Equity Graphing

Slice has the ability to graph each players potential equity on the current or next street.  The first thing to do is set up the graphing options which you do by selecting the Tools->Graphing Options menu option which will bring up a dialog like the one below.

The Number of Random Trials option specifies how many different random scenarios you want to run.  Increasing the number of random trials will increase the accuracy of the calculation (at the expense of a longer calculation time).

Next select whether you would like to graph equity on the current street or the next street.  Each of these methods is explained below:

Next Street Equity Graphing: In this graphing mode a random hand will be chosen for each player and then a random flop (or turn/river if a flop/turn is input in the Board range) will be dealt and the equity for each player will be calculated.  This process is repeated N amount of times where N is the Number of Random Trials option you have set.  The equity is stored for each trial and a histogram is created from that data.

Current Street Equity Graphing: In this graphing mode you must specify a board ( flop, turn or river).  A random hand will be chosen from each players range and the equity calculated for each player.  This process is repeated N amount of times where N is the Number of Random Trials option you have set.  The equity is stored for each trial and a histogram is created from that data.

An Example

 To create an equity graph enter the players ranges normally and then click the Graph button . In the example below we will graph a players equity on the next street (flop) with a small pair versus AA

Clicking the graph button will cause Slice to deal a large number of flops (or turn/river if there are board cards defined) and calculate the equity on each of those flops.  You will be presented with a graph that looks like the following:

From this graph you can see that on 60% of flops (i.e. 0.6 on the Fraction of boards axis) that AA (Player 1) will have at least 90% equity.  Player 2 with their smaller pair will usually have less than 20% equity however, on around 10% of flops they will have close to 90% equity vs AA.  This of course occurs when they flop a small set (and there is no ace on the board).

The graph can also help answer the question "On what percentage of boards will I have X% of equity?"  For example, if we wanted to know how often Player 1 has at least 65% equity than we would enter 65 in the control shown below:

and from this we can see that Player 1 will have 65% equity on around 87% of all boards.

By un-checking the cumulative histogram option you can see a histogram of the equity from all of the boards dealt.