Explain to me, mathematically, like I am a child

I was not sure if this post should go here, on in Poker Theory. I decided on here, as it deals with limit hold'em, even if it is in a theoretical stand point.

You are on the button, with 67s, in a situation where it is playable. Why would you not play it for a raise, if you are going to play it at all? In otherwords, if you are going to put money into the pot at all, why wouldn't you want everyone to have to put more money in? If the hand is +EV for a single bet, why wouldn't it be for more?

Also are hands like AJo, A10o, K10o, small pairs, suited one gappers.

If these hands are worth a play, shouldn't they be worth a raise? Please, only mathematical explanations dealing with expectation. Thank you.

[henrikrh]

Hands like 67 suited are speculative hands, that will on rare occasions score big, hitting their straight or flush on the flop, or making you are playable draw, or two-pair. These things are all very hidden, compared to raising with AK, and flopping and ace, no one will give you action becuase you raise indicates you have the ace. You can get lots of action when 67s actually hits, however it does so rarely, thus a raise isn't worth it becuase most the time it will go to waste, the raises will come later when you make a good hand or draw vs. some sucker with top pair. The hand is playable due to a sort of implied odds. Plyaing 67s etc. is in my opinion more theoretically correct than it is mathematically.

Raising might be good with them when you want to create deception or want to show it down to create a loose table image.

Hope this helps/ is correct.

[MyTurn2Raise]

SHHHH....don't give away my secrets
seriously, I do this all the time.

But, it does depend on the blinds tightness/looseness.

[newhizzle]

hands like 67s depend on implied odds, the bet that it costs to get in is not where you make your money, you make money after the flop with these hands, so you want to get in cheaply, a raise every now and then is ok for deception purposes, but should not be done often or in games where deception dosent matter, limping is more +EV

Basically, raising preflop won't double the size of the average pot you win -- but it will double the cost of folding the flop when you miss.

[The Goober]

As newhizzle said, its about implied odds. I'll try to be mathematical about it. If P(w) is the probably that you will go on to win the pot, and W is the amount that you will make if you win, and C is what it costs you to call, then for the call to be +EV, we get:

P(w) * W >= (1-P(w)) * C

So, if C is doubled because you are calling a raise, then W must be doubled as well (assuming that P(w) stays the same). That means that the *total* amount you will win must be doubled, not just what's in the pot right now. A raise PF is not the same as simply doubling the stakes, because you don't know how much action you will get later on.

[Octopus]

(Disclaimer: this is not my idea; I just can not find it in the archives.)

In short, the size of the bet on later streets compared top the size of the bets on early streets is important and playing for a raise pre-flop is not unlike flattening out the betting structure.

Think about what hands you would want to play if the betting stucture was 1-1-1-1; that is, bets and raises were the same size on all streets. Think about what hands you want to play if the structure was 1-1-2-4 (that is, our normal structure, but with a double sized bet on the river), or even 1-1-2-8. In particular, think about AA, AKo, 44, and your hand: 76s.

[davet]

Smaller pocket pairs and suited- connectors need to see the flop cheaply, as a flush will occur about 8% by the river. I don't have the all the charts in front of me, but we all know that a straight and two pair don't come by much more often, perhaps 15% and 25% respectavely?

Let's take the flush example, if you raise PF all the time, you will have commited 2BB to see the flop 100 times, creating 200 BB to see the flop, compared to 100BB to limp.

Assuming this raise puts you all in. If you hit 8% of the time, you will recieve your preflop win. Lets assume that Pot Equity is "family," 9-1. So you would be losing losing 200 BB when you don't hit, and winning 32BB on a win.

This is a 168BB loss.

Just limping would only cost you 84BB, a far easier number to handle.

Of coarse add in the times that someone is holding a better flush and the board becomes four- to- a flush, and we see you are stuck.

Propostion hands gain value in the later streets, when you are able to value raise and, most importatly dodge all the bullets associated with later betting rounds.

I know that this is fairly elementry, but if anyone can help with all the other math, we could probably get the EV down to an exact number, or rather, use poker stove.