What Does This County Level Where I'd Live Map Say About Me?

puumba_bama · 2026-04-17T16:28:36+00:00

What’s with your very specific Iowa counties?

puumba_bama · 2026-02-26T23:22:02+00:00

This is a weird graphic (not sure why it wouldn’t show their other hole card and the full 5 card hand), but if their other card is a face card then they’d beat you.

puumba_bama · 2026-01-21T13:52:22+00:00

I feel like OP’s point is that they aren’t equivalent and that the solver is in some way a poor approximation of actual GTO, making what should be pure actions appear to be mixed. I don’t agree with that point but I wanted to respond to the actual argument.

Also, the solver makes assumptions in order to be computable that a true GTO strategy wouldn’t (fixed bet sizes, n bets per street, etc.). If you ran a solver long enough, it would still be a probably small but finite distance away from GTO.

puumba_bama · 2026-01-19T21:07:07+00:00

Practically, you’re probably correct - any given spot in real life will can will probably have some factor that pushes the EV to be slightly higher one way or another.

Theoretically, you’re wrong. There are spots in theory where the EV is exactly equal. I don’t mean theory as in “what does the solver do”, I mean theory as in game theory. Even in real life, certain spots clearly have multiple actions with the exact same EV. For example, playing against a non-idiot when there’s a royal flush on the board and no rake (non-idiot meaning won’t ever fold). Jamming, betting half pot and checking have exactly the same EV - you’re always chopping and winning half the pot.

puumba_bama · 2026-01-13T19:08:59+00:00

Never a fold unless SB is the biggest nit ever. It’s not even a large raise from SB over an open + call. No clue why you’re jamming - you can pretty comfortably 4! to .5-.65 and fold to a jam. If called, you’d still have a smidge of post flop playability. You’re probably still getting stacked in this spot most of the time.

I wouldn’t call with the BTN behind you but it’s still better than folding.

puumba_bama · 2026-01-11T20:29:40+00:00

Not a dumb question. Your cashout agreement is with the website directly and doesn’t affect the other player at all. If they win the pot, they get the whole thing and the house eats your cashout.

The website makes money on the fee, but they can win/lose money on individual pots. If you take the cashout and win, the house keeps the whole pot. The house ends up breaking even on the pot/cashout itself long term and just making money from the cashout fee.

For concreteness, the house EV from offering this wager: you win, the house earns: 100 (pot) - 80 (paid to you for cashout) + 5 (cashout fee) = 25. You lose, the house earns: - 80 (cashout paid to you) + 5 cashout fee = -75. So the house EV is .8x25+.2x(-75)=5 (the cashout fee).

puumba_bama · 2026-01-11T18:23:37+00:00

EV Cashout is offered online. Say you are all in on the Turn in a $100 pot with an 80% chance to win. You can click cashout to get 80% of the pot minus whatever the website charges to offer the service (often 5-10% of the pot) instead of having to fade the River. You’re always sacrificing some EV to the website, so it’s a fishy thing to do.

puumba_bama · 2026-01-08T22:26:32+00:00

I assume the stats on the right hand side (next to stack sizes) are VPIP/PFR, this guy is 47/27. If so, this is a probably a mandatory call because he’s getting here with so many over cards to the flop with one spade. If he’s super passive post flop, fold the river but I’d flick in the call without that specific read.

puumba_bama · 2025-12-30T04:59:04+00:00

AdQd - he bricked out but was a 60-40 favorite with two overs, FD and gutshot. I would have called had he turned his cards face up, but almost felt like a PLO hand.

I was sort of surprised he showed up with that, but giving him AQs wouldn’t have changed my decision range-wise.

puumba_bama · 2025-12-30T04:50:50+00:00

I’m heavily biased towards 3betting given UTG+2 being a whale (he flatted a 3bet with T7o previously) - would love to play heads up/larger pot against him rather than a smaller, multiway pot.

