5CD: % dealt 4flush, or OESD

[Big Limpin]

What percentage of hands are you dealt a 4 flush, and also what percentage of hands are you dealt a open-ender?

This pertains to the situation where villain is raising all his draws along with his pairs...and hero is to guess how often villain is on a draw (before knowing the card exchange)

I'll do the math if necessary, but hoping someone has the %'s already and can post 'em

Thanks! [img]/images/graemlins/cool.gif[/img]

[flafishy]

All the odds you've every wanted to know: http://www.poker1.com/mcu/mculib_odds.asp

[Big Limpin]

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Most of the odds you've every wanted to know: http://www.poker1.com/mcu/mculib_odds.asp

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not there [img]/images/graemlins/frown.gif[/img]

[DOMIT]

Isn't this basically the same odds for HE on the flop?

According to SSI, if you have AKs, the prob of getting a flush draw on the flop (flopping 2 more of your suit on a 3card flop, meaning "your first 5 cards") is 8.14-1 [Table XIX].

As for OESD, he only lists QJo to get K-T or T9 on the flop, no straight, as 15.6-1.. but this does NOT include all possible OESD's.. if you started w/ JTo, you'd have 3 combos to help you: KQ, Q9 and 98.. therefore, the percentage would have to be better than the 15-1. I'd hazzard to guess closer to the 8-1, as the probability of flopping a straight is less than flopping a flush. If someone else has the exact numbers, I'd appreciate it as well [img]/images/graemlins/smile.gif[/img]

[Big Limpin]

Good method of attack D. I'll refine that a little.
Its 8.14:1 (10.94%) to "flop" a 4flush if i start w/ XXs
Its also 33.3:1 (2.92%) to flop a 4flush with XXo

In draw, I have XXs (12/51) of the time, and XXo (39/51) of the time.

P(4flush)= (12/51)*(0.1094) + (39/51)*(0.0292)
P(4flush)= 0.0481

So if i havent retarded up the math somewhere, hero/villain starts with a 4flush just under 5% of the time
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Now about the straights...*gulp*
I'm not even going to attempt to hash that one out.
Probably best course is to compare how likely a OESD is relative to a 4flush.

I think domit's guestimation that they are pretty close to flushes is reasonable. Any other guesses?

My hunch is that they are a touch less common. I base that on wild speculation.

Some of the OESD's are really OESFD's and are accounted for already by the 4flush numbers. On the other hand, a fair number of them will include a decent pair, and he will proceed in that direction. Maybe 3-4%?

But then again, if villain is playing all these hands for raises, he probably has the audacity to throw in gutshots (especially broadway) and perhaps also cathops when they are royal.

My guess is that a villain who is playing every draw he gets ...gets dealt a draw ~9% of the time. Thats probably accurate within a % or two.

[Big Limpin]

Now for the application:

If he is playing all draws, and can safely assume all 2pr and trips too (and draws 1 to trips), then if he draws 1...he has a draw ~55% of the time

Originally, i wanted to answer a question from Kurto, about what hands to play behind a villain who is raising all draws. That is, you will have to decide to play the hand or not before you see how many he draws. I made a chart of how likely he is to be betting a draw, based on what range of hands he is opening with.

Only a true maniac is open raising 22, but for 3 ranges:
-55 and better, with draws, hes on the draw 22% of his hands
-TT and better, with draws, hes on the draw 38% of his hands
-AA and better, with draws, hes on the draw 83% of his hands



*** note that this is if he's playing EVERY SINGLE DRAW HE GETS...which is probably a big strech. It's probably more likely hes playing like half of his draws. Obv the numbers would change to reflect that...

i.e. obviously if his range was some nittish >AA for the pair-hands, then he's not open-raising 3456. so the 83% number is clearly not realistic.

[MarkGritter]

Let's see... There are 13C4 different 4-flushes per suit, leaving 39 cards of a different suit to complete the hand (but not make a flush).

So 4 suits * 13C4 suited cards * 39 unsuited cards = 111,540, or about 4.3% of all 5-card hands. That comes out a little lower than your number.

OESDs are a bit tougher. If we ignore flushes for the moment, then we have:

2345, 3456, ..., TJQK = 9 different OESDs. Each OESD rank can be assigned to suits in 4^4 distinct ways. There are 40 cards left over that do not complete the straight (52 - 4 - 4 - 4). So 9 * 4^4 * 40 = 92,160 combinations. But some of these hands are flushes already!

Some of the straight draws are also 4-flushes, and vice versa. It's easier to calculate the number of straights which are also 4-flushes:

9 possibilities again. To be a 4-flush either 3 or 4 of the suits in the OESD must be identical.

4 suits identical: 4 suits * 9 OESDs * (52 - 4 - 8 cards completing the straight - 7 cards completing the flush) = 4 * 9 * 33 = 1188 combinations where the OESD is also a flush draw.

3 suits identical: 4 suits * 9 OESDs * 4 choices for card that doesn't match * 3 suits for that card * (13 - 3 - 2 suited cards that don't complete the straight) = 4 * 9 * 4 * 3 * 8 = 3456 combinations where the OESD is a 3-flush and the 5th card makes a 4-flush.

So:
111540 4-flushes
92160 OESDs
- 4644 draws to both
= 199056 draws, or 7.66% of all 5-card hands.

(Of course, some of these hands also include a pair.)

[Big Limpin]

good stuff mark, thx!
any idea why my approach to flushes was off? it seems so simple [img]/images/graemlins/confused.gif[/img]
so if you have 7.66% are 4flush or OESD...think that we can call that 9% if we include other stuff like AKQT, KsQsJs, etc? 'cause i really want to go for a beer, as opposed to fixing my posts [img]/images/graemlins/tongue.gif[/img] [img]/images/graemlins/wink.gif[/img]

[MarkGritter]

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any idea why my approach to flushes was off? it seems so simple [img]/images/graemlins/confused.gif[/img]


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The first part looks OK. When we start with two suited cards (12/51 of the time) then the probability that we get two suited cards in the next three is (11C2)*39/(50C3) = 0.1094.

The second part... we either get three of our first card or three of our second. There are (12C3) ways to "flop" three suited cards out of 50C3 possibilities = 220/19600 = 0.0112. Doubling that gives 0.0224 which doesn't agree with the number you used (0.0292).

Looks like you just grabbed the wrong row of the table:

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Three suited cards, Clubs or Spades 2.24 43.5 to 1 * Four parts of a Flush, much better if it includes Ace
Three suited cards, Diamonds or Hearts 2.92 33.3 to 1 * Unfavorable


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12/51 * 0.1094 + 39/51 * 0.0224 = 0.0429, which matches what I got.

[Big Limpin]

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Looks like you just grabbed the wrong row of the table:

[/ QUOTE ] [img]/images/graemlins/blush.gif[/img] [img]/images/graemlins/frown.gif[/img] [img]/images/graemlins/grin.gif[/img] [img]/images/graemlins/tongue.gif[/img]
el-oh-el. i go to pub now!