Math engine vs MC engine

So, after following the instructions on the previous page we should now have this tree:

If you now press F7 or to compute the data in the tree a different progress bar than we've seen before appears.



The fact that the progress bar is now blue indicates that the software has switched to Monte Carlo mode.
In Monte Carlo mode the data is achieved by performing a large number of random simulations through the tree.

In comparison, the Math Engine achieves its results by enumerating all possibilities.
As a result, the Math Engine will give mathematically correct results.

If we had a choice, we'd always prefer the Math engine. However, in some cases there's just too many match-ups to enumerate everything (like in our tree, because there's three active players). In that case, the software will automatically toggle to the Monte Carlo engine.

Requirements for the math engine

There's two situations where the math engine can't be used:
- There's more than two active players in the hand
- There's postflop play, but the flop is not defined

The hint message (see pic above) below the progress bar will inform you why the Monte Carlo Engine is being used.
In the case of our tree it reads that "there's more than two active players in the hand".

Should you for some reason want to disable the Math Engine and force the software to use the Monte Carlo engine, then you can do so under Engine->Disable Mathe Engine.

Advantages of the Monte Carlo Engine

Although the Math Engine is clearly perferable to the Monte Carlo Engine, the Monte Carlo engine dóes have sóme edge on the Math Engine.

The Monte Carlo Engine can:
- Work out hand distributions (link)
- Calculate Variance (will be displayed in EV popup)
- Calculate the chance of holding the best hand right now (will be displayed in postflop EV popup)

So in sóme cases, you may want the Monte Carlo Engine.
To learn how to get the best out of bóth engines, please read the next section.

Getting the best of the two engines

To get the best of both engines, turn on "Engine->Merge data from both engines".
Or use the quick-toggle in the upper left that reads "Merge MC and Math".



When computing, the software will now first run the Monte Carlo Engine, after which it will run the Math Engine.
The Math Engine will now overwrite all results from the Monte Carlo Engine that it can do better.

Monte Carlo: Errors in the results

Due to the Monte Carlo Engine's results being based on a large number of simulations, of which then the average is then taken, there's an error in every number this engine gives you. For example, after computing our tree and mousing over an EV number, we'll get a result such as the one below:

As shown in this screenshot, behind the EV number a second number std is given.
This number is an indication of the error in the estimation of the EV.



Please also note that in the MC engine, the EV performance of the individual holecards may be a bit scattered, due to each number having an error. See the pic above for an example.

 

 

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