Theory/Math: Calculating Pot Odds over Flop and Turn
01-13-2012
, 07:27 PM
Was thinking about the following scenario and wanted some help setting up a mathematical or at minimum a conceptual formula to determine break even points in calling in the following scenario and similar ones.
Hero opens
Q
9
T8
Villain 3bets and has AA**
Hero calls HU
Flop T2
4
Pot is $1k. SPR2.0
Villain pots for 1k.
Its a bit difficult to quantify how often we can call here. Lets say we call here getting 2to1 and then turn falls
We would then call here as well getting 2to1. But whats not that obvious is that our overall call of both streets is -ev because we essentially put in 2k into a pot of 1k with an average equity of about 35%.
But that doesnt necessarily mean our flop call was -ev, because there are several turns we have a lot higher equity such as our trips, 2pr and BD draw turns. There are also many turns we can safely fold.
So if the following variables are defined as:
F= Flop equity (for 1 street)
T= Turn equity
X= Turn Call %
PF= Pot size on Flop
PT=Pot Size on Turn
CF= $ called on flop
CT= $ called on turn
How would the ev of a call down be defined? It would be something like the following:
(F*PF-CF)+X(T*PT-CT)
However, F is a variable that I odnt know how to determine. When we speak of Flop equity we are talking about with 2 to come. But how can we determine our actual flop equity with just the turn coming? In Holdem its a bit easier because backdoor draws are much less relevant and could be estimated. But in PLO they are huge. This is where im stuck; THe F term in the equation is the obstacle.
I'm not trying to actually use this formula for anything, but think that seeing it and understanding it can help to intuitively understand how these variables have to relate in spots like the one above.
This simulation below helps us determine what T and X are but I think F is still the problem.
http://www.propokertools.com/simulat...2=aa&s=generic
Hero opens
Q
9T8Villain 3bets and has AA**
Hero calls HU
Flop T
24Pot is $1k. SPR2.0
Villain pots for 1k.
| ProPokerTools Omaha Hi Simulation |
| board: t24 |
| Hand | Pot equity | Wins | Ties |
|---|---|---|---|
| qcts9h8d | 36.47% | 1,516,263 | 8,718 |
| aa | 63.53% | 2,644,719 | 8,718 |
Its a bit difficult to quantify how often we can call here. Lets say we call here getting 2to1 and then turn falls
| ProPokerTools Omaha Hi Simulation |
| 193,640 trials (Exhaustive) |
| board: t246 |
| Hand | Pot equity | Wins | Ties |
|---|---|---|---|
| qcts9h8d | 34.03% | 65,671 | 432 |
| aa | 65.97% | 127,537 | 432 |
We would then call here as well getting 2to1. But whats not that obvious is that our overall call of both streets is -ev because we essentially put in 2k into a pot of 1k with an average equity of about 35%.
But that doesnt necessarily mean our flop call was -ev, because there are several turns we have a lot higher equity such as our trips, 2pr and BD draw turns. There are also many turns we can safely fold.
So if the following variables are defined as:
F= Flop equity (for 1 street)
T= Turn equity
X= Turn Call %
PF= Pot size on Flop
PT=Pot Size on Turn
CF= $ called on flop
CT= $ called on turn
How would the ev of a call down be defined? It would be something like the following:
(F*PF-CF)+X(T*PT-CT)
However, F is a variable that I odnt know how to determine. When we speak of Flop equity we are talking about with 2 to come. But how can we determine our actual flop equity with just the turn coming? In Holdem its a bit easier because backdoor draws are much less relevant and could be estimated. But in PLO they are huge. This is where im stuck; THe F term in the equation is the obstacle.
I'm not trying to actually use this formula for anything, but think that seeing it and understanding it can help to intuitively understand how these variables have to relate in spots like the one above.
This simulation below helps us determine what T and X are but I think F is still the problem.
http://www.propokertools.com/simulat...2=aa&s=generic
Last edited by HustlerLA; 01-13-2012 at 07:34 PM.
01-14-2012
, 12:56 AM
Quote:
However, F is a variable that I odnt know how to determine. When we speak of Flop equity we are talking about with 2 to come. But how can we determine our actual flop equity with just the turn coming? In Holdem its a bit easier because backdoor draws are much less relevant and could be estimated. But in PLO they are huge. This is where im stuck; THe F term in the equation is the obstacle.
However, F is a variable that I odnt know how to determine. When we speak of Flop equity we are talking about with 2 to come. But how can we determine our actual flop equity with just the turn coming? In Holdem its a bit easier because backdoor draws are much less relevant and could be estimated. But in PLO they are huge. This is where im stuck; THe F term in the equation is the obstacle.
| ProPokerTools Omaha Hi Simulation |
| 193,640 trials (Exhaustive) |
| board: t245 |
| Hand | Pot equity | Wins | Ties |
|---|---|---|---|
| qcts9h8d | 20.30% | 39,199 | 216 |
| aa | 79.70% | 154,225 | 216 |
so basically youre a 4:1 dog to draw out on the turn. this makes sense, as 36% on the flop is just like a flush draw, which approximates to 2:1 with two cards to come and 4:1 with one.
so on the flop youre only getting 2:1 when you are a 4:1 dog to improve, so the flop call is massively -ev if you plan on folding the turn often. but, like you question, how often does it matter? cause when you hit or turn a backdoor gutshot as your example, now youre getting better odds than you need. so does this turn equity make up for the flop -ev?
