Pot Equity

[binions]

I am starting a project to calculate pot equity in O8. This is the first in a series of posts. This post will look at pot equity for a nut flush draw.

These numbers are conservative, because they assume that if you make your flush but the board pairs, you will always lose to a full house, and that if 3 low cards exist, you will always split the pot (i.e. no one's low draw against you ever gets counterfeited).

FLOP

0 low cards - 22.8%
1 low card - ~20%
2 low cards - ~13%
3 low cards - 11.4%

The reason for the ~ is because if your hand is full of high cards, then a low is more likely to come, whereas if you have low cards blocked, a low is less likely. It varies by 0.5% either way at the extreme.

TURN

No low possible - 15.9%
2 low cards - 10.2%
3 low cards - 8.0%

Next up, pot equity of top set.

[binions]

"Low" Pot Equity Percentages

Note, these pot equity calculations assume that 64% of the time, you win half the pot if you make your low, and 36% of the time, you win a quarter of the pot if you make your low. Getting 1/6th or 1/8th was not factored in, but is quite remote and doesn't affect the numbers significantly.

Flopped Nut Low, No Counterfeit protection:

Flop - 30.7%
Turn - 35.4% (assuming you were not counterfeited on 4th street)

***********************
Nut Low Draw, No Counterfeit Protection

Flop - 19.2%
Turn - 14.9%

*********************
Nut Low Draw, With Counterfeit Protection

Flop - 26.7%
Turn - 19.6%

**********************
Backdoor Nut Low Draw, No Counterfeit Protection

Flop - 6.6%

**********************
Backdoor Nut Low Draw With Counterfeit Protection

Flop - 10.9%

*********************
Second Nut Low Draw, No Counterfeit Protection

Flop - 4.8%
Turn - 3.7%

These "low" pot equtities can be combined with high pot equities that your hand may have (ie flush draws, sets, etc) to come up with a total pot equity for any given hand on the flop or turn for any given situation.

For example, the nut flush draw combined with the nut low draw has pot equity of 13% + 19.2% = 32.2% on the flop.

[Wintermute]

In tonight's top story, a cheetah escpaed earlier today from the Morristown zoo.


NAME THE MOVIE

[binions]

Harold & Kumar go to White Castle?

[anatta]

I thought about doing this as I am just getting into O-8 and this hand came up...

On the turn, I had the nut low made with A2, but no counterfeit protection, and the nut flush draw. I was on the button, and the SB bet out on the turn, it seemed clear the turn card helped him and he had the nut str8. There were two callers.

These callers were pretty bad, so not necessarily against another A2. I just called the turn. I ended up missing on the river, but took 1/4. I wondered if I should have raised for value on the turn here? If not, if I had A23 would that make it a raise?

Anyways, thanks for your efforts on this.

[muse21]

I respect your work here. I have no idea if it is accurate or not because it is boring to me.

Do you ever think about your opponent or what he may be holding?

[binions]

[ QUOTE ]
I thought about doing this as I am just getting into O-8 and this hand came up...

On the turn, I had the nut low made with A2, but no counterfeit protection, and the nut flush draw. I was on the button, and the SB bet out on the turn, it seemed clear the turn card helped him and he had the nut str8. There were two callers.

These callers were pretty bad, so not necessarily against another A2. I just called the turn. I ended up missing on the river, but took 1/4. I wondered if I should have raised for value on the turn here? If not, if I had A23 would that make it a raise?

Anyways, thanks for your efforts on this.

[/ QUOTE ]

Was it limit? Or pot limit?

Your pot equity was about 43% with one card to come, which was a clear raise against 3 players in limit.

[binions]

[ QUOTE ]
I respect your work here. I have no idea if it is accurate or not because it is boring to me.

Do you ever think about your opponent or what he may be holding?

[/ QUOTE ]

I suppose I could post the math behind the percentages. As for the second question, flushes never tie for high. I assumed that if you make your flush but the board pairs, you have no equity. As for low, I have accounted for the fact that 36% of the time you have A2, someone else does too. So yes, I have tried to account for the range of hands you might be facing.

[anatta]

It was limit. I felt like just calling was wimpy, but in my mind I thought, I got 9 outs, 6 cards that give me nothing, and I could be quartered. I agree that I should have raised. Thanks again.

[ QUOTE ]
"Next up, pot equity of top set."

[/ QUOTE ]

have you completed this yet?

informative so far, thanks.