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View Full Version : Drawing Odds Confusion

Marsellus
05-15-2003, 01:42 AM
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.)

BruceZ
05-15-2003, 03:12 AM
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.)

GeorgeF
05-19-2003, 10:03 PM
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
05-19-2003, 11:09 PM
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.