Hold'em Brain: Starting Hands
The first step to winning Limit Hold'em is to choose good starting hands to play. The quality of a starting hand is not static. Some hands may be good or bad in different situations. It depends on the other players' actions and your position. This chapter will explain what to look for when deciding what to do with your starting hand.
1326 different combination of hands, but only 169 different quality of hands
There are 1326 different starting hands. This counts K♣T♥ and K♠T♦ as two separate hands. If we did care about the order that we received the two cards in, then there are 2652 different combinations of two card starting hands (52 x 51). For the first card, we can get any of 52 different cards. For the second card, we can get any of the remaining 51 cards. This method would count 8♣7♣ as a different hand than 7♣8♣. However, in Hold'em we do not care about the order that the cards are dealt to us. Since every combination is represented exactly twice, this means we can divide 2652 by 2 to get the number of different combination of hands, and that equals 1326.
These 1326 different starting hands can be separated into three main categories. Pairs (9♠9♥), suited hands (A♦5♦) and unsuited hands (A♣5♠).
Pairs
There are 13 different pairs, ranging from AA down to 22. There are six different possible combinations for each pair. The six different combinations for AA are:
| A♥A♦ | A♦A♣ |
| A♥A♣ | A♦A♠ |
| A♥A♠ | A♣A♠ |
Since there are 6 different combinations for each pair, and there are 13 different pairs, that means 78 out of the 1326 different hands are pairs or 5.9% of all hands.
Suited Hands
There are 78 different suited hands. Some examples are A♥K♥, A♥5♥ and Q♥J♥. How did I get 78 different hands? One way is to look at the number of suited combinations with each card. If we take the A♥ first, there can be 12 different suited hands with the A♥, ranging from A♥K♥ down to A♥2♥ (there are 13 cards of each suit, but since AA can not be a suited hand, there are only 12 suited hands with the A♥). With the K♥, there are also 12 different combinations, but one of them is already counted for with the A♥. This means there are only 11 additional different suited cards with the K♥. Subsequently, the Q♥ has 10 different new combinations, and so on until we get to the 3♥, which only has one new combination, 3♥2♥. Adding them up (12+11+10+9+8+7+6+5+4+3+2+1), the total number is 78 different hands with each suit. There are four different suits, so that means there are 312 different suited hands (78 x 4). This reflects 23.5% of all hands.
Unsuited Hands
There are 78 different hands of each combination of unsuited hands. But instead of 4 different suits, there are 12 different suit combinations. For example, AK can come in 12 different unsuited ways:
| A♥K♣ | A♥K♠ | A♥K♦ |
| A♦K♣ | A♦K♠ | A♦K♥ |
| A♣K♦ | A♣K♠ | A♣K♥ |
| A♠K♣ | A♠K♥ | A♠K♦ |
This means there are 936 different unsuited hands (78 x 12) or 70.6% of all hands.
Overall, there are 78 different combinations of pairs, 312 different combinations of suited hands and 936 different combinations of unsuited hands. These add up to 1326 total different hands. Here is a table with the full breakdown.
| Type of Starting Hand | Different Quality | Different Combinations | Total Number of Hands | Percentage of all Hands |
|---|---|---|---|---|
| Pair | 13 | 6 possible combinations | 78 | 5.9% |
| Suited Hand | 78 | 4 different suits | 312 | 23.5% |
| Unsuited Hand | 78 | 12 different suit combinations | 936 | 70.6% |
| Total | 169 | 1326 | 100.0% |
In Hold'em, we do not care about the particular suits until after the Flop. For example, before the Flop, A♣J♣ is the same as A♦J♦, and 9♦8♣ is the same as 9♠8♥. It is only after the Flop that these hands may start to diverge in strength, although sometimes they stay the same if flush factors are non-existent after the Flop. This means there are only 169 different hands that can be dealt. You can see this by looking at the above table and add up the "Different Quality" category. When we look at it in terms of 169 different hands, it is important to keep in mind that the different hands have varying weights. A pair has 6 different combinations, a suited hand has 4 different combinations and an unsuited hand has 12 different combinations.
