09%)||1.2-to-1 (44.96%)|
|13 Outs||2.6-to-1 (27.66%)||2.5-to-1 (28.26%)||1.1-to-1 (48.10%)|
|14 Outs||2.4-to-1 (29.79%)||2.3-to-1 (30.43%)||0.95-to-1 (51.16%)|
|15 Outs||2.1-to-1 (31.91%)||2.1-to-1 (32.61%)||0.85-to-1 (54.12%)|
|16 Outs||1.9-to-1 (34.04%)||1.9-to-1 (34.78%)||0.75-to-1 (56.98%)|
|17 Outs||1.8-to-1 (36.17%)||1.7-to-1 (36.96%)||0.67-to-1 (59.76%)|
|18 Outs||1.6-to-1 (38.30%)||1.6-to-1 (39.13%)||0.60-to-1 (62.44%)|
|19 Outs||1.5-to-1 (40.43%)||1.4-to-1 (41.30%)||0.54-to-1 (65.03%)|
|20 Outs||1.3-to-1 (42.55%)||1.3-to-1 (43.48%)||0.48-to-1 (67.53%)|
|21 Outs||1.2-to-1 (44.68%)||1.2-to-1 (45.65%)||0.43-to-1 (69.94%)|
|22 Outs||1.1-to-1 (46.81%)||1.1-to-1 (47.83%)||0.38-to-1 (72.25%)|
|Excellent||Outs times 2.13%||Outs times 2.17%||*Turn odds plus River odds minus Turn odds times River odds||More accurate than you'll ever need|
|Very Good||Outs times 2-1/8%||Outs times 2-1/6%||**Outs times 4%, minus (Outs - 8) if 9 or more Outs||As accurate as you'll ever need|
|Good||Outs times 2%, plus 1% if 5+ Outs, plus 2% if 13+ Outs||Same as Turn||**Outs times 4%, minus (Outs - 8) if 9 or more Outs||The easiest reasonable approximation|
|Bad||Outs times 2% plus 1%||Same as Turn||Outs times 4%||Not good if low or high numbers of outs|
* For example, using the Good approximation, if you have 9 Outs, then you have a 19% chance on the turn, a 19% chance on the river, and a 38% minus 19% of 19% (close to 20% of 20%, which is 4%) equals a 34% chance on the turn and river combined.
** From David Solomon, mentioned in Harrington on Hold 'em: Volume 2.