Odds and Evens
Every night we play I am asked a dozen times to tell people what are their odds of winning just like they do on the TV or to calculate who is the favourite probability wise with any number of all ins. I have explained how to do this on bar mats and scraps of paper that seem to be forgotten the next day. So I suppose this article is long overdue.
Firstly most people do not have the foggiest idea about probability. I scream at the TV every time I see Deal or no Deal, I just don’t know where they find the “half heads” who make up the contestants and dont know when the banker is overpaying. There must be a place near Burnley Lancashire where they find them because as we all know everyone from Lancashire is an interbred dwarf with a congenital malfunction and the intelligence of a lemming. Whereas we Yorkshire Tykes are …….
To understand one type of probability let us imagine Noel offers you three boxes and you are told that the boxes contain the following
1. a million pounds, keys to a Ferrari and an address for a nymphomaniac with her own merchant bank
2. a Lancastrian
3. and the other is better than the second it contains nothing at all.
You are asked to choose a box
You select one box at random and Noel then says that he will remove one box and guarantees that of the two remaining one box contains the prize. The banker calls and offers you the chance to stick or to switch. If you don’t agree that you would switch every time then imagine if there were 1000 boxes , you selected one and Noel removed 998 boxes with the same guarantee and the banker offers the same choice.
In switching you will have made the correct decision 66.66 % of the time with 3 boxes and 99.9 % of he time when there are 1000. If you still don’t get it then go to the back of the class and concentrate on basket weaving. This is called conditional probability, the correct decision is based on previous events. Poker is no different.
Firstly I need to state that the percentage chance (probability) you have of making a hand is not the same as the “odds“. I will explain how to calculate probabilities later but let us assume you have a 25 percent probability of making a hand after the flop.
The odds are = 100 -1 =3
25
So for four possible outcomes you will win one and lose three. Three to one
THIS IS CRITICAL….will you make a bet at three to one if you will only get double your money back ? Of course not. Would you make a bet on the toss of a coin if someone offered three to one against the next toss coming up “heads” …every time !!!
Poker is no different and knowing how to calculate your outs and thus calculate the odds is essential if you are going to win and win regularly. To calculate the odds correctly the mental arithmetic can be reasonably difficult, however there is a simple method that gives a very good approximation with little deviation from the exact result so long as you can multiply a number by 2. Ill come to this later.
Why is it important to know what the odds are because there are many times when you will call a bet on the flop with a weak hand if there are three other callers but you would fold when there are only two……..you must get paid the correct odds or more for your chips or you simply do not call.
Hand odds are the odds of you making a pair, a pair improving to trips, making a flush i.e improving your hand after the flop (with the turn and the river)
But what are the odds of getting a specific starting hand ?
Starting Hands.
If you have an Ace of hearts for your first card there are 51 other cards that may be dealt to you. There are 51 combinations with the AH, therefore there will be another 51 combinations with the Aclubs, but one of those ( AH AC) has already been used and thus only 50 combinations will be unique.
I cannot be bothered to add up 51+50+49 +48.…..+1
But the answer will be the same as = 52 x 26 = 1326
So what are the chances of being dealt a pair of aces ?
Let me see…..There are four of them, AH,AC,AD AS
The possible pairs are AH+AC, AH +AD, AH +AS, AC+AD,AC+AS, AD+AS
So six possible pairs of Aces .and 1326 possible starting hands
6 *100 = 0.452
1326
So the odds of dealing two cards from a pack and them being a pair of aces is about 220-1
What about the chances of getting a pair of kings….well there are the same number of combinations of kings (6) so it must be the same .
So the chances of any specific pair is 220-1
So what is the probability of being dealt any pair…….let me see now…there are thirteen pairs AA,KK,QQ……33,22
13 x 0.452 = 5.87 %
So therefore in 100 hands of poker I should get a starting pair between five or six times
Hand odds are your chances of making a hand in Texas Hold'em poker. For example: if you hold two hearts and there are two hearts on the flop, your hand odds for making a flush are about 2 to 1. This means that for approximately every 3 times you play this hand, you can expect to hit your flush one of those times. If your hand odds were 3 to 1, then you would expect to hit your hand 1 out of every 4 times.
