Perfect Play

[shadowman]

Oh yeah, I played today and did hold A's with a 10, Q and A of hearts.  next to cards were a J and K of Hearts!  OUCH!!! That stung.  Made up a little - 2 hands later it dealt me quad 3's for a little consolation!
 
Just remember that the act of holding different cards is more than enough time to change the exact microsecond you hit the draw button. That is all it takes to change your results. In other words, had to held the 3 royal cards you may have drawn two more aces or any of the other 1080 possible draws.
 
There's no reason to speculate at the draw cards anymore (since around 2000) as they tell you nothing about what "might have happened".

[7come11]

Please allow me to reiterate for my own edification:   the more RF"s attempted despite proven strategy the more RF's will be won while at the same time the more money/credits will be lost.   A wonderful time to play a wild eyed , hairy legged strategy and have the greatest fun is during our winner take all contests where bragging rights are at stake  not actual funds.  Go for the gold.  Great luck to you.  I hope you win and should you do so please consider improving our international relations by sending our Canadian friend, Grandpa, a hat.  
 
You're right, it is a risk/reward gamble - guess that's the main reason we all go to casinos.  Plus it's a fun night out! Not too into the contests, for me it's about winning and fun.
Deal - next royal Grandpa get's a hat!  What size
Thanks for the wishes and feedback and may all your hands be quads and royals

[7come11]

that is the correct stratitigy for these contests or vp tournaments but for real money correct play for total return is the way
 
So in real play, you would hold the 5 as well and go for the flush giving up chance at a royal?  Just want to make sure I understand.
 
I just see the risk worth it as a possible flush really doesn't pay enough when you're that close - on the other hand - there's many times we've all got 4 to the royal!
 
Thanks so much Royal Flush

[MikeA]

SHADOWMAN, ROYAL FLUSH, FAYGOy'ALL Check my numbers on this PLEASEWhen drawing 1 card to a flush, you have 9 cards that can fill your hand and those 9 are mixed into the remaining 47 still in the deck.  That's just a little over a 1 in 5 chance of drawing a flush.  You might think that because of the relatively high frequency of drawing that fifth card to the flush, that it would be a no-brainer.With holding a 3RF and having to draw 2 to make a Royal out of it, you could hit either a straight, a flush, or 3-of-a-kind or get even money by catching a high pair.  However, with all of that:Running an analysis using 10/6 DDB as the game, the numbers might surprise you.The Value of the 3RF in the case of Ah Kh Qh 5h 7c is 6.808.  The Value of holding 4 to the flush is 6.702!  HOLDING THE 3RF IS THE CORRECT PLAY!  The analysis is rather complex.Holding for the 4-card flush, there are only 47 possible outcomes.  29 of those are no-win results.  There are 9 possible high pair combinations and there are also 9 ways to hit a flush.It's more complicated with the 3RF hold.There are 1,081 possible outcomes with this because of the two cards you are drawing.  646 of those are no-win combinations.  However, there are 348 ways to make a High Pair, 27 ways to get 2 pair, 9 ways to get 3OK, 15 ways to get a straight, 35 ways to make a flush and 1 way to make a Royal Flush.  Now, change one card.  Say you have Kh Qh Jh 5h 6c.  In that case, the odds on filling a flush with a 4-card hold are the same as with the other combination using the ACE instead of the JACK.  The Jack gives you more ways to make a Straight.  30 ways instead of just 15!  The number of ways to lose decreases to 631.  And the Value of the 3-card-Royal-Flush goes up to 7.289 while the value of the 4-card flush hold remains the same at 6.702.One other scenario is that you have a gut-draw (non sequential).  The return falls for the 3RF but there is more difference between the 4-card-flush draw and the 3RF draw.  That's because of the 10 in the mix.10h Jh Kh 5H 5c.  The point is that is seems that no matter how you look at it with DDB 10/6 or 9/6....your best hold is always the 3RF.(GOD!  I hope I'm reading those analysis correctly!!!!!)The analysis might be different with other games but not on DDB unless you change the value of the flush from 6 to 5 or something like that. Since in neither case are the odds or values going to change because of the decrease in value of the Full House (you can't get one with the combination of cards we've been talking about) the EV of the two hands would remain the same.I haven't looked at the results if it were JOB or DB or BP type games.

