O8 - Hypothetical turn pot odds question - check my math

[L0QTiS]

You have A[img]/images/graemlins/heart.gif[/img] J[img]/images/graemlins/diamond.gif[/img] 4[img]/images/graemlins/diamond.gif[/img] 2[img]/images/graemlins/heart.gif[/img] in LP and are involved in a hand on a 2/4 table

Flop is 8[img]/images/graemlins/spade.gif[/img] 4[img]/images/graemlins/spade.gif[/img] K[img]/images/graemlins/diamond.gif[/img]

At the close of action on the flop, there are 4 players in and $23 in the pot.

Turn K [img]/images/graemlins/club.gif[/img]

There's a Bet, a call, and a fold to you ($31 in the pot) and $4 to you

Assume you aren't likely to share the low if you draw to it.

* Please explain your action and the pot odds involved (if any differant than mine below).
* What would be your MINIMUM amount to call here based on pot odds.

Check my math:

31:4 on the call amounts to 7.75:1, however I need to adjust for drawing to only 1/2 of the pot so I'm looking at 3.875:1

I have 16 clean outs to the low with 44 unseen cards (44:16 or 2.75:1) so it appears this is an easy call

Minimum $ in the pot necessary to call in this situation would be 2.75 * $4 * 2 = $22 - I'm not sure why this bothers me but it just seems low.

[Buzz]

L0QTiS - Take 31 chips of one color and 4 chips of a different color (or use coins). I'm using 31 blue chips and 4 pink chips.

Now I'm making two stacks, one with all four pink chips. Since it's for half the pot, the odd chip goes to high. Thus there are 13 blue chips in the pile with the four pink chips.

Now, since you have two opponents, I'm taking another 8 blue chips plus another 4 pink chips and adding them to the piles to use for implied pot odds. I've ended with 15 blue chips in the same stack as 8 pink chips. If you win and get half the pot, you'll win those 15 blue chips, and the risk to you on the third betting round will be 4 pink chips. Thus your implied pot odds are about 15 to 4.

I used the word "about" in that last sentence because there's no guarantee you'll have two opponents if you make low on the river. But I think that's a reasonable estimate. At any rate, I think your implied pot odds are likely 15 to 4, or 15/4 to 1, or 3.75 to 1. It's worthwhile emphasizing here that's for just half the pot.

I prefer to use implied pot odds. But if you just want to know your pot odds, they are 13 to 4, or 13/4 to 1, or 3.25 to 1.

Now we'll figure the odds against your making low on the river. Any trey, five, six, or seven, a total of 16 cards (out of a possible 44) will make low for you. The odds against your making low are 28 to 16, or 28/15 to 1, or 1.75 to 1.

Since your implied pot odds (for just half the pot) are greater (actually enormously greater) than the odds against your making low, and assuming you are reasonably certain you won't get quartered, you have favorable odds to call a bet. (Indeed, the pot odds alone are greater than the odds against making your hand).

To make a raise, the fresh money odds have to be greater than the odds against making your hand. Assuming you would get two callers, your fresh money odds for the whole pot would be 2 to 1. However, if you take eight blue chips and four pink chips and then divide them into two stacks of six chips each, one with six blue chips and the other, your share, with four pink chips and two blue chips, you should see that what you would actually win if you raise, assuming two callers, would be 2 blue chips. Those odds, the fresh money odds for just half the pot, are not greater than the odds against making your hand. (You'd need seven blue chips in the pile with your four pink chips to have odds to raise).

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31:4 on the call amounts to 7.75:1, however I need to adjust for drawing to only 1/2 of the pot so I'm looking at 3.875:1

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No. You effectively lose half the chips the call costs when you win half the pot. You neglected to consider that.

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I have 16 clean outs to the low with 44 unseen cards (44:16 or 2.75:1)

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No. Of the 44 unknown cards, 16 are favorable and 28 (not 44) are unfavorable.

28:16, not 44:16 is what you should use.

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Minimum $ in the pot necessary to call in this situation would be 2.75 * $4 * 2 = $22

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To put four bucks in the pot, you need to be assured of winning seven bucks when you make your low, assuming you won't have to share the low. That's 7 to 4 or 7/4 to 1 or 1.75 to 1. That's the same as the odds against making your hand.

Not figuring anything for implied pot odds, there has to be 7+7+4 = $18 already in the pot when you plunk in your four bucks. But that's not figuring in your implied pot odds.

To figure in your implied pot odds, take seven blue chips and stack eight pink chips on top of them. Then match than stack with a stack of 15 blue chips. then take away four blue chips from each stack. The total number of blue chips you have in the two stacks is how much money you need to have in the pot to call. Looks like $14 to me.

I'm just answering your questions and checking your math set ups. There are some other considerations (mainly the danger of getting quartered, but also the possibility of somehow winning for high or somehow scooping) we're both ignoring.

Buzz

[johnnybeef]

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I'm just answering your questions and checking your math set ups. There are some other considerations (mainly the danger of getting quartered, but also the possibility of somehow winning for high or somehow scooping) we're both ignoring.

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another thing that needs to be accounted for is the rake which will many times make it unprofitable if there is only one other opponent in the pot with you which in this hypothetical situation does not apply. this is why it is usually only correct to draw to half of a pot in a multiway pot.

hope this helps,
johnny