# Preflop math

• Bronze
Joined: 18.04.2009
Hello,

what is actual math for choosing some card for open raise depending on number of players in front of us?

It is strenght of our hand vs random 2 * number of player s= our equity

while it should be higher or equal to what we invest in pot / whole pot?

Or im missing something?

I mean raw math, besides of playability, type of players, rake, etc?
• 12 replies
• Bronze
Joined: 13.01.2012
I'm not very sure about UTG/MP but button is pretty easy.

Should be equity vs Random of about 1 player. Small blind will fold in low 80% here, since he can only 3bet or fold without trying to exploit BB. So mostly you can throw him out and since you have position your not in a terrible spot getting 6:1 to see the flop.

Since you have position you can increase your range by another 5% or so and thus the button open range of about 55%.

CO would seem to be range vs two random, I'll assume button is in usual 3bet or fold, that seems to be the recommended play. Cold calling can't be correct more than 2% so really can't figure it in to help SB over call and join the party.

However according to Equilab if
we raise 15% vs two randoms our equity is 48%,
raise 25% vs two 44%
raise 35% vs two 42%
raise 45% vs two 40%

From an odds point of view you need to steal 4 times in 7 tries to break even on the steal attempt. However, you have position on BB post flop so that helps in determining the value of the steal.

Finally there is a factor of the blinds going fast in 6max. If you push CO down to 20% then MP should be like 10% and UTG your opening a tiny range, and the blinds in limit will eat you up. You have to play hands to win pots to stay ahead of the blinds. I think that pushes up CO stealing to higher than expected amount.

Finally all of this math is ALL IN EQUITY, and we don't play that game in limit so the opening ranges get changed to not just be best hand but playable. Most limit players value hands at different values than No Limit players.

I think I have button figured out the others I think are just guesses. To be honest I play exploitively and look to my left and blinds when I decide to open.
• Bronze
Joined: 13.01.2012
Also for any open from any position the BB/SB working as a team have to call/raise you at least 3 times in 7, or you can raise ATC and show a profit. This would be an exploitative strategy for the stealer, but the blinds must make a GTO play to stop this and call with some range that is at least 42%.

I guess if SB fold 83% of the time and we player 100 hands then the sb would raise 17 of them and the bb would have to call at least 25 of the remaining 83 hands for a range of 30%

Since most likely only playing one of the two in any hand, lets say you fold to a BB CAP preflop, then you need 47% equity vs the BB to breakeven.

This puts the button and may CO base range at 37% or so. That might be a reasonable guess at getting the math of the CO in a one street view.

Maybe I'm way off just trying to guess.
• Bronze
Joined: 16.06.2011
Originally posted by dmyers1166

Should be equity vs Random of about 1 player.
I'm not sure if this is a good approach, cause they wont play against you with a random range.
• Bronze
Joined: 28.04.2010
Originally posted by kavboj84
Originally posted by dmyers1166

Should be equity vs Random of about 1 player.
I'm not sure if this is a good approach, cause they wont play against you with a random range.
assume they are random you dont know them and you have no indication of what kind of range he has or will be using against you. Therefor your only option is to play vs him is to assume he has a random range.
• Bronze
Joined: 16.06.2011
Wrong question asked IMHO. You can ask that if you want to guess what holecards are dealt to them , but not if you want to know the EV of the hand you open . And for me what matters is the latter, because if they fold, it doesnt matter if you open AA or 32o, because the EV of fold is 0, hence there is no point in examining your equity vs that part of their ranges. Except if someone calls you down with a 100% range until the river , then maybe you can count with all-in equity vs a random range, because it gives you a rough approximation to a somewhat reasonable extent, but if you wanna be fully precise, this approach can be used only for pre-flop all-in situations. For everything else it is highly misleading IMO.
• Bronze
Joined: 15.06.2009
I agree 100% with kavboj. The "rundown equity" versus random hands are taken too much into consideration. Not only here, but also often in discussions about when to limp in from the small blind, and when to open-raise from the small blind. (Not folding a K getting 5:1... ever heard it?)

Of course, if you don't know anything about the opponents, then the holecards is what you have to go on, but consider too how well you yourself play in marginal situations. If you crush - play many hands, if you just recently got to a new level - don't try to squeeze out +EV from 87o in the cutoff because it will not work.

@Rantrave: I don't think there is a universally accepted model for opening with X opponents yet to speak. Like kav says, maybe there would be if you all had 1BB left so you can go all in.
• Bronze
Joined: 23.06.2008
Congrats on the shiny avatar! Well deserved to!
• Bronze
Joined: 28.04.2010
Congrats on the shiny avatar! Well deserved to!
? hai ?
• Bronze
Joined: 18.04.2009
From Polish trainer in section of FL i got such asnwer.

Equity in pot is 100% to win the hand. Therefore you divide it to all players in pot.

So when we are on MP spot and we start preflop and we have decision of raise or not we got 1/6 ~ 16,6%.

So therefore our hand need to have 16,6 % of winning change vs 5x random 2 cards.

Beacuse we assume that dealer is fair and he deals random cards to oponents and us.

I hope im not missing anyhitng
• Bronze
Joined: 16.06.2011
That couldnt be more wrong. If you need only 16% EQ means that all players call you, so you invest 2 small bets and you gain 5x2=10 so if you lose 5 times 2 that makes -10 but for the 6th time you gain 10 and that breaks even.

The problem is:

1. There wont be 5 callers 99,999% of the time
2. They wont call you with 100% ranges
3. The hand doesnt end preflop
4. Even if it was they could still reraise you

IDK who told you this nonsense but he doesnt seem to understand how this game works.
• Bronze
Joined: 18.04.2009
Then how to calculate what equity my needs vs players in front of me?

What is pure math for that?
• Silver
Joined: 04.01.2008