Starting Hand Matrix
Since suits have no value in a starting hand, there are 169 possible starting hands in the 13x13 matrix. The starting hand matrix is layed out in the manner shown at left. There are:
- 13 pairs along the diagonal
- 78 suited hands in the upper right triangle
- 78 unsuited hands in the lower left triangle
If you take the 4 possible suits into account, there are:
- 4 ways to get a given pair (6x13 = 78 combinations)
- 6 ways to get a given suited hand (4x78 = 312 combinations)
- 12 ways to get a given unsuited hand (12x78 = 936 combinations)
- Making a total of 1326 total combinations (78 + 312 + 936 = 1326)
So, you can see why unsuited hands are the most frequent and pairs are the least frequent.
Example Hand Range for 9 Opponents
As you slide the blue thumb of the slider at the bottom you will see squares being colored in according to the range of hands selected. For example, if your playing against 9 opponents and you slide the thumb until you have the top 40 hands you will have the display similar to the one at the left. The hand range is characterized by three numbers representing the ends of the rows for suited hands, the ends of the columns for the unsuited hands, and the last square selected along the diagonal for the pairs in the range. The range shown represents the top 40 hands against 9 opponents consisting of:
- Pairs: 7 = 77+ (pair of 7s or better)
- Suited hands: 28998 = A2s+, K8s+, Q9s+, J9s+, T8s+
- Unsuited hands: TTJ = AT+, KT+, QJ+
Thus, if you were dealt a J4 unsuited, for example, you would fold it because it's not in your range. But, an AT unsuited would be.
Example Hand Range for 6 Opponents
In this example, playing against 6 opponents, you've created a hand range representing the top 20 hands consisting of:
- Pairs: 9 = 99+ (pair of 9s or better)
- Suited hands: 9TTT = A9s+, KTs+, QTs+, JTs+
- Unsuited hands: QQ = AQ+, KQ+
This hand range represents the top 20 hands against 6 opponents and 8.75% of hands dealt, hence it is quite tight, or conservative in play. It has a 21%-41% Win% range as compared to a fair Win% of only 14.3%. Thus, the odds are significantly in your favor if you play this range. You will, however, fold a lot of hands.
Saving a Hand Range
Once you get a hand range you like you can save it to the Favorites table using the Save button. The table at the left shows saved hand ranges for:
- Top 40 hands against 9 opponents representing 18.10% of hands dealt. The Range Descriptors are 7, 28998, TTJ for pairs, suited, and unsuited hands.
- Top 25 hands against 9 opponents representing 1..86% of hands dealt. The Range Descriptors are 9, 899T9, JQ for pairs, suited, and unsuited hands.
- Top 45 hands against 6 opponents representing 20.81% of hands dealt. The Range Descriptors are 7, 27888, TTTT for pairs, suited, and unsuited hands.
You can refer to this table as you need to when the number of opponents in the game changes.
Remembering a Hand Range
Numbers by themselves can be difficult to remember because they are abstract. There are several ways to try to remember depending on what works best for you.
If you are visual, one way to think about a hand range is to picture a table like the one at left. The rank goes in descending order downward with pairs at the top, suited hands in column 1 and unsuited hands in column 2. So, for example, in the Jack row, the lowest suited rank is '9', giving J9s as the lowest starting hand with a Jack in the top 40 hands. A J4s then would be out of range. It may be easier for you to visualize a table like this to remember the range rather than simply trying to memorize the number.
A summary of different techniques you may consider, such as the Major System, is given at the site Rememberg.com HERE.
Comparing Simulation to Actual Play
The former poker site called, “Pokerroom”, kept tabs of over 122 million starting hands for
a variety of cash games, including heads up, shorthanded, and full ring games. The resulting data was published on its web site and independently analyzed. The results showed that the top 40
hands accounted for virtually 100% of the profit.
The table at the left compares the top 40 hands obtained in actual play for a variety of opponents to simulated play, assuming an average of 5-7 opponents. The differences in simulation versus actual are:
- Simulations were played to the river with all hands, while in actual play not all hands would've been played to the river. Some hands would've been folded before then.
