Drawing Odds Confusion

[Marsellus]

while i was working out drawing odds the other night i ran into a situation that confused me and i am hoping someone may be able to clarify the scenario for me.

suppose you hold 9 /forums/images/icons/diamond.gif T /forums/images/icons/diamond.gif in late position and limp into the pot. suppose the flop comes down J /forums/images/icons/club.gif 7 /forums/images/icons/spade.gif 2 /forums/images/icons/heart.gif giving you a gutshot straight draw. any 8 would give me the nut straight. the way that i have calculated the odds of completing this hand is as follows:

1 - (43/47 * 42/46) = .16 or 16 %. indicating that i will complete this hand 16% of the time. convert that to odds and you'll arrive at .84/.16 = 5.25:1 against.

now before working this out, i would normally look for about 11:1 to call a flop bet under this circumstance which is essentially what you would arrive at if you calculated your odds one card at a time.

i don't think that anyone would argue that when you have flopped a 4 flush, you'll complete your hand about 35% of the time or converted to odds, 1.85 to 1 against which essentially makes it almost always correct to draw to a flush when you have flopped a four flush.

my question is should i be looking for 11 to 1 (pot odds) when i have flopped a gutshot draw or the 5.25 to 1 (calculation shown above)? and if i am not supposed to use the 5.25 to 1 calculation based on multiplying turn and river chances, then why is it ok and accepted to calculate a four flush based on the multiplication of turn and river chances? (ie. (1 - (38/47 * 37/46)) = .35 or (.65/.35) 1.85:1 against.)

i'm confused about this and would appreciate some clarification. /forums/images/icons/confused.gif

[BruceZ]

my question is should i be looking for 11 to 1 (pot odds) when i have flopped a gutshot draw or the 5.25 to 1 (calculation shown above)? and if i am not supposed to use the 5.25 to 1 calculation based on multiplying turn and river chances, then why is it ok and accepted to calculate a four flush based on the multiplication of turn and river chances? (ie. (1 - (38/47 * 37/46)) = .35 or (.65/.35) 1.85:1 against.)

In either case you should be looking first at the size of the pot relative to the odds of making your hand on the turn. Even for a flush, you cannot simply say you only need to be getting 2:1 from the pot unless you or all of your opponents are all-in, because it may cost you at least 1 additional bet to see the river, and this cuts down your effective odds, unless the bet you call on the turn is also called by several opponents. If your opponents are putting 3 or more bets in the pot on a round for every one of yours, then these bets on the flop and turn should be called, and you should raise in late position if 3 or more opponents will call your raise, or checkraise in early position. The reason it is usually correct to draw to a 4-flush is because you are usually getting a price of at least 5-1 to make your hand on the turn, considering the money that goes in before, on, and after the flop. You can usually win additional bets after you make your hand. This is also why it is often correct to call with a gutshot getting only 8-1, as long as you are confident it will be the best hand when you make it. If you were playing heads up and made a 4-flush, and your opponent bets giving you 3:1 to call, you are not getting the right price to see the turn based only on the money currently in the pot, and the odds of making a flush. That doesn't mean you shouldn't call or even raise for other reasons, however.

[GeorgeF]

I am not sure your 16% is correct. I get the prob of (8,X) and (Q,K) as 17.946%.

I got the prob from my website,
http://www.iodo.us/cgi-bin/THEAssistant.pl
I don't follow how you got 16%.

[BruceZ]

The 16% is just the odds of completing the gutshot by the river. It doesn't count the runner runner KQ. He is taking 1 minus the probability of NOT hitting the gutshot on either card. It's 43/47 to not hit it on the turn, and 42/46 to not hit it on the river, so it's (43/47)*(42/46) to not hit it on either card. 1 minus this is 16.466% which agrees with your website, since the gutshot can be J high or Q high depending on the other card:

Str. to a Q 1.480%
Str. to a J 14.986%
-------------------
16.466%

Runner runner KQ is (8/47)(4/46) =

Str. to a K 1.480%

Sum of all of these is 17.946%

Nice website. It would be great if you can expand this to two players, and maybe breakdown various hands and draws on the flop and turn as well.