can someone help me with the math behind pp's preflop?

[Jeffmet3]

Hey,

I definitely should know this better, but I'm still unsure with the math behind it.

So, assume nl$1000.

What's the largest percentage of my stack I should put in preflop a low pp, assuming that I will only win the hand if I flop a set?

For instance, if I raise to $35, and it gets repopped to $110, what's the math behind calling? How does this get impacted by another person putting in their $35 too, or $110?

Assume, that if I flop a set, I'll stack the other person like 80% of the time.

Sorry if this post is kind of convoluted and not asking a specific question, but I just want to try and understand the math behind it.

thanks

[Adrian20XX]

Two pages forward you have this thread: NLHE Implied odds for playing pocket pairs for set value

I've included a link to some math I've done before.

Regards ...

[Gonso]

You're going to make a set about 1 in 8.5 times (or 7.5 to 1). If you estimate that your hand will need to flop a set to win, you will need to 'average' a return of 7.5 to 1 just to break even long term, and obviously you want more than that since you're not playing to break even.

Say you have 44, raise, and get 3-bet. If you're considering calling for set value alone, check the effective stack sizes. If your bet was $7, and he made it $20 and has $50 left, you can't win enough to play your hand exclusively for set value. The pot and his stack combined is only $77, and you have to put in $13 more to call. 77 to 13 is about 6 to 1, not nearly the 7.5 to 1 you need just ot break even.

Worse, this is under the assumption that if you make your set he'll go broke. In practice this is very unrealistic, so you will need much more than a 7.5 to 1 return to make up for all the times you hit your set and they just fold.

In general, I like at least the possibility of winning about 15-to-1 on whatever I'd have to put in (very roughly). Against deep stacks this usually is possible, and I don't need that much against someone who I think will go broke with an overpair easily.

This also assumes that you don't think it's realistic that you can't win the pot with an unimproved small pair. Obviously if you can take the pot away from a player without a hand, it's easier to play 44.

[Jeffmet3]

[ QUOTE ]
Two pages forward you have this thread: NLHE Implied odds for playing pocket pairs for set value

I've included a link to some math I've done before.

Regards ...

[/ QUOTE ]

thanks, but i don't see the link?

but so assuming you stack them everytime, for $1000 stacks, $133 would be the maximum you'd put in with a pp preflop. This also assumes no dead money in the pot. So, I guess putting in $100 preflop can be correct depending on the dead money and the likelihood of stacking the opponent or at least winning a signifigant pot.

1000/7/5 = 133

[Adrian20XX]

The link is within the post that is two pages ahead thay I pointed out, within my reply to that post.

And I agree with the 15 times the bet that was suggested altough if feel more confortable with 20 times (the difference is not so big, as with 100BBs stacks you can call 6BBs in one case and 5BBs in the other case), as at 9.50 bets you only have EV=0 against a bigger pair, assuming both players get the money all in when the small pair flops a set, and as players will sometimes not be willing to put all their stacks, 9.5 can not get break even in the real world.

Regards ...

[Jeffmet3]

thanks, i checked, it out, really good.

but then to check to make sure i understand the formula correct:

6 players, 1000 stacks.

hero raises to $35, villain repops to $105. including $15 in blinds, the pot is $155.

$155 + $965 left in your stack is $1120.

Assuming the divisor of 9.5, $1120/9.5 is $118. That means that in this scenario, you would be willing to call $118 total, or $118 in addition to the $35 you've already committed?

[pzhon]

As you pointed out, your calculation ignored the losses/ties due to flushes, straights, and having your hand counterfeited. In total, you only win about 81% of time when the flop contains a card of your rank, with about 8% losses coming from a flopped overset, about 8% coming from your opponent's two outs to a higher set, and about 4% coming from flushes, straights, and getting counterfeited. The 4% makes a significant difference.

Calculations which include these have been done in a few places, and the conclusion is that you need the effective stack size to be about 12 times the size of the call if your opponent blindly pushes the flop.

In reality, in some situations you may be able to extract some value from the times you miss, e.g., when you flop an OESD, or when you can see the turn for free and might hit your set. Position is very important for this. You also can't expect to stack someone with QQ on an AKx board, or AK on a 654 board. Against some opponents, particularly LAGs who will often bluff you out on the flop but who will rarely stack off, no stack depth will allow you to call for set value alone.

[Albert Moulton]

Use the 5/10 rule. If you have to call less than 5% of the effective stacks (the lower stack between you and the raiser), then call.

If you have to call more than 10% of the effective stacks, then fold.

If you have to call between 5% and 10% of the effective stacks, then use your judgement based on your position, your image, and your understanding of the likelihood that the raiser will stack off to you if you flop your set. Sometimes you should fold. Sometimes you should call.

[Kurn, son of Mogh]

[ QUOTE ]
Hey,

I definitely should know this better, but I'm still unsure with the math behind it.

So, assume nl$1000.

What's the largest percentage of my stack I should put in preflop a low pp, assuming that I will only win the hand if I flop a set?

For instance, if I raise to $35, and it gets repopped to $110, what's the math behind calling? How does this get impacted by another person putting in their $35 too, or $110?

Assume, that if I flop a set, I'll stack the other person like 80% of the time.

Sorry if this post is kind of convoluted and not asking a specific question, but I just want to try and understand the math behind it.

thanks

[/ QUOTE ]

If opponent's stack > 9.375 (7.5/0.8) x the raise, then you have correct implied odds to call.

[Adrian20XX]

[ QUOTE ]
thanks, i checked, it out, really good.

but then to check to make sure i understand the formula correct:

6 players, 1000 stacks.

hero raises to $35, villain repops to $105. including $15 in blinds, the pot is $155.

$155 + $965 left in your stack is $1120.

Assuming the divisor of 9.5, $1120/9.5 is $118. That means that in this scenario, you would be willing to call $118 total, or $118 in addition to the $35 you've already committed?

[/ QUOTE ]

The $35 that you've already put in the pot now does not belong to you any more. It does not matter if the $155 pot was made by limpers, or your raise. So, if you now put more than 118 on the pot voluntarily, you will definitively will have EV-.

But this as I explained, does not contemplate neither straigth draws, flushes, or as someone pointed overcards when he for example has KK, you have 77, and the flop comes A72 rainbow, so he gets away without being stacked.

That's why I think that with 15 or 20 times instead of 9.5 you can have a very interesting EV+.

I'd love to see pzhon's links to the full calculations made.

And I see a few problems that will still probably there.

The number of overcards will still be afected by your opponent's pocket pair's range (for example if his range is QQ+ or KK+), and as his hand range for pocket pairs gets more open, you will need bigger stacks to compensate the bigger probablity of overcards that will get him away cheap.

When you have a flush draw, even if you put him on AA, you will not be able to put him on AsA, it will be unpossible to put him pre-flop in AsA or AA without As.

The straights can have problems, when you have 77 and he flop comes 89T, if he has QQ he steals from you the Js for the straight and leaves you with 6 outs instead of 10, but against AA you have 10 outs on the flop.

Regards ...