What does an equity graph show me?
An equity graph shows you how often a given hand
has a certain minimum equity against another hand (or hands) on the next betting round. For example, with no board cards, the graph will show you data for a number of flops. On the other hand, if you enter a simulation including three board cards, the graph will show you the expected values for a number of possible turn cards.
Why are multiple graphs being displayed on my results page?
Each graph is from the perspective of a different hand. The left axis has a label that tells you which hand's equities are being displayed.
I'm a little confused. How about some examples?
Sure thing. Let's take some hold'em samples.
Here is the chart for ace-king of diamonds vs. a pair of black sevens before the flop:
The left axis tells us the minimum amount of pot-equity for AK. The bottom axis shows the percentage of the time we have that equity amount. For instance,
we can see here that AK will have at least 30% equity on a little more than 50% of all flops. Note the shape of the graph - the equity stays fairly high in the beginning, then drops fairly quickly with not much in the middle. This reflects
the fact that AK will either be solidly ahead or solidly behind on most flops against a pair of sevens.
Now let's look at AKs vs A6o:
Here we have a classic case of domination with the suited ace-king proving a substantial favorite on most flops against ace-six offsuit.
Here's an example that takes place after the flop - A5o vs A2s
Here we see that when racing Ac5d against As2s on a board of Ks5s3h, most turn
cards will keep Ac5d solidly in the lead, while a smaller number will give As2s a certain or near certain win.
Can I graph odds distributions on ranges of hands?
But of course! Here's an omaha hi/lo flopalyzer chart for any ace-deuce hand vs. any random hand with a board of Kh6s4cJd:
And, just because we can, here are the results for any two random hold'em hands before the flop:
Is there a way to make the graphs bigger?
Yes. In the output page, click on any graph to enlarge it.
What is the exact sequence of steps used to generate the data?
The following is executed for each trial:
- If any board cards were specified in the simulation, they are dealt
- Random hands are picked for each player
- Random board cards are dealt
- Exact equity is computed for each hand
- A single datapoint is added to the graph
Are you using monte carlo (random) simulations or enumeration (exhaustive simulations) to generate your results?
The following simulations are exhaustive:
- All two-handed hold'em simulations before the flop
- All exact (only one hand possible per player) simulations for hold'em
- All exact simulations for omaha and omaha-hi/lo on the flop and turn
For all other simulations, you can expect 600,000 trials or 10 seconds of cpu time, whichever comes first.