Simulating multiple villains

As discussed previously, in order to keep your trees easy to work with, you should aim to keep the number of active players in it to a minimum.

The ideal number of players is 2, since:
- It's the best number to keep your trees from becoming extremely complex
- The math engine will work (provided there's no play on undefined flops), so the results will be mathematically accurate

However, there are some cases where you really want to have multiple villains and, as a result your trees risk becoming very complex.

Using the delete action to make one villain as strong as multiple villains

A trick to get around this is to use a Delete action to make a single villain appear to be multiple villains. The basic idea behind this trick is that you delete some of villain's folding range, thus boosting the chance of villain holding a good hand.

For example, let's say we're on the button and we have 3 villains acting before us. We estimate that each villain would raise with the top 20% of hands and fold otherwise. This would make the chance of no raise occurring before us 80%^3=51% and therefore the chance of there being at least one raise 49%. We now create the following tree:

And now we add a Delete action and place it above villain's Fold action (to switch actions, select one by left-clicking it, then click where you wish to insert). Now right-click the Delete action's condition and give it a weight of 50%. Press F7 to get an EV run. It will give you the frequencies of the actions (you can also press F5 for an equity run if you've haven't completed the whole tree yet).

Due to the fact that the Delete action retroactively removes 50% of the hands that were folds, the ratio of raise versus fold has now increased from 20% versus 80% to 35% versus 65%. Some experimenting with the Delete action's weight learns that at 72% the ratio reaches the desired 49% vs 51% distribution. It's now as if Cutoff in this hand is 3 villains instead of one.

Disadvantage of the delete trick?
This trick does NOT take into account that múltiple villains can have a playable hand. What it basically does is go past the line of villains. The first villain with a playable hand it comes across gets to play.