- Simulation doesn't account for psychological moves such as bluffing, which can occur in actual play. It also doesn't consider such factors as table position or stack size, which no doubt had an impact on actual play.
- The actual play data doesn't take into account the number of opponents, since the data was taken for a variety of games, including heads up, shorthanded, and full ring.
- Simulations take into account the number of opponents, where it is found that the range of hands that can be played increases as the number of opponents decreases.
Despite these differences, there is a strong correlation between simulated play and actual play.
- In actual play, pairs had a slightly wider range, going to a pair of fives versus a pair of sevens for simulated play. This extension of pairs to a pair of fives happens in simulated play also when the number of opponents is 1 or 2, and probably reflects the influence of games in actual play with fewer players where small pairs have more value.
- Suited hands were the same for simulated play and actual play.
Unsuited hands differed only in the Queen and Jack positions for the top 40 hands. Since
simulated play had two fewer pairs in the top 40 range, then two more hands need to be added (to keep the range at 40), which turn out to be QTu and JTu. These hands have connector
value in forming straights as well as possible top pair value so it makes sense that would fall into the top 40 range.
So, why not just always play the top 40 hands? You could, and it wouldn't be a terrible strategy, except for the fact that the range of hands you can play with better than fair chances of winning, as shown by the simulated data, widens as the number of opponents decreases. For example, in heads-up play there are some players who play every hand, but when the range of hands exceeds 90 or so the odds of winning start to go against you. That's why it's important to base your starting hand strategy on the number of opponents you are facing. The more opponents, the better the chances one or more of them will have a good hand, so the narrower your range needs to be to give you the edge in the long run.
Effect of Different Playing Styles
How your playing style affects your starting hand range:
- Tight-Aggressive: Play a tight range, say the top 20-30 hands against 9 opponents, but bet aggressively when you get a good hand. Mix up your play to be less predictable by occasionally bluffing or semi-bluffing by playing hands outside the range such as small pairs or suited connectors.
- Loose-Aggressive: Widen your range to play more hands and bet aggressively. May work against timid or very tight players.
- Tight-Passive: Narrow your range to play fewer hands and don't bet aggressively to keep your losses down.
- Loose-Passive: Widen your range to call more often, but don't raise or bet big unless you have a great hand.
Note: Many experts believe in two basic strategies, depending on the type of game and kind of players. These are:
- Tight-Aggressive play is best when mixed with occasional bluffing and hands outside your range to reduce predictability. For example, you may want to play a range of the top 40 hands, or maybe even the top 20 hands.
- Loose-Aggressive play can be good when you can see a lot of cheap flops in a loose game with a lot of limpers. For example, you might play the top 60 hands or so. This can also be used in a "fast" tournament, where luck can play a larger role and patience is less effective when the blinds are escalating rapidly and the tournament is over in mere hours. After the flop you are seeing 70% of your hand!
Limit versus No-Limit Hold'em
No-Limit Hold'em is more of a psychological game compared to Limit Hold'em. There tends to be more bluffs, more large bets and all-ins in No-Limit Hold'em to move players off their drawing hands. Hence, in No-Limit, being able to read your opponents (tells) and understand their playing styles, patterns, is important. There are often multiple folds around the table of starting hands with only 2 or 3 players left in the hand to see the flop.
Limit Hold'em, on the other hand, tends to be more of a mathematical game, taking into account pot odds, number of outs, odds of hitting your drawing hand, etc. It is not as emotional or psychological as No-Limit where opponents can pressure each other with large bets. Players tend to call more often since the cost is lower and more players stay in the game to see the flop. This tends to increase the value of connectors, especially suited connectors, which can draw out to a straight or a flush and win larger pots with more players in the game.
Effect of Number of Opponents on Win%
The chances of winning with a given hand, even with a pair of Aces—the best starting hand possible, drops significantly as the number of opponents increases. So, for example, against 9 opponents a pair of Aces is expected to win about 31% of the time, while against 1 opponent it should win a whopping 85% of the time.
