drawing to the low?

[gergery]

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[Cooker]

Let me clarify a few points: a 20% bet only needs 4 to 1 pot odds to break even in a non split pot game. I am not sure if you said 5 to 1 because of the reasons I give below, or if you made 2 mistakes that roughly cancelled (neglecting what follows plus thinking 20% is 5 to 1 against while it is only 4 to 1 against).

However, in a split pot game you have to significantly beat 4 to 1 in order to make a profit on a 20% winner for half the pot. This is because when you win your half, you only get half your bets back as well. This is an important concept in calculating whether you have odds to draw in high-low split games. Let me illustrate. Suppose your equity is 20% and the pot gives you exactly 4 to 1 on your flop and turn bets and no betting happens on the river (for simplicity):

EV = [( 4 * 1.5BB - 1.5BB/2) - 4 * 1.5BB]/5 = -.15 BB

The extra -1.5BB/2 in the pot size is to compensate the fact that you only got half your bets returned (on a typical high game hand 4 to 1 odds means you get your whole 1 plus 4 extra back when you win, so you lose 1 when you lose and gain 4 when you win). So what odds do you need to continue? To break dead even, you need a pot odds of 4.5 to 1 on flop and turn bets.

I suspect you knew this and that is why you said 5 to 1, but I thought it is a point that should frequently be pointed out for inexperienced players to pick up.

[Buzz]

[ QUOTE ]
But you calculation shows that A222 is indeed +EV just to play for the low, and there is a small amount of high EV even if they aren't suited.

[/ QUOTE ]

Gooper - Yes, but that's after you see this particular (fairly favorable) flop.

Before you see the flop, I think the hand has a negative EV.

[ QUOTE ]
With A222 you are going to flop the low around 10% of the time and you will flop a low draw about 30% of the time. That means
- 60% of the time you will lose 1 SB
- 30% of the time you will gain 1.69 SB
- That means you would only have to win .93 SB every time that you flop the low which I think is reasonable.

[/ QUOTE ]

I don't have time to get my head into this right now. I'm playing today and I need some sleep. Maybe I'll get to it tomorrow.

I did have my head into it (yesterday or the day before, whatever) when I figured the hand had a negative expectation before the flop. That wasn't a guess; I did the math. But I could be wrong.

[ QUOTE ]
Strange our calculations seem to be a a small amount different for both A/2 flop and the probability of getting quartered with A/2. I am going to have to check my math when I get home.

[/ QUOTE ]

I wondered about that myself. I actually have a lot of confidence in myself and in those particular calculations - but at the same time I recognize I'm capable of making mistakes.

Buzz

[GooperMC]

For the A/2 flop calcluations I was estimating based on calculations with an A2910 hand (I was at work) and it looks like I estimated a little low. After running through the actual calculations my numbers match up to yours.

Here are the precise calculations:
With A222 you are going to flop the low around 11.7% of the time and you will flop a low draw about 31.9% of the time. That means
- 56.4% of the time you will lose 1 SB
- 31.9% of the time you will gain 1.69 SB
- That means you would only have to win .21 SB every time that you flop the low which I think is more then reasonable.

I will check my probability of quarting calculations later (that one always hurts my head).

[GooperMC]

I was getting my numbers from here:
http://www.math.sfu.ca/~alspach/mag7/
http://www.math.sfu.ca/~alspach/mag8/

My head hurt too much to try and sort this out, can someone who is smarter then me verify these calculations.

[gergery]

[ QUOTE ]
I was getting my numbers from here:
http://www.math.sfu.ca/~alspach/mag7/
http://www.math.sfu.ca/~alspach/mag8/

My head hurt too much to try and sort this out, can someone who is smarter then me verify these calculations.

[/ QUOTE ]


try this instead

The first sentence at that website says the following

"The reader is advised that this article and the succeeding article are nonsense and should be ignored. See Low Board Blues: Reprise and Coda for corrections"

[woodguy]

Greg,

C'mon man [img]/images/graemlins/grin.gif[/img]



Regards,
Woodguy

[GooperMC]

Thanks gergery. I feel a little bit stupud, but at least I now have correct numbers.