EBGryph
EBGryph
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January 13th, 2025 at 5:27:34 PM permalink
Playing Ultimate Hold 'em on Wizard of Odds, I came across a scenario where it told me to fold.

Holding 4Qh
Board 7h 5s 256c

Strictly off of the 21 out rule, I'm seeing:
4xA,K
3x2,7,6
2x5

Total of 19 single card outs. Under the 21 should be a play. Is there a high level way for me to see this properly as a fold? Additional EV loss is marginal at -0.09, but I want to make sure I'm not missing something simple that's impacting a significant number of my low board hands.

Light bulb moment, because my queen is out kicked significantly over 66% of the time, do I add in some number of queens to the dealer outs?
PlayYourCardsRight
PlayYourCardsRight
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January 13th, 2025 at 7:02:18 PM permalink
Your queen is outkicked by everything except Q3 and the board also has flush and straight possibilities. That is a fold.
EBGryph
EBGryph
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January 13th, 2025 at 7:42:05 PM permalink
I agree, but that doesn't give a way to apply an applicable rule. For example, K3o on the same board also plays check check, but is then a play, and you can apply similar outkick logic, arbitrarily.

Basic strategy is never going to be perfect, i was just wondering if there was a simple add on to the 21 out rule to accommodate. Ex. On 19 or 20 dealer outs, play if kicker is greater then 6, similar to Crazy 4 hand strength.
unJon
unJon
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January 13th, 2025 at 8:04:18 PM permalink
Quote: EBGryph

I agree, but that doesn't give a way to apply an applicable rule. For example, K3o on the same board also plays check check, but is then a play, and you can apply similar outkick logic, arbitrarily.

Basic strategy is never going to be perfect, i was just wondering if there was a simple add on to the 21 out rule to accommodate. Ex. On 19 or 20 dealer outs, play if kicker is greater then 6, similar to Crazy 4 hand strength.
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I tend to think of a possible flush as an additional out and a possible straight as a possible out also.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
Romes
Romes
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January 13th, 2025 at 8:10:38 PM permalink
If I'm reading this correctly, board = 7h-5s-2c-5c-6c ...and you have Qh-4h. Also, your Q will always lose or tie as your 4 does not play in your best 5 card hand.

So the cards your Q can beat = 3, 4, 8, 9, 10, J... but not specifically "3-4" of course (but for this I don't think you need to worry about that 1 combination).

Assuming no other cards known, 4 of each (except the one 4 you have), so 4x6 = 24-1 = 23. Personally, I'd adjust this for the 3-4 (and possible flush), but even if you took it at 22 or 21... still qualifies for "21 or more outs," no?

Am I misreading something? EDIT: FYI I count "win" outs... aka cards I can beat.
Playing it correctly means you've already won.
unJon
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January 13th, 2025 at 8:14:39 PM permalink
Quote: Romes

If I'm reading this correctly, board = 7h-5s-2c-5c-6c ...and you have Qh-4h. Also, your Q will always lose or tie as your 4 does not play in your best 5 card hand.

So the cards your Q can beat = 3, 4, 8, 9, 10, J... but not specifically "3-4" of course (but for this I don't think you need to worry about that 1 combination).

Assuming no other cards known, 4 of each (except the one 4 you have), so 4x6 = 24-1 = 23. Personally, I'd adjust this for the 3-4 (and possible flush), but even if you took it at 22 or 21... still qualifies for "21 or more outs," no?

Am I misreading something? EDIT: FYI I count "win" outs... aka cards I can beat.
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I think you counted the cards he beats. The 21 out rule is counting the cards that beat you. But maybe I’m not following what you are saying.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
aceside
aceside
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January 13th, 2025 at 8:15:48 PM permalink
I just played this online calculator. These are the computer strategy:

Holding 4hQh; Board 7h 5s 2c5c6; calculator says Check.
Holding 4hQh; Board 7h 5s 2c5c8; calculator says Check.
Holding 4hQh; Board 7h 5s 2c5c9; calculator says Raise.
Holding 3hKs; Board 7h 5s 2c5c6; calculator says Raise.

The first three decisions are all marginal, so the less-than-21-out rule is good enough. If you really want something more accurate, and you may add this, one board under card to guarantee a Raise on marginal hands.
100xOdds
100xOdds
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January 14th, 2025 at 4:23:08 AM permalink
Interesting.
Never would have thought q4 would be a fold on that board.
My general rule is if paired board and not 4 flush, I'm allowed 2 overcards.

