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Do these programs calculate the same, and how are the calculations done?
They don't although the results look very similar.
There are many ways to do those calculations but all of the currently popular one work by making small adjustments at every step. So for example the solver looks like EVs the current strategy produces for raise/call/fold and adjusts the frequencies in the direction of the best action.
CFR/fictitious play/gradient descent based algorithms are all variation of this and the only problem is to choose the one which converges fast, is fast to execute and uses as little memory as possible.
One way to describe them is that they are all different strategies to climb the hill which you have no map for and can only navigate using what you see at given time. The difference is about the way you choose your steps, how big steps you take and how you handle stepping into wrong direction.
Cepheus (the project of Alberta University which solved limit Holdem) uses CFR+ algorithm which has some nice properties (mainly being good at close to 0 accuracies and having good theoretical convergence properties) and some not so nice ones (converging slower at the beginning, using a lot more memory than needed, having additional overhead for regret->strategies and back calculations etc.).
We use something different which is in my view the best described as a mix between fictitious play and gradient descent. This needs more tuning to be good at close to 0 accuracy (although last version is already way better there) but it allows for optimizations which will not be possible when using CFR like algorithms and is already faster at getting to very good accuracy so in a sense it's more of a practical than academic way of doing things.
I have no idea what other solvers use but you can ask the authors.
As to the results: what we did was to compare our results to Cepheus and to other small solvers we have available. The thing is it's easy to make mistakes when comparing those things and you can't really achieve it until you see the whole tree which was the reason for my reaction at the beginning of this thread (you can't claim you verified anything if you don't have the whole tree).
It is true though that all signs suggest that all available commercial solvers produce very similar results and that it's not possible to produce significantly different strategy once you are very close to the equilibrium.
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I would max explo both sides back and forth, but what ends up happening is it goes in circles. Just having difficulty wrapping my head around it.
Going back to my hill climbing anology: sometimes you see a path which leads up and you decide to take a step, say 100 meters long one. What happens is you end up on the other side of the peak. You turn around, you see the path leading uphill again and you take another 100 meter leap only to go back where you were before. The trick is to take a smaller step. While this sound like an obvious thing, it's not as trivial to make work when you have more dimensions (because there are more hands and available actions) so some care is needed to avoid jumping around like that but still ensure reasonably fast climbing pace when you are far away from the peak (if you always take 1m steps it will take a long time to climb 8000m high mountain).
Last edited by punter11235; 07-24-2015 at 07:23 AM.