As the number of opponents goes up the chances that at least one of them with draw to 2-pair, a straight, a flush, 3-of-a-kind, etc., goes up. So, with pocket Aces there are two potential strategies:
- Bet aggressively before the flop to reduce the number of opponents who might draw out on you.
- "Sandbag", that is go slow, to not scare players out, but to build up the pot in the hopes of winning a bigger pot.
The jury is out on the best strategy, but choose one based on your assesment of the situation at the time including such factors as: How big is your stack? How liklely are players to fold to your large bet? Are your opponents "loose" and likely to stay in, even with inferior hands?
Effect of Your Position at the Table
In a large game, where you sit at the table can make a difference in the range of hands you play. You may want to consider having three ranges to accomodate your position at the table.
- Early: If you're the first to play ("under-the-gun") you have almost no information, except possibly advance tells, about whether any of your opponents have strong hands or not based on whether they raise, fold, or call. For that reason you might want to play a narrower range of starting hands. Instead of the top 40, for example, maybe you would play the top 20 or 30.
- Mid: In Mid position you have a little bit more information, but there are still players to go after you. If someone raises in front of you, especially the player under-the-gun, they may have a better hand than you, probably a pair or a high card such as an Ace or King. The pot may also get larger with calling players behind you, giving you better pot odds. This might be a good spot to play your Mid hand range unless someone bets big or goes all-in in front of you.
- Late: In late position, you have more information. You know how many players have raised or re-raised and how many have folded or just called in front of you. You may want to fold against raises and re-raises, but play a wider range against callers ("limpers").
Typical Hand Distribution at Showdown
This table shows the chances of you, or any of your opponents, having a given hand at showdown. For example, there is a 43% chance of having a pair, while only a 5% chance of having 3-of-a-kind or a straight. Pairs are most frequent, followed by 2 pair at 24% and then just high card at about 17% with Flush and Full House occuring about 3% of the time. Quads and Straight Flushes are extremely rare. You may never see one!
Win% for Starting Hand Types
This table shows the chances of winning with a given hand. As shown, 2-pair wins slightly more often at 31%, with 1-pair next at 27%. That means that 1 or 2-pair wins about 68% of the time. Following that is 3-of-a-kind, which wins about 12% of the time. Straights, Flushes, and Full Houses win about 9-10% of the time. Quads and Straight Flushes are so rare they are practically zero and having a high card, such as an Ace, only wins about 2% of the time.
Your Likely Starting Hands
Most of the time (about 71% if the time) you'll get an unsuited hand—two cards of different suits, which is why most of the time, in a tight game against 9 opponents, you'll be folding 4 out of 5 hands with an unsuited hand that lies outside your range.
Assessing your hand based on pot size
The size of the pot versus the size of the bet you have to make to win it (Pot Odds) may also influence whether you play the starting hand or not.
Pairs can be converted to a set (3-of-a-kind) if a matching card appears on the board. The odds of getting a set on the flop are about 7.5 to 1, which means that if you have a small pair that lies outside your range, the size of the pot needs to be 7.5 times or better times the size of your bet to justify staying in against an aggressive opponent who appears to have a good hand.
The odds of converting a suited hand to a flush on the flop are quite small—about 118 to 1, but the odds of getting a flush draw are only 8.1 to 1, and the odds of getting a flush by the river, starting with a suited hand, are only 15 to 1. So, the bottom line is don't bet heavily on getting a flush!
TT versus AKs
Some hands get better with fewer opponents, some with more opponents.
For example, TT (pair of tens) is better than AKs for up to 4 opponents, but AKs (Ace-King suited) gets better as the number of opponents increases from 5-9.
So, pairs become slightly more valuable as the number of opponents decreases, while high ranked cards become more valuable as the number of opponents increases.
Note: Because high ranked cards beat lower ranked ones, there is a tendency for players who stay in the game—especially in a 10 player game—to have at least one high ranked card such as A, K, Q, J.
In general, you can expect your opponents who don't fold to have one of the following:
- One or two high ranked cards such as A, K, Q, J
- A pair
- A suited connector such as T9s
- An unsuited connector such as 98u
Only a pair is a "made" hand. All the rest are drawing hands.