LO8 - When is it correct to chase runner-runner for the nut low

[cornhuskerfan]

A situation came up several times in Vegas that got me thinking.

The game was $4/$8 Omaha8 with numerous bad players that played too many hands and chased too many long shots. I can literally remember playing against two different players who did not fold a single hand, not one, preflop in separate 3 hour sessions. So I got to thinking…., <font color="red">how big does the pot need to be on the flop to consider chasing runner-runner low cards in hopes of getting ½ (or even ¼) of the pot? </font> Please check my logic and let me know where I screwed this up.

The Situation:
You hold A 2 9 K rainbow. The board reads J [img]/images/graemlins/heart.gif[/img] J [img]/images/graemlins/club.gif[/img] 8 [img]/images/graemlins/heart.gif[/img]. You assign a 0% chance of holding any high equity.

The Math:
There are 25 cards that could come on the turn that are helpful (4 each of 7s, 6s, 5s, 4s, 3s). The probability of catching a good card on the turn is 20 cards out of 45 unseen cards - 0.444. Then, you’ll need to catch 16 good cards on the river out of 44 unseen. 16/44 = 0.364. So the probability of catching good on both the turn and the river is 0.444 x 0.364 or 0.162. [img]/images/graemlins/confused.gif[/img]

Split Pot:
If I catch good on both the turn and the river, I’ll get a portion of the pot – either ½ the pot or ¼ of the pot (or maybe 1/6 of the pot – yuk). Since chasing runner-runner low to get a portion of the pot is a long shot (0.162), the pot will need to be pretty big. To create a big pot, it is necessary to have many contestants. With a large number of contestants in an Omaha8 game, the chance of another player holding the nut low as well must be considered. I used Alspach’s Poker math to estimate this probability at 0.3 (&lt;http://www.math.sfu.ca/~alspach/mag8/&gt;)
Therefore there is a 0.7 chance of winning ½ the pot and a 0.3 chance of wining a ¼ of the pot. So, if I catch runner runner low, I expect to get ((0.7 x ½) + (0.3 x ¼)) or 0.425 of the pot.

The Flop::
There is a 0.162 chance of catching runner runner by the river for me to win a 0.425 portion of the pot
0.162 x 0.425 means I have pot equity of about 7%. Therefore, I’d need the pot to be “huge” to make a call chasing runner runner low. I’d need 15 small bets to be in the pot to justify a 1 bet call. To get this number I took the number of bets (1) divided by the probability of winning (0.162) x the proportion of the pot that you’d win (0.425).
To get 15 bets in a pot preflop, I’d need 5 people to put in 3 bets or 8 people to put in 2 bets or 3 people to put in 5 bets (which is a cap in Vegas limit poker).
It gets much worse if you are facing a raise (or worse yet, 3 bets cold on the turn)
If you are facing 2 bets on the flop and still have 7% pot equity, you’d need there to be 29 bets (6 people in a capped preflop pot). &lt;&lt;2 bets divided by the probability of winning (0.162) * the proportion of the pot that you’d win (0.425)&gt;&gt;
If you are facing 3 bets cold, you’d need there to be around 45 bets (9 people in a capped preflop pot). &lt;&lt;3 bets divided by the probability of winning (0.162) * the proportion of the pot that you’d win (0.425)&gt;&gt;
<u>The Bottom Line: </u> you can call on the flop chasing runner runner nut low, if the pot is huge (15 or more small bets) and the flop betting is not raised and you don’t expect it to get raised (i.e., you are in last position).