I never take into account 3 to a flush or gutshot straight.
Should I??

So is q4 no good because I lose to most other Queens?
So for the Op's board, I should consider there are 3 overs? A,k and Q because of kicker problems?
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
100xOdds
100xOdds
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January 14th, 2025 at 4:27:06 AM permalink
Quote: aceside

I just played this online calculator. These are the computer strategy:

Holding 4hQh; Board 7h 5s 2c5c6; calculator says Check.
Holding 4hQh; Board 7h 5s 2c5c8; calculator says Check.
Holding 4hQh; Board 7h 5s 2c5c9; calculator says Raise.
Holding 3hKs; Board 7h 5s 2c5c6; calculator says Raise.

The first three decisions are all marginal, so the less-than-21-out rule is good enough. If you really want something more accurate, and you may add this, one board under card to guarantee a Raise on marginal hands.
link to original post


Wait.. board 75256 is a fold but 75259 is bet?
Why??
How is a 9 weaker than a 6 if I have q4?
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
unJon
unJon
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January 14th, 2025 at 6:30:05 AM permalink
Quote: 100xOdds

Quote: aceside

I just played this online calculator. These are the computer strategy:

Holding 4hQh; Board 7h 5s 2c5c6; calculator says Check.
Holding 4hQh; Board 7h 5s 2c5c8; calculator says Check.
Holding 4hQh; Board 7h 5s 2c5c9; calculator says Raise.
Holding 3hKs; Board 7h 5s 2c5c6; calculator says Raise.

The first three decisions are all marginal, so the less-than-21-out rule is good enough. If you really want something more accurate, and you may add this, one board under card to guarantee a Raise on marginal hands.
link to original post


Wait.. board 75256 is a fold but 75259 is bet?
Why??
How is a 9 weaker than a 6 if I have q4?
link to original post



At a guess the 9 gives more dealer Qs that chop rather than beat you and removes a couple of dealer straights. It’s marginal enough already that little things tip balance.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
aceside
aceside
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January 14th, 2025 at 6:35:20 AM permalink
Let me list all the related computer strategies here:

Holding 4hQh; Board 7h 5s 2c5c6c; calculator says Fold.
Holding 4hQh; Board 7h 5s 2c5c8c; calculator says Fold.
Holding 4hQh; Board 7h 5s 2c5c9c; calculator says Bet.

Holding 4hQh; Board 7h 5s 2c5c6d calculator says Fold.
Holding 4hQh; Board 7h 5s 2c5c8d calculator says Bet.

So, both the rank and suit matter in this marginal situation.
EBGryph
EBGryph
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January 14th, 2025 at 6:46:26 AM permalink
I like the addition of the one board under card to tip the balance. Curious if it's actually better overall from an EV standpoint, or if it hurts in other spots.

Thanks for all the responses, definitely an interesting spot, for as close as it is.
aceside
aceside
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January 14th, 2025 at 6:49:45 AM permalink
Apparently it is better for your EV overall.
gordonm888
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gordonm888
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January 14th, 2025 at 6:53:53 AM permalink
Yes. I would count ~2 (of 3) Queens as also beating me , because I am likely to be outkicked (by QJ, QT, Q8) or tied. Also flush and straight possibility.

The rule of 21 is not perfect. There are exceptions both ways.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
unJon
unJon
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January 14th, 2025 at 7:58:51 AM permalink
It’s been a few years since I looked at this but my memory is that “21 Outs” is really something like “20 and a half outs” and things like three to a flush are worth somewhere close to half an out.

If I find some time I’ll dig up the math I did at the time.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
NameBanned
NameBanned
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January 14th, 2025 at 10:11:49 AM permalink
More straight possibilities with the 6. 4,8 and 4,3.

Against a 9, the only possible straight is 6,8.
100xOdds
100xOdds
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January 14th, 2025 at 3:05:34 PM permalink
Quote: unJon

It’s been a few years since I looked at this but my memory is that “21 Outs” is really something like “20 and a half outs” and things like three to a flush are worth somewhere close to half an out.

If I find some time I’ll dig up the math I did at the time.
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So a 3 flush with gutshot would be 1 out?
Now I need to start counting instead of how many overs I'm allowed.
I currently do 'Non-paired board is 1 over, paired is 2 overs, 2pair or trips is 3 overs' as an easy shortcut
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
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