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Interpretation and first thoughts about Texas Hold’em Poker Statistics

On our page Texas Hold'em Poker Statistics and Probabilities we provide Poker Statistics, which we divided into three different groups:
1. Probabilities of being dealt specific Starting Hands (called Pocket Cards or Hole Cards)
2. Probabilities of Flops relating to your Hole Cards
3. General Flop Distribution

To give you a jump start on what to do with these statistics, we would like to make some comments on how to interpret these statistics for No Limit Texas Hold'em. Especially the Flop Statistics can be used easily to define profitable or non profitable situations which you will encounter often in No Limit Texas Hold'em.

Remarks regarding the probability of dealt Hole Cards

Pocket Rockets: In Internet Forums etc one often reads that American Airlines (AA) sometimes should be played slow from early position, so that your opponents can not get a read on you. You are dealt a hand like AA once in 221 hands. In a normal Online Sit & Go Tournament you seldom play more than 100 to 120 hands. If you do not reach the money, you will be playing way under 100 hands. You hardly ever get AA twice in the same Sit & Go tournament. So use this great starting hand to win a nice pot! Try to get more money into the flop by raising preflop! If you really want to canvas the strength of your Hole Cards, we recommend a different approach:
When you are the first player to enter the Pot (for instance UTG - UTG standing for Under the Gun, see Poker Vocabulary - or the players to act before you have all folded), then never limp, but raise. No matter whether you hold AA, 66 or 87s ! Again: If you decide to enter the Pot and you are first to act, raise! Your opponents will not know what hand they are facing. If you always limp with middle Pocket Pairs (TT to 77) and Suited Connectors and only raise with AA, KK, QQ, AKs, AK and AQs, good players will soon find out! Other advantages of raising preflop:
- The initial Raiser usually gets credit (and respect) for having a good hand. If the Flop is AK4, how should your opponent know you raised with 87s before the flop? Often, you will be given respect and you will be succesful with your continuation bets on the Flop.
- You sometimes win a Pot with a medium strength starting hand without even seeing a flop.
- In general, you will be getting more action when you really raise with hands AA and KK. (after seeing you raise with 77 and JTs, your opponents might try to reraise you out of a Pot preflop, but this time you have the goods. (one of my favorite situations, by the way...)
Only in the following situations should you limp with AA from early Position: Your opponents have played against you before and know that you often limp with a middle Pair or Suited Connectors from early position. The table is very lively and most pots are raised preflop. You have to be pretty sure someone will raise behind you! The worst case scenario is to see 5 other limpers behind you and then a Flop with 3 connecting low cards hit. Time to say goodbye to your Aces...
One final Remark: We did not just advise you to raise UTG at a full table with 87s!!! If your hand is not good enough to raise in a specific situation, it usually is not good enough to limp with either! Let's assume you limp with 87s UTG. After that, four other players decide to limp, too. The Big Blind raises to the fourfold of the Big Blind? If you now call, you have invested just as many chips as you would have if you had initially raised.

Suited Hole Cards: Every One at the table gets suited Hole Cards 23.52 % of the time! Suited Hole Cards are no rarity! If many players get involved in a Pot and the Flop comes with three suited cards, then proceed very carefully! Especially weak players love seeing flops (even calling raises) with any two Suited Hole Cards. (We have more on this subject below!)

Remarks regarding the probability of Flops relating to Hole Cards

Pocket Pair flops a Set or better: If you look at the Flop with a Pocket Pair, you will hit a Set (Three of a Kind) or better in 11.80% of the cases. These are situations, where there just is 'no way back'. Only weak players let themselves be bluffed out of a Pot in this situation. Only Exception: There are three suited and connecting cards on the board, for instance 987. But even then, it is almost impossible to let go of the hand.
The chance, that two Players who both look at a flop with a Pocket Pair, both hit a Set is very, very small! If this happens, you can consider it as your destiny to lose all your chips on that hand. Luckily in 50% of the case of this happening, you will be the player with the higher Set and will win all your opponents chips.
On the other Hand the following Situation is very frequent in Tournament Poker: 8 Players remain in a Sit & Go Tournament. You have 1'200 Chips (The average Player has 1'875 Chips). Blinds are 200/100. You are UTG + 2. UTG and UTG+1 both fold. You look at your Hole Cards and you find the following Pocket Pair: 44. What's the best Play now?
Here only two Answers can be correct: All-In or Fold. You can find arguments for both answers, depending on your image, the opponents, previous hands etc.To Limp here is a clear mistake! If you limp, you will hit a set 11.80 % of the time. But you are paying 16.66 % of your Stack to see the Flop! Even if your opponent calls your All-In when you do hit the Flop, this Situation just is not profitable! With small Pocket Pairs you should only limp, if it does not cost you more than about one twenty-fifth (1/25) of your Stack. To fold a Small Pocket Pair from early position is not a disgrace!

