WHY shoving beats limping w/ less than 10 bb

[jasonv12]

In response to Rebecka (rghy2) and a few others on why they may or may not limp with intentions to call off, please read this carefully and post your thoughts.

I wasn't initially going to reply to this, but I feel like I should. I apologize in advance if this gets long winded, but I'm only trying to help.

That said:

In every individual hand of poker, what goal do we always have? This is a goal that follows every format, every stack size, etc. We have the goal of making profitable decisions. A decision is profitable because it has a positive Expected Value also known as EV.

So here we see this idea of EV and we are like "So what? Why does this matter?"

The obvious answer is we can see the expected value of limping versus the expected value of shoving.

However there is even more we can learn from this. I'll explain all that in a minute, but back to EV.

EV at its most basic form is simply Expected Value = [Value of Outcome] X [Odds of Outcome]
(or things that equal value of outcome X things that equal odds of outcome)

So to apply this...

So let's try to apply this to this example of limping vs. shoving 10 bbs.

So the first case is shoving.
For one random example let's look at shoving KQo from the button. We have 2 hands to get through. If they are defending let's say 20% of hands, which includes A4s+, A9o+ Q10o+, 66+, and 109s+, we have 48.1% equity when called.
Knowing this, we can also infer that with blinds and antes, there are 2.5 bbs dead when the steal is successful, and an average double up is for 11.75 bbs (average between the small and big blind already out depending on who calls).

So now... the formula for EV. We have 2 situations, we will be called and be forced to realize our equity in the pot. If each player is calling 20% of the time, we will be called by *someone* 36% of the time (includes times both players call -- aforementioned equity includes this as well).

So: [11.75 bbs when flip is won]x[0.36 X .481] and [-10 bbs when flip is lost]x[0.36 X .519] if for when we are called.
The second half of our equation is for when we steal the pot, which will happen the remaining 64% of the time. In those cases, [2.5]X[.64]
If we multiply each scenario out and add them together, this will equal our total expected value in the long run in this situation.
The first half when we win 11.75X.36X.481=+2.0 bbs
The first half when we lose -10X.36X.519= -1.9 bbs
The second half when the steal is successful 2.5X.64=+1.6 bbs
2-1.9+1.6=+1.7
The play yields on average +1.7 bbs.
You might say now, well what if they are calling with 25% of hands? Or 30%? Or even 40%? (which would include hands like J8o and 79s by 40%)
I won't redo all the math, but I promise this would yield roughly similar EVs. Why?
Because KQ's equity also gets better as the calling range opens up.

It has 50.5% equity against 25% of hands, 51.1% equity against 30% of hands, and 53.7% equity against 40% of hands.

So what if they are only calling 10% of hands or something. We still have a similar EV.
Against 10% of hands, KQo still has 39.1% equity, but will be called only 19% of the time from the button.

[11.75 bbs when flip is won]x[0.19 X .391] = 0.87 bbs
[-10 bbs when flip is lost]x[0.19 X .609] = -1.16 bbs
[2.5]x[0.81] = 2.03 bbs
0.87-1.16+2.03= +1.74 bbs

We can also do this with other hands that we might shove, but KQo provides a good, clear balance of a typical hand that someone who commented earlier might have limped. This is an exercise that can be helpful when looking at hands you actually played and if you are a mathematical/deep thinker like I strive to be, can be really helpful in reviews because it can help in realtime decision making in the future.

Now we can look at calling.
This can be broken into: [pot+bet] X [call and win] - [pot + bet] X [call and lose]

So first of all a major concept to understand. We hit a pair or immediate draw on the flop about 1/3 of the time when holding two unpaired cards. Since we can't continue with KQ if we don't hit a pair or draw on the flop, that has to be factored into our call and win and call and lose sections. So if we hit a pair, we still don't just win the pot, but we have equity against his range. Since his range contains every hand since we were unable to narrow his range by not raising, our equity against 100% of hands when we hit a pair on a random board we hit a pair on is 82% (ran an equity simulation on Slice Poker Equity Calculator to figure that out). So if we take (.33X.82), we get .27.

So we went from having a 48.1% winning when all in to 27% winning just by seeing a flop. We gave up almost half our equity based on the fact we can't continue in cases where we are already good or might draw out.
This is why calling is so passive. Even if KQo is ahead or has overs to the board, we will never realize the equity we have when our opponent bets because we cannot continue.
Furthermore, we missed the 1.6 BBs we'd get from a successful steal. And allowed AT LEAST the BB to realize equity that it may have folded preflop.

So putting this all into the formula further shows this.
The pot is the 2.5 bbs + the 1 bb to call AND the 20% of hands that called the all in in the first part will put you all in preflop here.
So... Assuming you call off if someone puts you all in behind you.
[5.5 bbs] X [.27 X {11.75X.2X.481}] - [5.5 bbs] X [.73 X {-10X.2X.519}] = -3.2 bbs
5.5 comes from 2.5 bbs for blinds and antes + 1 bb to call + 20% chance of shove X your 10 bbs.

To make this even worse, this doesn't even include the small blind completing and playing 3 ways, which would happen fairly frequently. And doesn't include the increased chance of the small blind squeeze for a normal raise size for when there is a limper, which would put us in a really awkward spot.

I told someone that shoving was unexploitable and she argued that it was very exploitable and did a good job at explaining why she thought it was. Here's the thing, we can deduce this from all the math and ideas above, but one thing only accomplished with a shove is that we always realize all of our equity, meaning we will never be forced off our hand in any case where we will win with it. So if it is a shove with positive EV, it is always a good play, regardless of if it is the best play. That's why shoving is unexploitable.

So long story short, shoving would give you on average 4.9 bbs more than limping does when on the button with KQo and 10 bbs. This trend would be true in almost all these situations.

[lorenz0wns]

yep, good post brah. generally i'd be pushing all day if my M is less than 10. for those who don't know what m is,

https://en.wikipedia.org/wiki/M-ratio

[DocHo11idaze]

Yup always shove >10bb's

[HopsBar28]

This is a good, clear explanation, but I suspect that 90+% of players are "feeling" players - they don't use the math, even if they are capable of understanding it. I mean, we all play that way SOMEtimes, but most players play that way all the time, imo.

[Drock1116]

There comes a point in your chip stack when it makes sense to shove. But you should wait until you get there.......

[tracyrickrobby]

very good reading!! jasonv12 will be a pro one day! mark my words!! we will be cheering him on as we watch him at the Final table of the WSOP!!

[chrisdione]

The only person that may disagree with this would be Phil Helmuth. He has what works for him but most of the time the shoving method is best. Can't argue with his success though.

[lorenz0wns]

The only person that may disagree with this would be Phil Helmuth. He has what works for him but most of the time the shoving method is best. Can't argue with his success though.

his play sometimes works for him for sure but tbh he plays a decent amt of tourneys. imo his short stack play is atrocious and suboptimal.

[jasonv12]

his play sometimes works for him for sure but tbh he plays a decent amt of tourneys. imo his short stack play is atrocious and suboptimal.

[mjpokey]

poor phil...sucks to be a poker brat doesnt it lol