Understanding these factors becomes useful if we can narrow our opponent's hand down to just a few quality hands. For example, it is possible that a tight pre-Flop player will only raise with six different hands from the under the gun position: AA, KK, QQ, AKs, AKo and AQs. With all other hands, it is possible he would either fold or call. Here are the possible combinations these hands could have.
| Hand | Possible Combinations | Percentage of the time the under the gun player holds this hand |
|---|---|---|
| AA | 6 | 15.8% |
| KK | 6 | 15.8% |
| 6 | 15.8% | |
| AKs | 4 | 10.5% |
| AKo | 12 | 31.6% |
| AQs | 4 | 10.5% |
| Total | 38 | 100% |
Since this player will only raise under the gun with those hands, it means he will only be raising under the gun 2.9% of the time (38/1326). If you have played against this player often, it should come as a surprise to you when he does raise under the gun since he does it so seldom.
If you held JJ, you would know that you are in a dangerous position against this specific player. Against AA, KK, QQ, your hand of JJ is a major underdog. Against AKs, AKo, and AQs, it is only a slight favorite. Here is a chart that shows how often you should win if you were all-in before the Flop.
| Hand | Possible Combinations | Percentage of the time under the gun holds this hand | Your winning percentage with JJ | JJ's Equity (Third Column x Fourth Column) |
|---|---|---|---|---|
| AA | 6 | 15.8% | 19% | 3.0% |
| KK | 6 | 15.8% | 19% | 3.0% |
| 6 | 15.8% | 19% | 3.0% | |
| AKs | 4 | 10.5% | 54% | 5.7% |
| AKo | 12 | 31.6% | 57% | 18.0% |
| AQs | 4 | 10.5% | 54% | 5.7% |
| Total | 38 | 100% | 38.4% |
Note - the information from the fourth column, and all subsequent winning percentage numbers, are from the Texas Hold'em Calculator on Cardplayer.com.
If you assume no other players are going to play and the blinds will fold, then calling this tight pre-Flop raiser is a losing play even with a strong hand like JJ! Assume you are going all-in at this point (meaning you only have three big bets left in your stack), then you are risking three small bets to win four and a half small bets (three from the pre-Flop raiser, one from the big blind and a half from the small blind). This means you would need to win 40% of the time to break even. With these assumptions, the table above shows that JJ only wins 38.4% of the time on average, so in this instance playing JJ is slightly below the goal of 40%.
In practice, JJ is a playable hand even against a tight pre-Flop raiser. Most players will raise with more hands than the ones listed in the previous table and you will have positional advantage. Let's add in AQo, JJ and TT as two other raising hands by this player, and see how JJ fares in that case.
| Hand | Possible Combinations | Percentage of the time under the gun holds this hand | Your winning percentage with JJ | JJ's Equity (Third Column x Fourth Column) |
|---|---|---|---|---|
| AA | 6 | 10.5% | 19% | 2.0% |
| KK | 6 | 10.5% | 19% | 2.0% |
| 6 | 10.5% | 19% | 2.0% | |
| AKs | 4 | 7.0% | 54% | 3.8% |
| AKo | 12 | 21.1% | 57% | 12.0% |
| AQs | 4 | 7.0% | 54% | 3.8% |
| AQo | 12 | 21.1% | 57% | 12.0% |
| JJ | 1 | 1.8% | 50% | 0.9% |
| TT | 6 | 10.5% | 19% | 8.5% |
| Total | 57 | 100% | 47.0% |
Note - There is only 1 possible combination that your opponent has JJ because you have JJ as well.
Now the average winning percentage for JJ is much higher, jumping from 38.4% up to 47.0%. With the assumptions listed above, JJ now has a high enough of a winning percentage to play the hand. The under the gun raiser is now raising with 4.3% of his hands (57/1326) rather than 2.9%, and this makes a big difference to JJ.
The AQo debate
AQo is an interesting starting hand. Normally it is a high quality hand, and most players will open-raise pre-Flop with it. In some situations, it is a hand that is worthy of re-raising. However, in the same situation as we just discussed in the previous section, the correct decision is to fold! This issue was brought up in John Feeney's book "Inside the Poker Mind" (page 33-34). After his book was published, this issue was hotly debated on some internet forums.
