In this article, we ranked starting hands in Texas Hold'em by the winning chance.

Using our poker odds calculator engine, we first calculated the "fixed-preflop, post-river" winning probability of all 169 types of starting hands. Then, we ranked and ordered the starting hands from the best to worst in the table and chart below.

Essentially, we use the winning chance as a measure of hand strength.

Rank | Hand Type | 6p. win odds | 9p. win odds |
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- We define the "fixed-preflop, post-river" winning chance as follows. The hero's hand is fixed to be the hand of interest. For example, this could be paired A. Then, in N players game, our simulation deal random cards for the (N - 1) other players game. Next, we would deal all the shared cards randomly up to the river. We then check if the hero is the winner and keep track how many times has the hero won using the fixed hands. Finally, we repeat this whole process again for 10,000 times. The winning probability is simply = (number of times winning after post river)/10,000
- "6p. odds" is the "fixed-preflop, post-river" probability of winning a 6-players game. It worthwhile to note that we assume no ones folds in the game. This give rise to the worst case probability or the worst case equity. In a real game where players folds, your chance of winning should be higher. The same interpretation can be applied to the "9p. odds".
- Why don't we use hand ranges? It is because we don't have real statistics of how frequent a type of hand is played. We could guess it but then it is becomes subjective. If we knew the close-to-real likelihood of each different type of hands being played, then we could provide non-opinionated estimate of the winning chance. If you have this type of data, we would be happy to get those statistics from you.
- The starting hand ranking or strength is always sorted by the 6-man game winning probability. Unfortunately, this will cause the 9-man winning chance to be not sorted perfectly. There are 2 possible reason: (i) We need to do more simulations to improve the accuracy of the estimated odds, or (ii) Game dynamics in a 9 players game are indeed slightly different.

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

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.

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.

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.

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.

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.

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.

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.

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.

In our analysis of poker hand ranking, we used winning probability as a metric to rank each starting hands. We show that the top 7 hands have a significant winning advantage over any other hands, especially the best hand - paired A. We hope that poker enthusiasts can used this information and our poker odds calculator to improve their game.

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