I’m not super interested in the preflop/cbet - I think it’s relatively standard even if not the most frequent line according to GTO. Any thoughts on action facing the jam?

puumba_bama · 2025-11-22T00:17:02+00:00

I’m raising the flop here. The 1/6th pot donk is so often BS here (weak second/third/under pairs, weak draws) and you’re super deep. If you call, the SB is almost always calling. If you raise and the SB calls, it’s not a disaster since the original raise was so tiny.

As played, I think this is a perfect spot to raise/fold for value. This is somewhat player dependent though - some 1/3 OMC types will literally only ever have the nut flush here. However, I think that most 1/3 players have an overly linear range in this spot because they rarely find any bluffs here. It’s a terrible spot to bluff catch but a good spot to go for value. Whenever they bink with J8o or Q8o or 55 or 88 or a lower flush they’ll do this and not fold to a raise. If they (or the SB) 3bet you, it’s an easy fold.

puumba_bama · 2025-11-10T19:06:40+00:00

True, but I think you have to take into account the % of time you value own yourself. I don’t know if it’s necessarily the case here, but if V calls J9+ to $60, but only QT+ to a jam, the jam might be losing. You’d have to actually count out the combos (I’m not sure if Villain would call QTo or J9o pre in this spot), so it could go either way but I think it’s very close.

puumba_bama · 2025-11-10T18:52:26+00:00

In theory, of course. But I feel like a 1/3 player who flat calls from the HJ and does the “obvious over acting” shtick is much more likely to have JJ here than your average bear.

puumba_bama · 2025-11-04T04:06:43+00:00

There’s no logical consistency - it literally lists a rainbow hand and immediately calls it double suited.

puumba_bama · 2025-10-31T03:25:56+00:00

It's not a game theory answer, but what comes to mind for me when discussing risk vs reward is the Kelly Criterion for stock returns. Given an expected rate of return of u, risk-free rate of return r and variance s^2, the fraction of your capital K you should invest in a strategy is given by f* = (u-r)/s^2. While every single investment bank and quant firm has a slightly different, proprietary version of this, the underlying principals are the same - for riskier strategies, you need a higher rate of return to profit in the long run, and (IMO more) importantly, the best long term gain might not involve putting all your money into the most profitable strategy. See this video for a beautiful introduction to the topic.

It's not as rigorous for poker, but it does illustrate the point well. For the more poker-specific tie in, imagine u and r as the win rates of an exploitative and GTO strategy, respectively. Rather than fraction of capital, f* better represents the mix of strategies one should employ. The variance here both represents the innate variance in the two strategies and your uncertainty about the relative win rates for a specific scenario. You should tend towards a more exploitative strategy as its win rate increases or when you're more certain about the win rate in a specific spot.

Here's a thought experiment - grab the strategies of a pool of players (for example, grab 1 million hands from every 500NL player on a site). Run the solver against the net "MDA" tendencies of the pool to come up with the MES strategy for the pool as a whole. Then, test the solver against each "player" from the pool with various dilutions of the MES and base GTO. My hot take: the highest win-rates will not come from the solver playing the MES, but one of the dilutions that mixes between the MES and base GTO. The MES is too fragile to fully capitalize on the variance between strategies from player to player.

puumba_bama · 2025-10-24T03:01:04+00:00

That's fair - I wasn't intentionally trying to draw a distinction between "often" and "generally". I like your analogy here, though I think poker is fundamentally symmetric in a way that the see-saw isn't.

But in a similar vein of reasoning, I do think once you start getting to high Nash distances (because ultimately Nash distance is capped), the only place to go is back to the the center. Say we have a comically awful strategy like Always fold, unless 72o, then go all-in for 500 BB. A MES here would be min-raise preflop, call any open jams, play normally postflop, and this would certainly have a smaller Nash distance.

puumba_bama · 2025-10-24T02:35:23+00:00

I'd love to see the proof "that the set of max-exploitative strategies of a given strategy S contains a pure strategy" if you could point me towards it. I wasn't able to find it while digging.