Here are the assumptions. An early position player open-raises. You know that he plays very tight and will only raise with high quality hands. You know he would raise with AA, KK, QQ, JJ, TT, AKs, AKo, AQs, AQo, JJ and TT (in Feeney's book, he makes different assumptions on possible hands that the open-raiser may have). Your target is to win at least 40% of the time on average against this player. That would be the target for an all-in player. You do have positional advantage but there is also a chance another player holds a strong hand behind you. So using 40% as the target should get you close to the cutoff point.
| Hand | Possible Combinations | Percentage of the time under the gun holds this hand | Your winning percentage with AQo | AQo's Equity (Third Column x Fourth Column) |
|---|---|---|---|---|
| AA | 3 | 6.25% | 7% | 0.4% |
| KK | 6 | 12.5% | 28% | 3.5% |
| 6 | 12.5% | 30% | 3.8% | |
| AKs | 3 | 6.25% | 24% | 1.5% |
| AKo | 9 | 18.75% | 26% | 4.9% |
| AQs | 2 | 4.17% | 48% | 2.0% |
| AQo | 7 | 14.58% | 50% | 7.3% |
| JJ | 6 | 12.5% | 43% | 5.4% |
| TT | 6 | 12.5% | 43% | 5.4% |
| Total | 48 | 100% | 34.1% |
Note - Because you have AQo, it means there are only 2 other ways to make AQs and 7 other ways to make AQo.
On average, you expect to win 34.1% of the time. This does not meet the 40% threshold in the all-in situation. There is a chance AQo is playable at a level below 40% because of positional advantage and possible poor post-Flop play by the opponent, but 34.1% is so far lower than 40% that playing AQo in this situation just does not make sense.
But what if the same player who raised was in middle position rather than early position? This change in position means that he would add to his list of open-raising hands. Or we could keep the player in the same under the gun position and assume he would raise with more hands. In either case, the key is that the player is also willing to raise with hands that are worse than the hands listed above. Let's say the player adds five other hands to his open-raising hands, and let's say those five hands are 99, 88, AJs, ATs and KQs. The same analysis can be done with these hands included to see how it changes your decision when you hold AQo. Here is the table.
| Hand | Possible Combinations | Percentage of the time under the gun holds this hand | Your winning percentage with AQo | AQo's Equity (Third Column x Fourth Column) |
|---|---|---|---|---|
| AA | 3 | 4.35% | 7% | 0.3% |
| KK | 6 | 8.70% | 28% | 2.4% |
| 6 | 8.70% | 30% | 2.6% | |
| AKs | 3 | 4.35% | 24% | 1.0% |
| AKo | 9 | 13.04% | 26% | 3.4% |
| AQs | 2 | 2.9% | 48% | 1.4% |
| AQo | 7 | 10.14% | 50% | 5.1% |
| JJ | 6 | 8.70% | 43% | 3.7% |
| TT | 6 | 8.70% | 43% | 3.7% |
| 99 | 6 | 8.70% | 44% | 3.8% |
| 88 | 6 | 8.70% | 45% | 3.9% |
| AJs | 3 | 4.35% | 69% | 3.0% |
| ATs | 3 | 4.35% | 69% | 3.0% |
| KQs | 3 | 4.35% | 70% | 3.0% |
| Total | 48 | 100% | 40.5% |
Now you can beat your opponent's average hand 40.5% of the time and barely meets the 40% threshold. Playing AQo in this situation is clearly better than in the previous situation.
Starting Hands can Change in Value
There are some hands that you are happy to play in a certain situation but not in another situation. The variables that can change your decision include your position, previous players' actions and the characteristics of players yet to act. One of the keys to the changing values of hands is whether it is a drawing hand or not. Here are a few examples of hands that you would play differently on certain situations.
AQo
As shown in the previous section, although AQo is usually a re-raisable hand, it should be thrown away if a tight pre-Flop player open-raises in an early position. If the early position player open-raised from middle or late position instead, then you would feel comfortable re-raising. If the early position player who open-raised was not as tight as originally described, then it means he could be raising with worse hands, and thus a re-raise with your AQo is fine.
ATo
In late position when no other player has come in yet, this is a fine hand to steal the blinds with.
Even if any of the blind hands call, ATo is likely the best hand. If the blinds do not call, then you would be happy to win the pot right there. If there is a limper or two, ATo may still be the best hand depending on who the limpers are and what position they are limping in from. However, if there are a lot of limpers, then ATo goes way down in value and becomes a marginal hand. Other players may be limping in with hands such as AQo and AJo, which would dominate ATo. If there is a raise and a couple of callers, ATo is a hand to throw away.
JTs
In early position, some players feel JTs is a good enough of a hand to limp in with and hope to encourage other players to limp in along behind them. Their idea is that their limp may help build the pot as other players are willing to limp along. If that happens, then the player with JTs has put himself in a multiple player pot, a good situation for JTs. In late position, JTs is a hand that has enough value to open-raise to steal the blinds. However if there is just one raise from a reasonable opponent in early or middle position and no other player has called, then it is best to throw this hand away as it does not perform as well in a heads-up pot.
