Texas Holdem Probability Table

03.03.2021by

Based on the tabulated data and chart generated, there are a few interesting observations to be made. The are listed below:

1. Pair A is best hand

There should be no surprise that Pair A is the best hand. Having a pair A, helps you to easily get the best possible double pair combo or three-of-kind combo. While it might be harder to strike straight or flush with it, those scenarios are typically less likely to happen. Thus, making pair A better in general.

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2. Offsuit 72 is the worst hand

  • Texas Holdem Heads-Up Preflop Odds. This table was created by enumerating through every possible board and opponent hole card combination for each of the 169 texas holdem preflop starting hands. The numbers are exact to the rounding I used, which was.
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This might be less known to people and it could be counter intuitive. Some might have thought that perhaps Offsuit J2 would be worse than Offsuit 72. But, that is not the case.

To understand why this is the case, we can start thinking about what are combinations that are most likely to lead to a winning combo assuming no one folds. Given any hands, we are more likely to win with double pair, followed by 3-of-a-kind, straight flush and so forth.

With offsuit 72, we are more likely to win double pair of pair 7 and pair 2, followed by three-of-a-kind and so on. However, it is also worthwhile to note that it is highly like other players has a better double pair or three-of-a-kind. This bring us to the next important lesson to learn.

3. Having a suited, closely connected hand with A, K or Q is better than having pairs that is less than 9

If you were to investigate the table or chart, the hand ranked 5th is Suited AK. What is even more interesting is pairs hand only took 6 spots from rank 1 to rank 20. Most of the remaining spots were taken up by suited, closely connected hands with a high card like A, K or Q.

The reason for this is similar to previous point that we made. It is more frequent that players will win using double pairs or 3-of-a-kind. Therefore, having a higher card helps to push you to a better standing to win.

One final note on this topic - Pair 9 is the last pair hand ranked in the top 20 hands. Playing any other pairs hand may not be as good as conventional wisdom might suggest.

4. Winning chance drops fast within the top 7 ranked hands

This is the lesson that really took us by surprised. While developing our poker odds calculator, we did had a sense that odds of winning was somewhat asymmetric. But, the chart above really solidify how much the asymmetry was.

Within the top 7 ranked hands, the probability of winning drops really fast from paired A to paired K and so forth. If you get the top 7 hands, you really should work hard to get through the preflop.

5. You are more likely to win a 6 players match than a 9 players one

A player with hands that are in the top 7 ranks in a 6 players game have a much better chance of winning in a 9 players game. For example, Paired A has roughly 49.5% preflop winning probability in a 6-player game compared to only 35% in a 9-players game. While 14.5% difference is not as big as it sounds, it has a significant impact on the pot odds that you will need to make a value play. In short, it might be easier to make money off a 6 players game rather than a 9 players game.

6. In a no-folding six players match, your hand range to play is very large

This point is not as crucial as other points we have made. But, we find this observation quite interesting although it is unlikely to happen in real life.

Suppose that we are in a no-folding 6 players Texas Hold'Em match. During every betting session, our pot odds is 5-to-1. This means that for every $1 we bet, we stand to win $5.

Based on this pot odds, our break-even pot equity or winning odds is around 16.67%. Using the chart above, we can see that we can play any hands better than rank 106. This means that players can play 105 types of hands out of 169 types (59.2% of all types) and still perform better than break even! Basically, you have a very large hand range to play in this type of situation.

Texas Holdem Table Cover

Nonetheless, this is a just-for-fun analysis, which does not happen that often in real life. Based on some of our experience playing, it could happen sometimes during preflop though.

7. Our hand rankings are similar to Sklansky hand groups

Texas holdem probability tablet

Sklansky hand groups was formulated by David Sklansky and Mason Malmuth. Both of these old school poker players understand the math very well. It is no surprise that our hand rankings aligns very well with their proposed hand groups.

Sklansky hand group proposes that Tier 1 group consists of pair A, pair K, pair Q, pair J and suited AK. These cards are essentially ranked 1 to 5 via our Monte Carlo simulation. The same observation can be made for Sklansky Tier 2 and Tier 3 hand group.

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Position at the Table

Your position at the table is simply your position in relation to the theoretical dealer. The dealer is well known as the best position since the player in that position plays last on each betting round (except the preflop). The advantage in playing last is simply the chance to see how all the players at the table react before making a decision to bet, call, or fold. It is always better to play last in any betting scheme.

The person to the left of the dealer is in the worst position on the table since this is the player that has to act first and this player is forced to put in half the maximum single bet before seeing any cards (referred to as the small blind position). Nobody likes to bet on a hand they have yet to see but this is exactly what happens in this position.

The person to the left of the small blind position is the big blind position. This player is forced to go in for one bet (and in fact initiates the betting without seeing their cards). The big blind position is known as the second worst spot on the table to act from and usually someone in this position that is betting has something worth betting with (when there are lots of players at the table).

The person to the left of the big blind acts first before each player receives their first two cards. This is referred to as 'being under the gun' in poker slang. The clockwise motion of play allows those who act later (in late position) to be at a significant advantage in the game. As a result, those in late position can play weaker hands or 'gambling hands' with less fear of financial obligation or loss.

The blind positions and the player under the gun (early positions) should be much more selective with their hands, as they don't have the privilege of watching other players betting/raising before they must decide if they want to stay in themselves.

Texas Holdem Probability Table

For example, lets say you're under the gun (first to act). You have Queen-Jack off-suit and have placed a bet. A player after you raises and everyone but you folds – what should you do? Chances are good that this player has a better hand than you, with at least an ace or a king or a pocket pair. Unfortunately, you've already bet, because you had no idea what the other players at the table had in the pocket. A real gamble in this case. The worst part about this scenario is that you will always have to play before this person and in so doing give that player a big advantage over you throughout this hand. This is a typical situation where position is key to acting or not acting on a questionable hand.

Conversely, being in the dealers position for the above scenario not only gives you the benefits of observing how the other players are betting, but it also gives you the ability to adjust and influence the size of the pot. After all other players have bet, a raise by the player in the dealers position could potentially double the size of the pot or could limit the number of people who stay to see the next betting round. Usually players who have committed to one bet are very likely to commit to another bet, but this is the very situational trap that many undisciplined players fall prey to.

Position on the table is key to your style of play and your ability to be aggressive or passive with respect to betting strategies. Beware of the players who use their positional advantage with great skill. These are players you should want to learn from.

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