Basic math question

[MrMoo]

For some reason I can't wrap my head around this.

From an article I'm reading:
[ QUOTE ]
$3/6 heads-up game. Blinds $1/$3. To steal, the small blind raises $5 to win $4. Using simple arithmetic, we calculate that the preflop raiser needs to steal the blinds 55% of the time to make an immediate profi

[/ QUOTE ]

What is the "simple arithmetic" needed to figure this out? How do you get that 55%?

Thanks.

[Stephen H]

By immediate profit they seem to mean that even if you lose all the times you're called, you'll *still* make money. The simple math they did:

X = percent of the time the BB folds and you win
1-X = percent of the time the BB doesn't fold and you lose.

$4 * X = avg amount per hand you win from the BB folding
$5 * (1-X) = avg amount per hand you lose from the BB not folding

Setting these equal to each other to find the value for X where EV = 0 gives you
4X = 5(1-X)
4X = 5 - 5X
9X = 5
X = 5/9 ~= .55

So there you go. Of course, this doesn't account for what might happen if the BB calls and you get post flop and start throwing bets around after that...but that's more complex blind steal/defense discussion.

[DCWildcat]

That's definately not simple arithmetic

[Yawkey]

This is just the precentage of your bet compared to the pot plus your bet.

55% = 5(your bet)/ (4(pot) + 5(your bet)) * 100

[eurythmech]

I object!

It is actually closer to 56%.

As a general rule, the %fold you need to make an "immediate profit" is related to the "blind relation" according to the following formula:

(2bb - sb) / 3bb = fold% needed. I think.

[TomCollins]

[ QUOTE ]
That's definately not simple arithmetic

[/ QUOTE ]

Loc: Kentucky

[W. Deranged]

Easiest way to think about it is this: you are raising $5 to win a pot that will be $9 if BB folds ($1 SB + $3 BB + your $5). $5/$9 will be the odds you need to break even... that's 55.6% or so.

[MrMoo]

Thanks to everyone who answered. I appreciate the help.

[TomBrooks]

Thank you for that explanation.

Queery: 1. Based on this figure, what hands should you raise with when it's folded to you in the SB?

Followup: 2. What would the percentage be and what hands should you raise with for a 1/2BB-1BB blind structure?

[Stephen H]

[ QUOTE ]
Thank you for that explanation.

Queery: 1. Based on this figure, what hands should you raise with when it's folded to you in the SB?

Followup: 2. What would the percentage be and what hands should you raise with for a 1/2BB-1BB blind structure?

[/ QUOTE ]

My answers:
1) I have no idea. [img]/images/graemlins/smile.gif[/img] I'm still pretty much a beginner at poker, and at this stage I'm attempting to learn the math and get my feet wet a little bit in the actual game. I'm not sure that this value is particularly meaningful, or, rather, usefully translatable into a range of starting hands, as it makes some assumptions that you always have the worst hand, and so forth. I think it's more interesting as an intellectual exercise just to show how profitable blind stealing is at given structures, and for comparision to different structures as well (shown nicely in the next question!)

2) Looking at the percentage for .5 - 1 blinds, the formulas are just as simple, except that now you risk 1.5 to gain 1.5.

1.5*X=1.5*(1-X)
1.5X = 1.5 - 1.5X
3X = 1.5
X = .5 or 50%.

Which simply shows that you only need to be successful 10 times in 20 instead of 11 times in 20 to be break-even. I think the main lesson is that you need to be a little tighter on your blind steals in 1/3 SB/BB than 1/2 SB/BB, all other factors being equal. But wasn't that particularly obvious anyways?

I'll think about the starting hand stuff a little bit more and perhaps try to post something insightful later. My first instinct tells me it depends on what hands you're willing to play out of position versus one caller anyways, plus some raw steal attempts..basically, if you would "normally fold", you would instead steal a given amount of the time, totally randomly..not based on your cards at all, selected such that your opponent folds enough that it's profitable for you. Remember, I never suggested this percentage was useful; I just showed the math I suspected was used by the article the OP referenced.