A7o vs 76s
In a heads-up situation, A7o is a better hand than 76s. The first reason is that A7o has the advantage of having the high card. The second reason is that A7o dominates 76s in that when a 7 hits the board, the kicker will usually mean the difference in the hand. However, if there are many other players involved in the hand, then the value of A7o decreases dramatically relative to 76s. In a multiple player pot, A7o will likely be dominated by another hand with an A and a higher kicker. The advantages that A7o enjoyed over 76s in a heads-up situation are have vanished in a multiple player pot. A7o no longer has the high card equity nor is it assured of being the dominating hand. Instead, it is the hand that is more likely to be dominated. On the other hand, in a multiple player pot, 76s does not need to worry about being dominated because it is looking to make a draw with 76s, not a pair. 76s and A7o have changed spots on the relative strength ladder when the situation is changed from a heads-up scenario to a multiple player scenario. With fewer players, A7o is the better hand, with more players 76s is the better hand. Thus A7o is a good open-raising hand from late position to steal the blinds, while 76s is a good hand to play in a cheap multiple player pot.
ATo vs T9s
This match-up is similar to the previous one. In a direct heads-up situation, ATo is far superior to T9s. However, when these hands are in the big blind against an tight early position raiser, T9s is a better hand. In the section on the AQo debate, it is clear that AQo does not play well against a tight early position player. The same reason holds true for ATo in the big blind against a tight early position raiser, even though it only costs one small bet to see the Flop. Also, the problem of being out of position in all future rounds makes it tough to play ATo under these circumstances. On the other hand, T9s has a chance of being a playable hand since it is not dominated by most hands that a tight early position player would raise with. If other players call, T9s will gain even more equity compared to ATo because T9s has drawing qualities and is more likely to be independent from the other callers' hands. Hands that dominate ATo (AK, AQ, AJ) are hands that most players will play most of the time. The same cannot be said for hands that dominate T9s. Here is a table comparing ATo and T9s versus a tight early position player. It shows that T9s is a better hand in this situation and the difference is big enough that calling a raise with T9s is correct but not with ATo.
| Opp.'s hand | Poss. Combos | % Opp has this hand | % ATo wins | ATo Equity | Poss. Combos | % Opp has this hand | % T9s wins | T9s Equity |
|---|---|---|---|---|---|---|---|---|
| AA | 3 | 6.5% | 8.8% | 0.6% | 6 | 10.2% | 22.7% | 2.3% |
| KK | 6 | 13.0% | 29.1% | 3.8% | 6 | 10.2% | 21.7% | 2.2% |
| 6 | 13.0% | 29.1% | 3.8% | 6 | 10.2% | 20.4% | 2.1% | |
| AKs | 3 | 6.5% | 25.0% | 1.6% | 4 | 6.8% | 38.7% | 2.6% |
| AKo | 9 | 19.6% | 26.6% | 5.2% | 12 | 20.3% | 41.0% | 8.3% |
| AQs | 3 | 6.5% | 25.1% | 1.6% | 4 | 6.8% | 38.8% | 2.6% |
| AQo | 9 | 19.6% | 27.1% | 5.3% | 12 | 20.3% | 41.4% | 8.4% |
| JJ | 6 | 13.0% | 28.8% | 3.8% | 6 | 10.2% | 19.0% | 1.9% |
| TT | 1 | 2.2% | 30.9% | 0.7% | 3 | 5.1% | 17.6% | 0.9% |
| Total | 46 | 100% | 26.4% | 59 | 100% | 31.4% |
When you are in the big blind against a tight early position raiser, you would prefer a suited connector like T9s or 76s over two high cards like ATo or A9o. In this case, T9s wins 31.4% on average, while ATo only wins 26.4% on average.
Now let's change the position of the open-raiser. Instead of raising from an early position, let's say the tight player was open-raising from the button. In late position, he would be raising with many more hands. He may raise with hands such as A7, KT, Q9, and JT if it is folded to him. Do you see what is happening here? Against these hands, ATo is a much better hand than T9s. ATo is the dominating hand against some of the hands that the button would raise with. On the other hand, T9s now has a much greater chance of being dominated. Also, hands like KJ and QJ (hands that the player on the button would raise, but would not if he was in early position) are favorites over T9s, but are slight underdogs to ATo. ATo is now a better hand than T9s against a raise from the button.