Beta Calculator FAQ

Why does the beta calculator give different results than the old version?

The old calculator uses handranking restrictions during the fictitious play calculation. The beta calculator takes the "old" calculator's results as starting-point, and then runs fictitious play without handranking restrictions. The beta results are much closer to real Nash Equilibria than the old ones.

Note that the old version uses an optimization step after the fictitious play calculation. This improves hand selection and gives the appearance of unrestricted ranges. Although this optimization does a good job of compensating for the shortcomings of restricted ranges, results are still far from perfect.

What does it mean to use "handranking restrictions"?

With handranking restricted ranges, there is a predefined ordering of hands for every range. eg: AA>KK>AKs>QQ>...>72o. If Hand1>Hand2 in the handranking, Hand2 can not be included in the range unless Hand1 is also included. In the example above, QQ can only be played if AKs is also played. If it QQ happens to be +EV while AKs is -EV, the calculated range will either miss a +EV hand (QQ) or include a -EV hand (AKs).

Ignoring mixed strategies, a handranking restricted range can only have 170 different values, compared to 2^169 for an unrestricted range. Using handrankings drastically simplifies equity calculations, at the expense of accuracy/flexibility.

Are ranges restricted in the beta calculator?

No. The beta calculator allows completely arbitrary ranges, including mixed strategies.