I've been reading a couple of no-limit books and have a question concerning solver output which should be very easy to answer.

What happens is I'll read something like the solver has chosen to make a 3 big blind bet. Is that because the solver is given one or more possible bet sizes and of those given bet sizes this is the one it determines to be best or is it because out of the world of all possible bet sizes (which would be 1 big blind up to the size of the effective stack) the solver has determined that a certain size is best?

Thanks in advance,
Mason

The former. You define what the possible bet sizes can be. If you specify too many bet sizes, it will take forever to solve, even with the fastest computers with the most memory and most cores. By forever I mean it could take over a week or even a month to solve if the solver could bet any size from 1BB to the effective stack size. Also the more possible bet sizes, the more complex the solve will be, and the less useful for a human to understand or implement. Three or four possible bet sizes (per street) should be sufficient for most hands. What those possible bet sizes should be is dependent on the texture of the flop and ranges of the players, as well as whether it's the flop, turn or river.

Hi George:

Thank-you, and this is exactly the way I understood it to be. However, my understanding is that solvers have gotten faster recently. So is what you're saying for a week to a month or more still accurate.?

The reason I asked the question is that I'm reading Jonathan Little's book 100 Essential Tips to Master No-Limit Hold 'em and he'll make statement like this which appears on page 167:

bet 5.3 bb 32.6% / Bet 2.2 bb 6.1 % /
check 61.3 %

So just to confirm, the 5.3 bb bet size and the 2.2 bb bet size are just numbers that Little came up with on his own and are not supplied by the solver in any way? This seems to me to be more like machine output than human input since a human would be more likely to say something such as 5bb and 2bb rather than 5.3bb and 2.2bb.

Thanks again,

Mason

I don't know about the speed of the newer solvers. Part of the equation is the accuracy. If you're happy with "within one percent" it's going to be a lot faster than within .1%.

He chose those bet sizes. You have to specify the possible bet sizes in the solver. If he specified a lot, they all would have been used at some frequency. It could be he ran a solve with several bet sizes and then chose the two with the highest frequency and re-ran the solve with just those two to simplify the results.

While 5.3bb, 2.2bb and such look strange, it's probably the amounts that correspond to certain percentages of the pot, which wouldn't be strange, as most NL players think that way. For example, those two amounts are approximately the amounts for a 1/2 pot sized bet and a 1/5 pot sized bet for an 11bb pot. Whether a choice between 1/2 pot and 1/5 pot is wise is another matter. If he chose those bet sizes I would think he would justify why those and not others.

As for whether he came up with them "on his own", keep in mind he has a number of coaches on his site, some of which are adept at this sort of thing.

yeah it was probably a boiler plate setup of something to the effect of 10% pot, 40% pot, pot, & jam

he's not entering bb sizes each time but using a standard template he likely used for al his sims

I think that's right. I noticed that in the example I gave the 2.2 big blind bet size is approximately a half pot bet since the pot at that time is 4.5 big blinds.

This is something he should have explained in the book, which by the way is very confused when it comes to how game theory and poker actually work.

For example, on page 163 he's the preflop raiser (probably for 2 big blinds) and the flop is A76 and he says "and your opponent check/calls your 1.5 bb bet (you should bet this flop with almost your entire range)." I suspect that he has no understanding as to why the solver has you betting 'almost your entire range' when making a bet at that bet size. That is he doesn't understand exactly why the smaller bet size means you should bet more hands for value (and if the bet size was small enough you should actually bet some negative EV hands) coupled with multi-round game theory.

Thanks for the response,
Mason

Hi George:

Thanks again for the response.

Very few people know this but I did a fair amount of work on my own relative to game theory and poker back in the 1980s. (Part of the reason for this was the book Winning Poker Systems by Norman Zadeh.) You can see the result of this in the chapter "Betting and Game Theory" that first appeared in the 1988 edition of my book Gambling Theory and Other Topics. (We're finishing up the new expended edition of this book and I plan to have a free kindle give-a-way in a couple of weeks for this new version.)

What this chapter shows is that when the bet is large relative to the pot some of your hands that you can bet for value should be checked to maximize your EV. But it also shows that when the bet is small relative to the pot you should actually bet more hands and if the bet is small enough this can include hands whose EV is actually negative. (This result is consistent with the appendix in Zadeh's book.)

Best wishes,
Mason

mason, i haven't read jonathan little, but based on what i've heard others say of him, i would not be surprised if he were not the best resource for reading about solver work

having said that, i'm not of much help pointing you in a better direction

Hi rickroll:

No. Your answer was exactly what I was looking for. When critically reading someone else's book, whether I'm going to write a review or not, I like to be sure that what I think the author is saying is indeed what the author is trying to convey. And you helped confirm this. So, thanks again.

On a different note, when reading some of this stuff, and this is not aimed specifically at Little, I can't help but think that many of these authors have looked at so many solver results that they have a good idea of what the solver will produce for many situations (and that, for instance, is where some of these bet sizes come from). However, this doesn't mean that their understanding of why game theory / solver produces the results it does is accurate because much of this stuff can be counterintuitive.

As an example, I read in a different book that on those hands where the solver gives a mixed result, such as sometimes betting as a bluff and sometimes checking, the EV is the same no matter which way you play it. And this is wrong. The EV is only the same if the defender's response to your bet is based on GTO. But, for instance, when you bet these hands as a bluff, your EV will be dramatically different (on these specific hands) against an opponent who calls every time as opposed to one who never calls.

Also, one of the nice things that these solvers do, from an author's perspective. is that it allows the author to give the right answer. This is true whether the author really understands as to why the solver gives the answer that it does or whether they come up with a confused reason as to why the solver gives the answer that it does. But in either case, the solver is still giving the correct answer and the author is passing this on.

Mason

sounds good

one thing to note, and again, i'm long since retired so others will know far better than I

is that solver's are not cure all solutions

a solver will be giving a response based on assumptions of our opponents


take a typical live opponent at low stakes - this person limp/raises KK+, folds worst non suited hands, limps all medium strength hands and suited/running hands, and will open raise for his better broadways and aces

a solver output is never going to assume that kind of range - this is where you hear the term "node locking" where you put in your opponents special deviations

so if jonathan little accounts for this in his solver work then it should be ok - if he doesn't and just runs the solver generically, assuming everyone is following a typical opening range chart - people aren't limping, etc etc then it's all going to be worthless

this is a major reason why people advocate against using solvers for live low stakes because it's going to be very difficult to properly node lock for your opponents tendencies because they vary so dramatically and you're arguably better off getting max exploit value each hand

if you know your opponent is going to call your raise regardless of sizing because he doesn't like to fold his big blind, then you are absolutely better off to raise much larger with your premiums against this guy to try to narrow down that SPR as much as possible to just get it in on the flop when you have a hand like AA - he's not going to adapt, this is what he's done for years, if he does adapt, it's unlikely to make any difference because the amount of hands you'll see together are so finite that you're unlikely to get another AA vs him in the bb again to which he now understands to overfold to your extra large opening raise because your bet sizing is linearly correlated to your hand strength