Odds are given below for hitting a draw by the river with a given number of outs after the flop and turn, and examples of draws with specified numbers of outs are given.
Example: if you hold 22 and the flop does not contain a 2, the odds of hitting a 2 on the turn is 22:1 (4%). If the turn is also not a 2, the odds of hitting it on the river are again 22:1 4%. However, the combined odds of hitting a 2 on the turn or river is 12:1 (8%). For mathematical reasons, only use combined odds (two card odds) when you are in a possible all-in situation.
Outs | One | Two | One | Two | Draw Type |
1 | 2% | 4% | 46 | 23 | Backdoor Straight or Flush (Requires two cards) |
2 | 4% | 8% | 22 | 12 | Pocket Pair to Set |
3 | 7% | 13% | 14 | 7 | One Overcard |
4 | 9% | 17% | 10 | 5 | Inside Straight / Two Pair to Full House |
5 | 11% | 20% | 8 | 4 | One Pair to Two Pair or Set |
6 | 13% | 24% | 6.7 | 3.2 | No Pair to Pair / Two Overcards |
7 | 15% | 28% | 5.6 | 2.6 | Set to Full House or Quads |
8 | 17% | 32% | 4.7 | 2.2 | Open Straight |
9 | 19% | 35% | 4.1 | 1.9 | Flush |
10 | 22% | 38% | 3.6 | 1.6 | Inside Straight & Two Overcards |
11 | 24% | 42% | 3.2 | 1.4 | Open Straight & One Overcard |
12 | 26% | 45% | 2.8 | 1.2 | Flush & Inside Straight / Flush & One Overcard |
13 | 28% | 48% | 2.5 | 1.1 | |
14 | 30% | 51% | 2.3 | 0.95 | |
15 | 33% | 54% | 2.1 | 0.85 | Flush & Open Straight / Flush & Two Overcards |
16 | 34% | 57% | 1.9 | 0.75 | |
17 | 37% | 60% | 1.7 | 0.66 |
Examples of drawing hands after the flop | ||||
Draw | Hand | Flop | Specific Outs | # Outs |
Pocket Pair to Set | [4♠ 4♥] | [6♣ 7♦ T♠] | 4♦, 4♣ | 2 |
One Overcard | [A♠ 4♥] | [6♥ 2♦ J♣] | A♦, A♥, A♣ | 3 |
Inside Straight | [6♣ 7♦] | [5♠ 9♥ A♦] | 8♣, 8♦, 8♥, 8♠ | 4 |
Two Pair to Full House | [A♦ J♥] | [5♠ A♠ J♦] | A♥, A♣, J♠, J♣ | 4 |
One Pair to Two Pair or Set | [J♣ Q♦] | [J♦ 3♣ 4♠] | J♥, J♠, Q♠, Q♥, Q♣ | 5 |
No Pair to Pair | [3♦ 6♣] | [8♥ J♦ A♣] | 3♣, 3♠, 3♥, 6♥, 6♠, 6♦ | 6 |
Two Overcards to Over Pair | [A♣ K♦] | [3♦ 2♥ 8♥] | A♥, A♠, A♦, K♥, K♣, K♠ | 6 |
Set to Full House or Quads | [5♥ 5♦] | [5♣ Q♥ 2♠] | 5♠ Q♠, Q♦, Q♣, 2♥, 2♦, 2♣ | 7 |
Open Straight | [9♥ T♣] | [3♣ 8♦ J♥] | Any 7, Any Q | 8 |
Flush | [A♥ K♥] | [3♥ 5♠ 7♥] | Any heart (2♥ to Q♥) | 9 |
Inside Straight & Two Overcards | [A♥ K♣] | [Q♠ Q♣ 6♦] | Any Ten, A♠, A♦ A♣, K♠, K♥, K♦ | 10 |
Flush & Inside Straight | [K♣ J♣] | [A♣ 2♣ T♥] | Any Q, Any heart | 12 |
Flush and Open Straight | [J♥ T♥] | [9♣ Q♥ 3♥] | Any heart;, 8♦, 8♠, 8♣, K♦, K♠, K♣ | 15 |
To calculate your hand odds, you first need to know how many outs your hand has. An out is defined as a card in the deck that helps you make your hand. If you hold [A♠ K♠] and there are two spades on the flop, there are 9 more spades in the deck (since there are 13 cards of each suit). This means you have 9 outs to complete your flush - but not necessarily the best hand! Usually you want your outs to count toward a nut (best hand) draw, but this is not always possible.