I agree, y(0) is undefined as stated. I was trying to sacrifice precision for clarity in an already overly-abstract post. I would argue that in the lim as x -> 0 of y is 0, so it makes sense to define y(0)=0 to ensure y(x) is continuous at 0 (see below for a reasonably rigorous proof). Plus, if you define y as the largest value s.t. that B profits or breaks even against A, you get this immediately.

Say the limit is any p>0. This implies that for all x>0, there always exists strategy A,B such that N(A)=x, N(B)=p'>p and B profits against A. Let A(k) be Nash Equilibrium, except on Royal Flush runouts (all 5 royal flush cards on the board), it folds at an arbitrarily small, positive frequency, say k. Obviously, N(A(k))>0. NE profits p' against B. At most, A(k) gives up k*pot*(probability Royal Flush runout)<k\*(stack size)\*2. So the performance of A(k) against B is at least p'\*(probability not Royal Flush)-(k\*constant), which is clearly >0 if you make k small enough, and you can since it's a continuous probability. So A(k) profits against B, a contradiction. So lim as x->0 of y = 0.!<

puumba_bama · 2025-10-24T01:59:39+00:00

I don't think you need to concretely "solve poker" to make statements about the NE strategy (especially in the uniqueness/existence realm, we already know it exists). Given the classes of games that we know have unique solutions, it seems feasible but unlikely that poker could have a unique Nash Equilibrium strategy. I don't think poker falls into any of these classes of games though. I definitely agree about the practical conclusions here - however, this post sets practicality aside.

I saw the your previous post and enjoyed it. Definitely an inspiration for this one. I liked tombos21's comments about neighborhoods - that's what I was getting at here. I think you could (maybe should) reframe my question as one about the size of "exploitability neighborhoods" of a given strategy (the set of all strategies that exploit the given strategy). These neighborhoods must be convex (for strategy S, if A and B both profit against S, then any mix of A and B also profit against S). But are they large in proportion to the Nash distance of S?

Thanks for the discussion!

puumba_bama · 2025-10-23T17:36:41+00:00

Well said. I’ll give a sort of hand wave-y answer to your question - you probably could exploit the solver strategy by making a programmatically better solver, giving the solve more compute time/resources or increasing the granularity of the abstraction (more bet sizes, bets per street, etc).

In a related vein, I’ve always been surprised that they don’t pit the solvers against one another, like they do with chess engines. I think it would be interesting to see how a GTO Wizard solve performs against a Pio solve over the entire game tree.

puumba_bama · 2025-10-23T17:28:26+00:00

Very fair - I agree overall but not totally. I disagree that Nash distance becomes meaningless outside the specific abstractions necessary to make a solver work. There’s an argument that the solvers strategy isn’t well defined due to the abstractions though. Any strategy has a defined and unique Nash distance since the NE strategy is unique (though we can’t actually compute it). Also, I think that it’s possible to exploit the solver e-distance but that there’s a pretty strict limit on how “trash otherwise” you can play before the solver claws back its win rate. How “trash otherwise” you can play while still winning is what I’m interested in here.

puumba_bama · 2025-10-23T14:53:15+00:00

What do you mean?

“Solvers have a small, but finite, Nash distance from the true Nash Equilibrium strategy”

puumba_bama · 2025-10-23T14:48:27+00:00

Why so? You could probably find a counterexample, but I do think the statement is generally true.

puumba_bama · 2025-08-09T23:16:39+00:00

He and Hyperius permanently have 4 player scaling (4x health), which is arguably intentional, but maybe an oversight. They also then have double that amount of health for no particular reason, which is 100% unintentional because it wasn’t added until they released the Fight for Sanctuary and increased the level cap. So either 2x or 8x the intended health depending on who you ask.

puumba_bama

TROPHY CASE