i dont know if its correct, but cant you just look at the flop equity with 2 to come? you have 36%. lets assume the guy is committing himself, so if you just shove the flop, you are paying 2k to win 3k, which is 40%. so its a bad flop shove by 4%, and i would probably just guestimate that continuing and playing the turn is simialrly slightly -ev
i guess i might call anyway and rationalize that if the turn pairs the board such as T242, now all my 2pr outs are dead, and i can safely fold, which makes up for some of the ev had i just shoved the flop. this is similar where if you bet the flop with the flush+str draw, and someone makes a committing raise, while you might be +ev just to get it in, you can safely just call flop and call off turn, but save yourself some moeny if the turn pairs
01-14-2012
, 06:15 AM
Guys, I just made this hand and flop example up; it wasn't intended to actually look for a strat on call or fold. Im looking at the situation and trying to get a more detailed and comprehensive sense of decisions where:
** also I meant to make SPR=4.0 on the original example as well.
Villain bets pot with SPR>1 and he will likely Pot most turns.
Lets look at another example.
SPR4. Villain pots it we call and have 33% equity (2 to come). Turn SPR is 1. He pots it and we have 33% equity again. We call. In this case our turn decision was correct but we dont have enough information to even determine if our flop call was incorrect. It so happens that on this specific turn we only had 33% equity thus not making up enough for our speculative flop call.
But what if 40% of turns gave us 60% equity? Then surely the flop call would be +ev. This is what Im hitting at. Just trying to really get a more detailed discussion and formulate a relation between all those parameters I defined above.
Think about this following example. This one is easy to understand and to make the correct play, but perhaps delving into the relation of these parameters will help with more unclear spots.
Hero has 789jr
Villain has AA** (and assume we know this)
Flop A56r. Villain pots flop with SPR of 4.
We obviously call. Our equity is 36% but that number isnt even really what we want to know nor the key factor into our call decision. I believe its more of a integral of all the equities for every turn we face. But we have the option to fold some and call others so that 36% really just doesn't cut it.
Lets say we brick turn. K turn. Villains pots it SPR is now 1. We have to fold.
But our flop call was certainly +EV because our equity is 75% on 25% of turns. http://www.propokertools.com/simulat...ayzn&s=generic
Applying this to real life, we need even higher turn equity because the less defined villain's range is the less accurately we can continue on certain turns and fold others. Thus making our speculative flop calls less profitable due to inperfect turn decisions as a result of not knowing turn parameters T and X with certainty.
The reason this is more difficult of a situation to estimate than compared to holdem is because various turns give us such differing equities; some just barely enough to call again, some massive favorites, some slight favorites. Its akin to doing structured range analysis where we estimate our equity on the spectrum of villain's range ala Gbucks. But instead we are doing structured equity analysis where we are estimating our equity on a spectrum of turns.
** also I meant to make SPR=4.0 on the original example as well.
Villain bets pot with SPR>1 and he will likely Pot most turns.
Lets look at another example.
SPR4. Villain pots it we call and have 33% equity (2 to come). Turn SPR is 1. He pots it and we have 33% equity again. We call. In this case our turn decision was correct but we dont have enough information to even determine if our flop call was incorrect. It so happens that on this specific turn we only had 33% equity thus not making up enough for our speculative flop call.
But what if 40% of turns gave us 60% equity? Then surely the flop call would be +ev. This is what Im hitting at. Just trying to really get a more detailed discussion and formulate a relation between all those parameters I defined above.
Think about this following example. This one is easy to understand and to make the correct play, but perhaps delving into the relation of these parameters will help with more unclear spots.
Hero has 789jr
Villain has AA** (and assume we know this)
Flop A56r. Villain pots flop with SPR of 4.
We obviously call. Our equity is 36% but that number isnt even really what we want to know nor the key factor into our call decision. I believe its more of a integral of all the equities for every turn we face. But we have the option to fold some and call others so that 36% really just doesn't cut it.
| ProPokerTools Omaha Hi Simulation |
| 600,000 trials (Randomized) |
| board: a56 |
| Hand | Pot equity | Wins | Ties |
|---|---|---|---|
| 7x8y9zj | 39.11% | 233,131 | 3,022 |
| axayzn | 60.89% | 363,847 | 3,022 |
Lets say we brick turn. K turn. Villains pots it SPR is now 1. We have to fold.
| ProPokerTools Omaha Hi Simulation |
| 600,000 trials (Randomized) |
| board: a56k |
| Hand | Pot equity | Wins | Ties |
|---|---|---|---|
| 7x8y9zj | 30.72% | 183,273 | 2,069 |
| axayzn | 69.28% | 414,658 | 2,069 |
But our flop call was certainly +EV because our equity is 75% on 25% of turns. http://www.propokertools.com/simulat...ayzn&s=generic
Applying this to real life, we need even higher turn equity because the less defined villain's range is the less accurately we can continue on certain turns and fold others. Thus making our speculative flop calls less profitable due to inperfect turn decisions as a result of not knowing turn parameters T and X with certainty.
The reason this is more difficult of a situation to estimate than compared to holdem is because various turns give us such differing equities; some just barely enough to call again, some massive favorites, some slight favorites. Its akin to doing structured range analysis where we estimate our equity on the spectrum of villain's range ala Gbucks. But instead we are doing structured equity analysis where we are estimating our equity on a spectrum of turns.
Last edited by HustlerLA; 01-14-2012 at 06:38 AM.