The Turn:
Now, I have the same problem on the turn when I catch good. Do I continue to chase a low card to the river to get ½ or ¼ of the pot? The math is about the same. There are now 16 good cards out of 44 or 0.364. So, 0.364 – probability of making a hand x .425 – portion of the means I have about 16% pot equity So, we’d need 7 big bets in the pot to call 1 big bet on the turn &lt;&lt;1 bet divided by the probability of winning (0.364) * the proportion of the pot that you’d win (0.425)&gt;&gt;
From the flop discussion above, we must have at least 15 small bets preflop to call a flop bet. You can only call on the flop if it is checked or there is 1 bet; therefore, there are a least 7 big bets on the turn, so the 1 bet call on the turn is automatic if you catch good.
But what if you are facing a bet and a raise on the turn? With 16% equity, you’d need about 13 big bets to justify calling 2 bets on the turn. &lt;&lt;2 bets divided by the probability of winning (0.364) * the proportion of the pot that you’d win (0.425)&gt;&gt;
If you are facing 3 bets cold on the turn, you’d need 19 big bets to justify a call with 15% equity. &lt;&lt;3 bets divided by the probability of winning (0.364) * the proportion of the pot that you’d win (0.425)&gt;&gt; This would be a gigantic pot ($150 pot in a $4/$8 game).
<u>The bottom line:</u> You can call 1 bet on the turn if the pot is unraised. You can call 2 bets on the turn if there are 19 bets in the pot. To get 19 big bets in a pot and still have the correct calling odds on the flop and the turn, you’d need about 8 players in the hand each having put in 2 small bets preflop, 1 small flop bet, and 1 big turn bet…..not likely. You can’t really play for a raise on turn.

The River:
The river plays itself. If you catch good, call (bets and raises). If not, fold. You have about .425% pot equity &lt;&lt;1 bet divided by the probability of winning (1.0) * the proportion of the pot that you’d win (0.425)&gt;&gt; The pot has at least 7 big bets (the criteria for calling on the turn), so you are paying 1 bet to get 42.5% of at least 7 big bets.
What if 2 jackasses cap it on the river? You have 42.5% equity in a pot that has at least 7 big bets. If 2 jackasses cap it, there will be 21 big bets in the pot when you are faced with your last call (5 bets from jackass #1, 5 bets from jackass #2, 4 called bets from you, plus 7 bets to start with). Since you “own” 42.5% of this pot (21 bets x 42.5% = 9 bets that you own) and you only have to call 1 last bet, the call is automatic.

<u>The bottom line:</u> Call all bets and raises on the river when you hold the nut low. Duh! [img]/images/graemlins/tongue.gif[/img]

[jjgoldy5]

Situation is much different when you have counterfeit protection (i.e. pot size doesnt need to be as big as you have a much greater chance at catching good 2x in a row)

[nhtool]

I'll usually treat a runner runner nut low draw like a gutshot--the pot has to be around 10 small bets on the flop. But I rarely chase it unless I:

1. have some sort of miracle high draw
2. have counterfeit protection
3. am pretty sure no one else has the nut lo draw

It's important to note that if the pot is big enough to draw to a backdoor low, there's a very good chance at least one other player has a backdoor low, in which case you are drawing to get 1/4 or 1/6...

[toots]

I've been using the oversimplistic maxim of "in general, don't." (All the normal disclaimers apply if I have a good chance at the high; the maxim applies to low-only runner-runner draws.)

Nice to see the math that more or less supports that maxim.

Thanks for posting all that work, husker.

[benwood]

Thanks for this valuable info,cornhuskerfan.Like jjgoldy5 said,your chances are much better when you have counterfit protection.Could we possibly get you to run the numbers on this,too?Thanks a lot.Ben
(Buzz,Do you agree with these numbers?)

[cornhuskerfan]

I used the same logic to determine the number of small bets required in a pot to chase runner-runner low on highish flop (2 high cards). Here's what I came up with. I had to do some rounding (i.e., # of bets is a whole number) and estimate some winning percentages with different holdings. Let me know if you agree/not.

On a highish board (2 high cards), you will have the correct pot odds to call one small bet, chasing runner-runner low for 1/2 (or less) of the pot, on the flop if you have the following hands and the pot contains <font color="red">n </font> bets:

You hold an "AB" hand (A2xx) with 0% high equity - <font color="red">15 </font> small bets (for example, you hold A [img]/images/graemlins/spade.gif[/img] 2 [img]/images/graemlins/diamond.gif[/img] 9 [img]/images/graemlins/heart.gif[/img] 9 [img]/images/graemlins/club.gif[/img] and the flop is K [img]/images/graemlins/club.gif[/img] J [img]/images/graemlins/club.gif[/img] 8 [img]/images/graemlins/club.gif[/img])

You hold an "ABC" hand (A23x) with 0% high equity - <font color="red">9 </font> small bets (for example, you hold A [img]/images/graemlins/spade.gif[/img] 2 [img]/images/graemlins/diamond.gif[/img] 3 [img]/images/graemlins/heart.gif[/img] 10 [img]/images/graemlins/club.gif[/img] and the flop is K [img]/images/graemlins/club.gif[/img] J [img]/images/graemlins/club.gif[/img] 8 [img]/images/graemlins/club.gif[/img])

