need threshold guidance for shoving w draws

[Guruman]

lets say I have a non-favorite draw headsup (something with 8-10 outs) on the flop and I have to decide if i want to commit all of my chips.

if effective chip stacks are:

-less than the size of the pot: I have almost zero fold equity so this is probably a bad play.

-1000x pot size: now I'm risking too much to buy the fold.

I poked around and could not find any good theory on this stuff. Is there a good rule of thumb for the upper and lower thresholds we should be seeing before making open shoves or crai with draws?

thx!

[geoncic]

Good question. I am a beginner, so please to not take my advice. In fact, enlighten me if I am off my rocker.

1) If no fold equity and the pot is larger than your stack, is it because you're SS and the blinds are eating your or you called a PF raise? It all depends on the texture of the board to me and what I can put my opponent on. if a low his board and I put him on two over cards or large pocket pair and I'm getting 8-10 outs, I'm probably pushing. Two overcards might give you fold equity. pocket pair would call you down, but you're still alive with your outs.

2) 1000x the pot size, find a better spot to put your money in. That's just gambling.

I just realized that I think you implied they pushed you in for all of your chips.

1) depends on board. low and coordinated, they probably have large pockets, call if you are committed. otherwise fold if your outs may help them

2) fold.

[geoncic]

There's more that matters. Position, PF action.. we need more information.

[monkover]

well you gave the answers yourself?!

[kazana]

As with all shove or fold situations, technically, this only depends on two factors:
Pot equity and fold equity.

Figure those out (key: guesstimation), compare it to the odds you'd be laying, and you should get the idea whether shoving is an option or not.

The problem is that while your pot equity is fairly easy to estimate (it's around 30-40% depending on how many outs you have and redraws for villain), it comes down to guessing what villain will lay down, and how well his range connected to the flop and therefore how likely it is he has a hand that he will not lay down.

But, for the short stacked version this is easy:
Even assuming that you're always behind, with 8-10 outs you're somewhere in the neighbourhood of a 2.2-1 to 1.6-1 underdog (this depends on how many outs you have and which redraws villain has, etc).
So even with 0 fold equity it'd be correct to shove if you have less than the pot to bet. Every % point you have in fold equity is pure profit from there onward.

1000x the pot, well, I wouldn't waste much time thinking of that, because I highly doubt I'll ever play that deep. But it seems pretty obvious that pushing is not quite optimal.

[Guruman]

obv pushing is bad at effective stacks of 1000x pot size.


the question is if we start shrinking effective stacks at what point do we start crossing thresholds where pushing with draws becomes the correct strategy.

Which of these ranges of effective stack sizes tend to be good candidates for open shoving or CRAI with 8-10 out draws?

100x pot
50x pot
25x pot
10x pot
5x pot
3x pot
2x pot


Really I'm just looking for a general stack/pot range where this kind of move is acceptable with a reasonable read.

[relativity_x]

easy.

Think of what hands your opponent calls a shove with. Then consider your equity against his calling range.

If hero's shove equity > villain's calling range equity, shove all day.

Generally, I'd include FE into hero's shove equity, but FE is very small at uNL against unknowns. Therefore, I find it's safer to assume 0 FE to ensure you're making the most winning plays.

[CmnDwnWrkn]

Also very important to consider is whether or not you will have the nuts if your opponent calls and you DO make your hand. I think people overlook this sometimes. No sense pushing if you make your hand but your opponent has you beat anyway.

Also consider your opponent's possible draws. Sure, you might make your draw, but if your opponent draws to an even better hand, you're cooked.

[kazana]

Depends on fold equity.

If he folds (FE), you always win the pot.
If he calls (1-FE), you expect to win the pot + your shoving amount roughly 35% of the time, the other 65% of the time you lose your shove amount.

An example:
Lets assume the pot on the flop is 9 BB and you both have got 90BB left. Your shove would be 10 * pot.

So you expect to get:
EV = (1-FE)[.35 * (11 * pot) - .65 * (10 * pot)] + FE * pot
EV = (1-FE)(-2.65 * pot) + FE * pot

If you're looking for the break even point this is it:
0 = -2.65 * pot + 3.65 * FE * pot
2.65 * pot = 3.65 * FE *pot
2.65/3.65 = FE
~0.73 = FE

So you'd need at least 73% fold equity to make shoving a winning play.


If you run the same numbers for 5x pot:
EV = (1-FE)(-1.15 * pot) + FE * pot

Break even:
1.15/2.15 = FE
~53% = FE


You get the picture? Plug in some other numbers, create a spreadsheet or something like that, and you can find out how much FE you'll roughly need to make shoves with draws for whichever depth of stacks profitable.

[relativity_x]

A way to think of what the numbers mean in the EV calculation for non math guys.

If you win the pot, you net 90+9 = 99 BB. If you lose, you lose 90 BB.

so your EV is: EV=.35*99-.65*90=<font color="red">-23.85BB</font>

This means your FE has to account for 23.85BB to make this a breakeven play, which means you need a lot of FE.

Another example:
Effective stacks are 45 BB and the pot is 50 BB on the flop with Hero acting first.

Hero shoves 45 BB into a 50 BB pot, so hero risks 45 BB to win 95 BB 35% of the time and loses 45 BB the rest.

Hero's EV=.35*95-.65*45=+4 BB without even considering FE, so obviously pushing is +EV assuming your equity is at least 0.35 of the pot.

Conclusion:
The bigger the pot and the smaller the effective stacks, the less FE you need for a push to be +EV. On the contrary, the smaller the pot and the bigger the effective stacks, the more FE you need to make a push +EV.

Also note that just because a play is +EV, it does not mean that the play is optimal.