Looking at the Flop with 'Trash' Hands:
Many Beginners try to see the flop no matter what their Hole Cars are. They even call with Hands Like 94 off suit, to see the Flop. Let's take this situation to analyze, why it generally is not profitable to see the flop with trash hands like 94 off suit:
After consulting the Poker Statistics, we know that in 29% of the cases you hit one Pair on the Flop. In 71% of the cases you will hit nothing with 94. In 14.5 % (half of the 29 %) of the cases, your one Pair will be a Pair of Fours! This will often be bottom pair! This is not a situation you will win the pot often or win a lot of money with. Even with the 9 you will seldom hit Top Pair. Let's assume the Flop is 973 and you have 94, you are not in a profitable situation: When you raise, you will often win a small pot because every one just folds. What do you do if someone reraises you All-In? Or just reraises you? Even if we assume your opponent did not hit a Set, what hand could he be playing? If your opponent raised preflop, he might have AA, KK, QQ, hands that all have you beat. Maybe he limped with A9 or K9s? There are many hands your opponent could have that have you beat. This is a typical situation where you can win a small pot or lose a big one!
With hands like 94 you have to hit Two Pair or better, to feel confident about your hand. With two unpaired Cards you will flop Two Pair exactly 2.02 % of the time! You will flop a Set 1.35 % of the Time. A Full House 0.09 % of the Time. The Probability of flopping Quads is 0.01 %. This means, 3.47 % of the time (1 to 27.8) you will hit a good Flop!
Let's say, you have 1'500 Chips and the Blinds are 30/15. An opponent raises to 100. You call with 94. You are paying one fifteenth (1/15) of your Stack to hit the flop hard in 1 of 27.8 cases. This is not a profitable move! Even if you limp for 30 Chips (1/50 of your stack), this is not attractive. In this situation, you have to double up every 28th time to make limping with 'Trash' profitable. 30 Chips are one fiftieth of your stack. Every 28th time you hit the Flop hard. Meaning: Every second time you hit the flop, you have to double up! No Flop in the World will guarantee that your opponent will double you up every second time! Conclusion: Be smart and fold Trash Hands!

Hey, but 94 suited certainly is not a Trash Hand!?
How many times have I heard a weak player say the sentence 'But they were suited!^'? From The Flop Probabilities we learn the following fact: With suited Hole Cards you flop a Flush 0.84 % of the time! So when you have 94s and the Flop comes J72 of the Same Suit, you have usually hit the Jackpot. But usually you will not be paid off, because your opponents will be very cautious to invest a lot of money into a suited Flop.
In 10.9 % of the cases you will Flop a Flush Draw. In No Limit Hold'em Drawing Hands are not so valuable as in Limit Hold'em, because strong opponents will not offer you good enough Pot Odds, to make this a profitable Situation for you.
Also an All-In move with 94s and a Flush Draw with low Cards is not an optimal situation. If you have A4s and go All-In, your Odds of beating a caller who has Top Pair are much better. Example:
You have Clubs Nine

. Your opponent holds Diamonds Queen

. The Flop looks like this: Clubs Ten

.
The probability of winning the Pot when you go All-In (and get called) is roughly 38%. In the same situation with A4s (instead of the Nine of Clubs you hold the Ace of Clubs) you would have three additional Outs (the three remaining Aces in the Deck would give you a Pair of Aces and beat the Pair of Queens your opponent holds. The Probability of winning the Hand would rise to 46 %. Even with 98s your Chances of winning the hand improve, because the three Sevens (the Seven of Clubs is already accounted for in your Flush Draw Outs) would improve your hand to a Straight.
Conclusion: Fingers off hands like 94s! Drawing Hands are much stronger, if you have Overcards to the Board and thus have additional Outs.

Remark: If you flop a low Flush (i.e. with 94s, sometimes one does get a Trash Hand on the Big Blind and no one raises), you should play this situation aggressively! This has the following reasons:
1. If your opponent has a good hand, he will probably call or reraise. You have to give your opponent the possibility to make a huge mistake! If you checkraise, your opponent usually folds and you won his extra bet. If you raise, your opponent can make a reraise (to find out where he stands with Top Pair) and you can win more chips! If your opponent has previously seen you raising with a Flush draw (Semi-Bluffing), he might try to push you out of the Pot by going over the Top.
If your opponent is very passive both approaches will not extract any extra chips. He would neither reraise, nor would a Checkraise work, because he would just check behind you.
2. If a fourth card of the same suit comes on the Turn, you have either lost all the Action, because the Board now is obviously very dangerous! If you do get Action, chances are that you are running right into a higher Flush and will lose a lot of money.

Remarks regarding the general Flop Statistics

The Flop Distribution Statistics show you with which general Situations you will be confronted when playing poker, and how often these situations arise. Think about how you want to play these Situations!

The Flop is paired
You have two Overcards: Hole Cards AK, Board TT5

17 % of the time the Flop is paired. Let's say, you have AA and raise, the Flop will be paired in 17% of the Situations. A Flop like TT8 often leads to potentially dangerous Situations. You have to be prepare yourself for these situations, because they arise so often. Read Poker Books, participate in Forums so that you know how to handle this standard situation. There are different kinds of Paired Boards, you should prepare yourself how you want to play this situation against specific kinds of opponents:
You have a lower Pair to the Board: Hole Cards 88, Board: 9QQ
You have a higher Pair: Hole Cards AA, Board TT8
You have the 'middle' Pair: Hole Cards JJ, Board KK7
You hit the single Card (High Pair) on the board: Hole Cards AK, Board 44K
You hit the single Card (Low Pair) on the board: Hole Cards AJ, Board QQJ

Phil Gordon's Little Green Book coveres this theme very well. Phil Gordon Phil Gordon describes exactly how to he usually handles which of these situations. There are also many Possibilities of flopping a Full House or a Straight. Each situation demands a different approach.

Flush Draw Danger
55 % of the Flops contain two cards of the same suit. You have to know instantly, that in this situation the following approaches usually are wrong:
- Slowplaying: If you flop a Set and there is a Flush Draw possiblity, slowplaying usually is a mistake!
- Making small probe Bets: If someone calls your Probe Bet in this situation, he could be just calling you with a Flush Draw and hereby even be making the call with profitable Pot Odds.

If you have a good hand, i.E. Top Pair Top Kicker and the board displays a possible Flush Draw, raise decently. To give your opponent bad Odds you should raise about a third to a quarter of the Pot Size as not to offer your opponent good enough Pot Odds to profitably draw out on you.
If your opponent is known to overpay his Flush Draws, then make it expensive! Go ahead and raise Pot Size! If he keeps calling, you forced him to make an even bigger mistake!

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