The quick amongst you might be wondering "But what if someone else is holding a spade, doesn't that decrease my number of outs?". The answer is yes (and no!). If you know for sure that someone else is holding a spade, then you will have to count that against your total number of outs. However, in most situations you do not know what your opponents hold, so you can only calculate odds with the knowledge that is available to you. That knowledge is your pocket cards and the cards on the table. So, in essence, you are doing the calculations as if you were the only person at the table - in that case, there are 9 spades left in the deck.
When calculating outs, it's also important not to overcount your odds. An example would be a flush draw in addition to an open straight draw.
Example:
You hold [J♦ T♦] and the board shows [8♦ Q♦ K♠]. A Nine or Ace gives you a straight (8 outs), while any diamond gives you the flush (9 outs). However, there is an [A♦] and a [9♦], so you don't want to count these twice toward your straight draw and flush draw. The true number of outs is actually 15 (8 outs + 9 outs - 2 outs) instead of 17 (8 outs + 9 outs).In addition to this, sometimes an out for you isn't really a true out. Let's say that you are chasing an open ended straight draw with two of one suit on the table. In this situation, you would normally have 8 total outs to hit your straight, but 2 of those outs will result in three to a suit on the table. This makes a possible flush for your opponents. As a result, you really only have 6 outs for a nut straight draw. Another more complex situation follows:
Example:
Once you know how to correctly count the number of outs you have for a hand, you can use that to calculate what percentage of the time you will hit your hand by the river. Probability can be calculated easily for a single event, like the flipping of the River card from the Turn. For two cards however, like from the Flop to the River, it's a bit more tricky, luckily there is a simple and quite accurate method
Now that you've learned the proper way of calculating hand odds in Texas Hold'em, there is a shortcut that makes it much easier to calculate odds:
After you find the number of outs you have, multiply by 4 and you will get a close estimate to the percentage of hitting that hand from the Flop. Multiply by 2 instead to get a percentage estimate from the Turn. You can see these figures for yourself below:
Sample Outs and Percentages from Above Chart | |||||
4 | 9% | 17% | 10 | 5 | Inside Straight / Two Pair to Full House |
5 | 11% | 20% | 8 | 4 | One Pair to Two Pair or Set |
6 | 13% | 24% | 6.7 | 3.2 | No Pair to Pair / Two Overcards |
7 | 15% | 28% | 5.6 | 2.6 | Set to Full House or Quads |
As you can see, this is a much easier method of finding your percentage odds
Using 100 divided by the whole percentage number, such as 24%, we can easily see that 100/24 is equal to about 4. We minus 1 from that and get a rough estimate of our odds at about 3:1. Let's try this all the way through with an example:
You hold: A♣ J♠
Flop is: 5♣ T♦ K♦
Total Outs: 4 Queens (Inside Straight) + 3 Aces (Overcard) - Q♦ or A♦ = 5 Outs
Percentage for Draw = 5 Outs × 4 = 20%
Odds = (100 / 20) - 1
= 5 - 1
= 4:1
Again, 4:1 odds means that can expect to make your draw 1 out of every 5 times. If the 1 out of 5 doesn't make a ton of sense to you, think about the 1:1 odds of flipping heads or tails on a coin. You'll flip heads 50% of the time, so 1 out of every 2 times it'll come up heads.