Flop Characteristics and their Effect on EV

[@christopherhancock3353]

Around 40:00, slide titled “Category Insights”, you show that straights are the least meaningful factor. But isn’t there a great deal of multicollinearity with straights and “grouping”? And I think that’s seen on the “Dimensional Rankings” slide a bit; the groupings with the highest coefficients are straightening flops. The “groupings” variables are more granular and explain more of the variation, so the straights variables, which are more coarse, can’t explain much more variation or capture much more of the magnitude of change to EV

[@SolverSchool]

You're 100% right here. To be honest, there are a bunch of things I'd want to change about this analysis now almost 4 years later.

[@ukrobochips8817]

A very interesting and informative presentation, thanks. GLATT's

[@SolverSchool]

Thanks - appreciate the feedback!

[@ukrobochips8817]

@@SolverSchool No worries. Can I ask, have you done anything similar regards prefered cbet size across different board textures?

[@SolverSchool]

I haven't spent a ton of time on different bet sizes yet. Typically when looking at boards, I'll offer it a few bet sizes at first and see what the solver prefers before simplifying to 1 or 2 sizes. In general, on more dynamic boards, we'll want to size bigger since a larger part of our range is vulnerable and needs more protection.

[@user-hi1mj4mc3w]

Fascinating insight and presentation. MTT player, so perhaps I'm way off, but BB defense Pre ranges seem off imho. Would they not have more Ax in their 3bet range as I thought the presence of rake desensitized flatting? Did you use Monker for the preflop ranges? Cheers

[@SolverSchool]

Thanks for the kind note. I did this analysis almost 2 years ago, so at the time, I was playing live 2/5 cash games. I modeled this after the games I was playing in - which were a bit more passive preflop. I used Upswing's ranges as a base and adjusted from there, skewing a bit passive. However, if I were to redo the analysis now and focus on the online 6-max games, the BB would have more 3-bets.

[@knowlestoo]

So if you pick descriptor variables that fully describe the change from one flop to the next, why doesn't the r-squared value come out at 1? I feel like there's some key stats knowledge I've forgotten. Something like there's differences in the degree of change between flops within a descriptive group and that loss of fidelity leads to the output for the group as a whole being a less than complete description of the data set. Nice work.

[@SolverSchool]

Thanks. The R-squared doesn't come out to 1 because we aren't fully accounting for every variable that could predict EV. There are other factors - such as position, the interaction of our ranges, etc - that impact the EV. And those factors aren't included within this model.

[@knowlestoo]

@@SolverSchool thanks for the reply but that's not it. Position is fully accounted for by restricting the whole model to COvBB or whatever it was - as in its not a parameter in this model. Same with ranges. The fact that r-squared increased when you changed the flop rank groups indicates there's more accuracy to be found by choosing better description variables. It's the balance between sufficiently accurate model with high r-squared and manageable descriptors. Now I'm wondering whether I should dig out my actuarial texts because a differential model such as the ones they use in insurance might give a better fit for the use case.

[@SolverSchool]

​@@knowlestoo​ you're right, position is not the best example to bring up for this specific situation. I only mention that because this model in different formations (e.g. MP vs BB) will yield a different R-squared. The point is that we're approximating somewhat and fitting this into a linear model. The challenge we'll face in this scenario is getting an R-squared as close to 1 as possible while still maintaining some level of simplicity and ability to extract meaningful results. There are definitely other factors that we could explore - interaction variables between specific cards come to mind immediately. But I also want to make the model outputs as implementable at the tables as possible. Thanks for the comments though! If you have any thoughts as to additional variables to test, would be happy to do so. I've also taken this work a bit further and am creating another video in the upcoming weeks. Best, Mike

[@knowlestoo]

@@SolverSchool Yes, that makes sense. Changing the positions, changes the ranges which changes the level of error by having groups such as, say, AQ+. As in, AQ+ means something different in the context of one range (it is 100% of a range of just AQ+, for example) compared to another. What I meant by differential model is 'Is there consistency, either linear or exponential, between gradual changes in hand strength across boards' So AKs is the one base, what's the change to AQs then AJs and is there a relationship between them so that by knowing the base for AKs, AKo, etc we could understand EV for all Axs, Axo, etc. It could be the case that the differences between AKs-AQs-AJs, etc. are the same as KQs-KJs-KTs (they'll both have a similar drop off as the gap gets big enough to prevent 2-card straights) meaning the human needs to know the base EV for A, K, etc on each flop and all other EVs can be derived from there. Looking forward to the next one.

[@Orekid1]

I wish he used A as an independent grouping, there is a big difference between an AHL board and a HHL board.

[@Orekid1]

oops, commented too quick, he did to this... lol

[@SolverSchool]

Yeah in my first iteration at this, I used HHL only and realized the difference was too big so I replicated it with the A grouping.

[@RobSteel117]

I think the Axx boards are misleading here. It would not be ideal for BB to open all those tiny AXo and so often be dominated Ax vs Ax. GTO ranges give BB A8o+ and A5o. Also you have BB calling AKo 100%, I would say 50% at most. So your input has too many Ax combos credited to the BB IMHO

[@SolverSchool]

Yeah I agree with this. I did this a few years ago when I was playing a lot more live poker, and used ranges closer to 200 BB equilibrium solutions, despite the fact that this is a 100 BB scenario. If I were to do this analysis over again, I'd use ranges closer to 100 BB equilibrium ranges.