I've read "Professional No-Limit Hold’em: Vol I", Flynn, Mehta, Miller.

I've watched Splitsuit's SPR video & Pokerbank's discussion.

I've read another 2+2 thread "Explain SPR like I'm 5".

But I'm no further ahead understanding this concept than when I heard of it ~10 years ago.

I know Mason & David occasionally read "Beginners Questions" - maybe they'll reply to this question (it's an important & high-profile issue).

Thanks.

easiest solution for yourself would be to not focus on spr. there's other things which would help your game more.

SPR is just a number that’s supposed to help with rules of thumb like the rule of 4 and 2. I don’t think it’s even that commonly used anymore these days.

But if you have two fixed hands/ranges and stack sizes and know exact implied odds (or the bet is all-in) the SPR can tell you exactly what to do. For example, if your hand has 33.3% equity against villains range and his bet is all-in, the SPR before the betting round shows if you have a profitable call or not. SPR <1 means you should call, SPR > 1 means you should fold.

SPR, defined as (effective) stack to pot ratio, is a risk to reward ratio. It is usually used to make an all-in bet on the flop or commit to betting. The math for an all-in bet shows the following for +EV:

Given eq , SPR < eq/(1-2*eq)

Given SPR, eq > SPR/(1+2*SPR)

We will focus on the second equation. It says that the needed equity increases with SPR. (It also can be shown that this equation can be reduced to the equation showing equity needed decreases with pot odds.) That means you need strong hands for high SPR values. That is why, with low SPR, if is usually recommended you can commit with top pair or an over-pair or perhaps a low two pair. For high SPR, where the risk is relatively high with respect to the reward, you need strong hands such as high sets, flushes and straights.

I have not seen any math analysis supporting the SPR boundaries often quoted for low, medium and high SPR ranges s but I would think the first equation above might provide some clues. Or, as madlex suggested, perhaps implied odds might be worth looking at from a math perspective.

that equation is basically it. and, in laymans terms, its simply an analysis of "are the odds of him flopping something better than me higher than the amt im risking"
ie if we see a flop with tptk and 5 spr, he has worse than a 1;5 chance of outflopping tptk, so spr is good stackoff. if its 20spr, well, thats higher than his odds of having flopped 2p+ thus not a good stackoff. c?

SPR stack-off thresholds are not supported by game theory and the mathematics "supporting" them are unsound.

+1

SPR has been debunked

I'm not for or against SPR. However, it does have some logic behind it- the greater the risk the better hand you need.

Can you provide a reference or two showing mathematics debunking SPR.

In tourneys, I found thinking about SPR useful as a tool to help me think about what happens on the next street if I make or get a call.

I don't think it's been "debunked" as such, but solvers have shown that the SPR "rules", or guidelines, we learned several years ago are often not correct.
e.g. We were all taught stuff like "If you flop top pair with an SPR of <3, then you should be happy to play for stacks", or "Don't flat 4-bets if the SPR will be less than two, just shove pre." (GTO solutions often feature "strange" spots with really low SPRs after flatting 3-bets, 4-bets or even 5-bets.)
What actually happens at equilibrium is that some hands are +EV stack offs, given the size of the pot and remaining stacks, and others are not. Stack-off ranges depend more upon the board texture and range vs range than just the SPR number. For example, sometimes you have top pair (or even an overpair) in a 3-bet pot with an SPR of 3, but it's far enough away from the top of your range that you end up folding it. In the old days the saying was "Always go broke in this spot, because the SPR is so low". That was wrong.
Real-life example: I hardly play any more, but a couple of days ago, I flatted a cold 4-bet with KK, then folded on the flop to a pot-sized shove, because it was close to the bottom of my range on the Axx board. A few years ago, I would have 5-bet jammed pre; a year ago, I might sigh-call the jam. Today, I call pre, then fold flop.

You can’t “debunk” SPR, for the same reason you can’t debunk “percent”. Both are the result of using basic math. Nothing more, nothing less.

You might debunk guidelines or recommendations pertaining to specific SPR numbers. But the number is still there.

SPR is a strategy concept. Other than the math involved to determine SPR it all stops there. One individual's strategy may be to stack off no matter what with TPGK with an SPR of 6 or less. Another may use a lower number. It's a fancier way to say pot committed or to determine what equals pot committed. That's it. It's not to be proofed with pot odds or anything like that.

It's simply a way to make decisions easier. It gives a player a tangible automated risk threshold. It's not really a complicated concept. I think people put way more thought in to it than necessary.

Exactly. It's just a ratio that you can use as a general guideline. If you have a pot-sized bet behind on the river then the SPR is 1 by definition. That ratio is an objective fact of reality in the context of the hand; it can't be "debunked". How you use the ratio is somewhat open to interpretation depending on ranges, action, etc, but that doesn't change that the SPR ratio is what it is.