Another Fourth St. Decision
 

The pot is 3 handed. The board is Ad Kd 7d 2c. The game is 10-20 and the guy to your right bets $20. You somehow know that the player to your left has the lone ten of diamonds and an irrelevant rag. You have two pocket sevens. A raise will definitely fold the Td and a call will definitely keep him in. If you raise we will stipulate the first guy will only call. Also for simplicity sake we will not consider the river bet. Assume it doesn't exist.

The first bettor will make his bet with any AQ, AJ with the jack of diamonds, KQ with the queen of diamonds, KJ with the jack of diamonds, QJ both diamonds, Q9 both diamonds, or J9 both diamonds. Given he will play and bet all those hands but no others, with what size pot should you raise vs. call his $20 bet?

Re: Another Fourth St. Decision
 

Well, I was the first person to correctly answer the last Fourth Street Decision problem, but you gave all the credit to pudley4. I've learned my lesson - I'm just going to estimate this one. [img]/forums/images/icons/wink.gif[/img]

The bettor can have 9 hands that don't have a diamond (AQ) and 15 that do. If he does have any diamonds, you just want to call, because it only costs you one bet and you get the same number of bets into the pot. The weighted average of diamonds left in the deck is (9*9+12*8+3*7)/24 = 8.25. 8.25/42 is pretty darn close to 20%, so the diamond will hit 20% of the time. So, raising will save you the pot 20% of the times that the bettor doesn't have a diamond, or 0.2*9/24 = 7.5% of the time. So you want to raise when 7.5% of the pot is greater than the amount it "costs" you to raise.

Raising costs you about 20% of a bet when the bettor holds a diamond and one comes to beat you on the river (12 of 14 hands) and around 76% of a bet when the bettor has a made flush (3 of 24 hands). In the hands where the bettor is drawing dead, raising costs you nothing. So raising costs you about (12*.2+3*.76)/24 = 0.195, or about 20% of a bet.

So you want to raise when 7.5% of the pot is greater than 19.5% of a bet. So if the pot is 2.6 big bets or bigger, you want to raise. I still claim this is an estimate, and again I probably messed it up somewhere.

David

Re: Another Fourth St. Decision
 

$260(maybe a bit more?)...this is just a quick estimate. There is a chance that I am missing something and am way off, but I think I am probably in the ballpark.

Re: Another Fourth St. Decision
 

I would raise as the pot will always have at least 3BB at this point. You want to drive out the player with ten of diamonds
from beating you whenever the bettor doesn't have a big diamond.

Re: Another Fourth St. Decision
 

David,

I count 12 ways to have AQ, and 12 ways the bettor might have a diamond or two the way you presented this. So by raising, you lose half as many hands, but each time you lose you lose twice as much. Thus raising protects twice
as many pots for about the same cost. Always raise.

Mark

Re: Another Fourth St. Decision
 

There are 12 ways to have an AQ, but only 9 ways to have AQ with no diamond. That said, you will realistically nearly always raise.

Re: Another Fourth St. Decision
 

David,

Perhaps I see this wrong, but I don't think the following sentence is what you meant:
"Also, for simplicity sake we will not consider the river bet. Assume it doesn't exist."

If the river bet doesn't exist, then why would you ever raise? If the river bet doesn't exist, then this is the last round of betting, and that's it. If you call, you get two big bets from your opponents for just one big bet of your own. But if you raise, you get two big bets from your opponent for two big bets of your own. Clearly, you would never raise.

I don't think this was how you intended your question to be, so could you clarify what you meant when you said the river bet doesn't exist? Or am I just on crack?

Re: Another Fourth St. Decision
 

The third player is a rue, of the hands given our first player either has flush or has one card to getting one. thus don't raise since you will get the same return for your bet as raising with the same results. You have 7 outs to bet a flush, the pot size needs to be $120 (six to one you will improve).

Re: Another Fourth St. Decision
 

deadbart,

Right, I wondered why I was getting 12 [img]/forums/images/icons/confused.gif[/img] since I didn't think 12 and 12 was exactly right for another reason...

There are 9 ways for AQ, 12 ways for a diamond, and of those 3 are already ahead. So in fact, there are 9 ways that getting the player with Td out matters and 9 ways where it doesn't matter. So I still think that if there is a penny in the pot it is better to raise.

Mark

Re: Another Fourth St. Decision
 

I think there are 9 ways to have AQ without a diamond, 12 ways to have exactly one diamond (including AxQd) and 3 ways to have two diamonds.