Interpreting Equity Distributions

GTO Wizard’s range vs range equity distribution graphs are an excellent tool for visualizing which player has the stronger or nuttier range and the distribution of equity across each player’s range. Whether a player has mostly medium-strength hands or a more polarized mix of very strong and very weak hands has huge implications for their preferred betting frequency and size. These graphs display that information clearly and concisely.

On these graphs, the x-axis plots each player’s range from their lowest-equity hand, on the far left, to their highest-equity hand, on the far right. The y-axis plots the equity of each hand. The lines on these graphs always slope from the bottom left to the upper right. The things to pay attention to are: which player’s line is above the other’s at various points on the x-axis and by how much.

Check out this article to learn more about equity distribution graphs 📉

A Polarized Range vs a Condensed Range

Take a look at the graph below, where the 🔵 blue line represents BB’s equity distribution and the 🟢 green line BTN’s equity distribution. Which of these players has the more polarized range? How can you tell? What do you expect each player’s betting strategy to look like on this street? (I am deliberately not giving you the action that led to this distribution so you can practice deriving optimal strategy from the graph rather than from familiar patterns of previous action.)

BTN has the more polarized range here. Notice their green line is consistently well above or well below BB’s blue line, intersecting it only briefly in the middle, where the line slopes steeply upward. That means BTN’s hands are mostly very bad, with 0-15% equity, or very good, with 70%+ equity. That vertical stretch in the green line indicates BTN has no hands with 30-60% equity. The long, flat, horizontal section of the blue line represents medium-strength hands, with about 60% equity, predominating in BB’s range, with just a few very good or very bad hands at the extremes.

Knowing this, we should expect BB mostly to check. Those medium-strength hands do not benefit from betting, because they will only cause worse hands to fold and better hands to call. Their preference is to keep the pot smaller, get to showdown, and maybe induce some bluffs from BTN’s weaker hands 🙌

BTN is the one who wants to bet. Their weaker hands can get folds from better, and their stronger hands benefit from making the pot larger. Given the magnitude of BTN’s advantage here, we should expect large bets, if the stack-to-pot ratio permits it.

This graph is from a 100BB cash game simulation, BTN vs BB in a single-raised pot. After the BB checks and calls a 50% pot on an A♠ T♥ 8♠ flop and a 125% pot bet on a 2♣ turn, they see the 6♥ river with the ranges shown on this graph.

As we predicted, the BB checks 97% of their range in this situation, and the BTN makes large bets with a polarized range, using all in for more than 200% of the pot as their most frequent bet size.

Quiz: Match the graphs to the flops

Now that you’re familiar with these graphs let’s practice using them to evaluate flops. The following graphs depict the equity distributions for a single-raised pot, UTG vs BB, in a 100BB 6-max cash game on three very different flops: T55r, T86tt, and AK6r. See if you can determine which graph depicts which flop. A few hints follow, in case you have trouble.

Hints

In the first graph, the equity is quite evenly distributed. BB’s hands are a bit weaker on average, but neither player enjoys a significant range advantage. Both players have the strongest possible hands in their ranges.

In the second graph, UTG’s range is noticeably stronger except at the top end. Around the 95th percentile of hands, the BB’s blue line actually surpasses UTG’s green line, suggesting BB is more likely to have the very strongest hands despite their overall equity disadvantage.

In the third graph, UTG has a huge equity advantage that persists across all segments of hand strength 💪 Their weakest hands are much stronger than BB’s weakest hands, their medium hands are much stronger than BB’s medium hands, and their strongest hands are moderately stronger than BB’s strongest hands.

Answers

Conclusion

By studying these graphs, we can glean a lot about which player has more of which kind of hand and, consequently, how large of a pot that player will prefer to play. These preferences drive betting frequency and sizing. Considering these same factors in-game and visualizing what these graphs would look like in a given situation can help you make better decisions about whether and how much your range will prefer to bet.