You hold an "ABD" hand (A24x) with 0% high equity - <font color="red">10 </font> small bets (for example, you hold A [img]/images/graemlins/spade.gif[/img] 2 [img]/images/graemlins/diamond.gif[/img] 4 [img]/images/graemlins/heart.gif[/img] 10 [img]/images/graemlins/club.gif[/img] and the flop is K [img]/images/graemlins/club.gif[/img] J [img]/images/graemlins/club.gif[/img] 8 [img]/images/graemlins/club.gif[/img])

You hold an "ABZ" hand (A27x) with 0% high equity - <font color="red">11 </font> small bets (for example, you hold A [img]/images/graemlins/spade.gif[/img] 2 [img]/images/graemlins/diamond.gif[/img] 7 [img]/images/graemlins/heart.gif[/img] 10 [img]/images/graemlins/club.gif[/img] and the flop is K [img]/images/graemlins/club.gif[/img] J [img]/images/graemlins/club.gif[/img] 3 [img]/images/graemlins/club.gif[/img])

Now, lets say you hold "some" high equity (like a gut shot).
You hold an "AB" hand (A2xx) with "some" high equity - <font color="red">10 </font> small bets (for example, you hold A [img]/images/graemlins/spade.gif[/img] 2 [img]/images/graemlins/diamond.gif[/img] 10 [img]/images/graemlins/heart.gif[/img] K [img]/images/graemlins/club.gif[/img] and the flop is J [img]/images/graemlins/club.gif[/img] 9 [img]/images/graemlins/club.gif[/img] 7 [img]/images/graemlins/spade.gif[/img])

You hold an "ABC" hand (A23x) with "some" high equity - <font color="red">7 </font> small bets

You hold an "ABD" hand (A24x) with "some" high equity - <font color="red">7 </font> small bets

You hold an "ABZ" hand (A27x) with "some" high equity - <font color="red">8 </font> small bets

It's difficult to memorize all of this, so I sort of summarized it in my mind as follows:

AB hand with no high - 15 outs - never call a raise
ABC,ABD, or ABZ hand with no high - 10 outs - never call a raise

AB hand with long-shot high - 10 outs - never call a raise
ABC,ABD, or ABZ hand with long-shot high - 8 outs - never for a raise.

Or maybe a simpler rule would be "don't chase runner-runner low unless you have an ABZ hand or better and there is 10 bets or more in the pot - with one exception, if you have an AB hand and there is 15 bets in the pot". I like this one. I'm going to call this the rule of "10/15"

In almost all situations, the pot will need to be multi-way with 1 or 2 preflop raises.

[benwood]

Good job,cornhuskerfan.Valuable info.You're the nuts.
Ben

[scottjf8]

[ QUOTE ]
You assign a 0% chance of holding any high equity

[/ QUOTE ]

I dont' consider myself a good omaha player at all really (especially as good as Cornhuskerfan, since I play live with him alot) - but when I am chasing to hopefully win half the pot - especially with A2 that everyone plays, and might get quartered, I lose intrest in the hand once the flop is 2 high cards.... Why put money in that you *might* get back, or not get at all, or get some of it back if 2 others have A2 and it comes runner runner 5-6.

[WhooFleuryScores]

[ QUOTE ]
You hold A 2 9 K rainbow.

[/ QUOTE ]

This is your first problem.If you had say A2sK9s then this hand is a bit more playable;but the 9 is basically the worst card you can hold so if you are offsuit you are essentially playing a dangler (in fact even suited the 9 would still be a bit off).

I would fold the flop and look for a better place to get my money.

[benwood]

Quote:"I would fold the flop and look for a better place to get my money."

This is too tight,imo.It's great if all your cards are working,but the presence of a 9 in your hand shold not prevent you from playing an A2 hand.I personally play all A2 hands if the pot is not raised,but some other players who play better than me will pass some dry A2 hands depending on the situation(strength &amp; tightness of the game,position,etc).However,this is not a dry A2.The K is a strong card.I don't believe that I know any good players who would not normally play this hand.