[shadowman]

MikeA, your analysis is correct for RF3 with 3 high cards. However, if one of the RF3 is a ten then the number of high pair winners is reduced and this drops that value of that hold. In this case, RF3 (ace high ... two high cards), returns less than FL4 (two high cards).
Note that both holds are reduced because of the lack of one high card. The RF3 is reduced more because with two cards to fill in there are more high card winners.
 
Also, note that this is the ONLY situation where FL4 beats out RF3.

[MikeA]

I would have thought as you on that because of the loss of numbers of ways to hit pairs.  I thought also that I'd covered all the combinations last night.  I DIDN'T.  I forgot about the 2-high-card 3RF hands.Good catch!I was "slow" last night and am pretty "slow" this morning too!  It took me a while to understand why the 2-high card 3RF was different depending on whether or not one of those 2 high cards was an ACE!  Obviously (well not so obviously to ME this morning!) You cannot get a normal SF if one of the cards is an ACE.  You can only get the Royal.                ev         #     no   hp    2p   3ok    st    fl   fh    4k    234   ace   234+ a234+  SF    RF K?J?10?    6.79          1,081    739    240    27    9    30    34    0    0    0    0    0    0    1    1K?J?10?5?    6.383          47    32    6    0    0    0    9    0    0    0    0    0    0    0    03RF 2 high cards when one IS an ACE10?J?A?5?    6.383    47    32    6    0    0    0    9    0    0    0    0    0    0    0    0     010?J?A?    6.30895    1,081    754    240    27    9    15    35    0    0    0    0    0    0    0    1All of these are relatively "close calls".  8-One-Hundreths of a coin difference is pretty significant at $.02 per wrong play at the Quarter level.

[faygo]

MikeA, Do you have a fever? Is it raining so that you can't play golf? The skunk is gone and now you don't have that to worry about? Sometimes my brain just hurts trying to understand all that odds business.  It would probably do me well to get that much in depth but for now I leave it to memorizing  VPW.
When SM gave you the . My work was done.

[MikeA]

When SM gave you the . My work was done.Yeah...too little sleep last night.  But to simplify the rule:When having to decide between a 4-card-flush hold and a 3RF hold:HOLD A 4-CARD-FLUSH DRAW ONLY IF YOUR 3RF CONTAINS A 10 AND AN ACE.  IN ALL OTHER CASES, HOLD THE 3RF.Oh, one other exception....if the card in the off suit (6c in our example, happened to be a high card paired with one of the cards in the 3RF set, then you hold the pair!  That's sort of anticlimactic isn't it?    The high pair hold is better than the flush hold.

[EDC1977]

Example, dealt 5,j,q,a of hearts and some low other card (6 of clubs or something). It told me to hold all the hearts (including the 5).
Not sure about the perfect call on that...I'll always hold 3 to the royal in that situation.
If I'm wrong for tossing the 5, then so be it. Curious, what would you or anyone else do?  I think the software was wrong.  Sure, I'm more likely to hit a flush at 5-1, but that's peanuts compared to a royal. I would hold the 4 FL given the gap in the sequence and the software I learned on. Considering the different payouts for the flush draw and the likelihood of actually drawing the fifth heart vs. 1/42k? RF draw, I'd be more apt to stick to whatever puts me in an advantage situation unless I'm absolutely on a roll, then MAYBE I'd roll the dice and hold the 3RF.

[grandpa]

[QUOTE=bigsteve5273@yahoo.c]Please allow me to reiterate for my own edification:   the more RF"s attempted despite proven strategy the more RF's will be won while at the same time the more money/credits will be lost.   A wonderful time to play a wild eyed , hairy legged strategy and have the greatest fun is during our winner take all contests where bragging rights are at stake  not actual funds.  Go for the gold.  Great luck to you.  I hope you win and should you do so please consider improving our international relations by sending our Canadian friend, Grandpa, a hat.  
 
You're right, it is a risk/reward gamble - guess that's the main reason we all go to casinos.  Plus it's a fun night out! Not too into the contests, for me it's about winning and fun.
Deal - next royal Grandpa get's a hat!  What size
Thanks for the wishes and feedback and may all your hands be quads and royals [/QUOTE]