Strategy Questions

[Tony Felder]

Hi all,


 
I am a newer gold member and just found this forum. I have read alot of great tips that I will be using. I do have a couple of questions that I was looking for help with.
 
I play mostly TDB and DDB multi-play and these are the two situations that perplex me.
 
1. Dealt a full house of AAA66 or 77755 do you keep the full house or toss the pair to go for the 4OAK?
 
2. Dealt AAAK2 or 444K3 do you keep the kicker(as the chart says) or do you toss both?
 
I have tried both ways but not sure I am playing it right. Looking for some insight from others. Thanks!!

[Frank Kneeland]

Hi all,


 
I am a newer gold member and just found this forum. I have read alot of great tips that I will be using. I do have a couple of questions that I was looking for help with.
 
I play mostly TDB and DDB multi-play and these are the two situations that perplex me.
 
1. Dealt a full house of AAA66 or 77755 do you keep the full house or toss the pair to go for the 4OAK?
 
2. Dealt AAAK2 or 444K3 do you keep the kicker(as the chart says) or do you toss both?
 
I have tried both ways but not sure I am playing it right. Looking for some insight from others. Thanks!!I'm sure I'll get flack for answering a question with a question, but I need more information to answer yours.You said, "you're not sure you're doing it right,"1. On what are you basing your decision of what's "right"?2. Are you familiar with the math used to determine VP strategy?If the answer to #2 is no I can explain the math and you can figure out the correct answer for yourself. I think this would be better than just answering your question.This is the sort of thing you'll only believe and have faith in if you do see the equations in front of you.

[New2vp]

1. Dealt a full house of AAA66 or 77755 do you keep the full house or toss the pair to go for the 4OAK?
 
2. Dealt AAAK2 or 444K3 do you keep the kicker(as the chart says) or do you toss both?Please don't look at the answer key until you calculate this for yourself.  And remember to show your work!  No credit unless you also justify why these answers are correct.1a.  Hold AAA   1b. Hold 77755    2a.  TDB: Hold AAA2   DDB: Hold AAA  2b.  TDB: Hold 4443  DDB: Hold 444. Disclaimer:  This is the answer for most common pay schedules if you want to maximize your average payoff.  Very unusual schedules or different goals may dictate different choices.

[Frank Kneeland]

I'm disappointed that the thread starter has not replied back yet. I'm waiting to hear if you know the math to figure this out and if not, if you'd like me to go over it with you.It's a lot to type so I'm waiting to see if it's needed.

[Tony Felder]

I most certainly interested in seeing the math. I guess maybe my wording of whats "right" wasn't correct. Thanks for offering to help Frank!!

[Frank Kneeland]

I most certainly interested in seeing the math. I guess maybe my wording of whats "right" wasn't correct. Thanks for offering to help Frank!!OK super. I'll type up a long reply and show all the work and how to do it yourself. I'm singing tonight karaoke so look for it tomorrow.

[Frank Kneeland]

So the questions posed by Tony are as
follows:

I
play mostly TDB and DDB multi-play and these are the two situations
that perplex me.

1.
Dealt a full house of AAA66 or 77755 do you keep the full house or
toss the pair to go for the 4OAK?

2.
Dealt AAAK2 or 444K3 do you keep the kicker(as the chart says) or do
you toss both?

If we plug these hands into our
favorite VP trainer it'll pump out what draws are the best, but what
these trainers won't do is show the midget behind the curtain and the
equations used for solving this. I have always been of the mind that
for faith in VP strategies it is imperative that we only use VP
trainers as a time saver if we understand what's being done for us.
This is an equivalent policy to school teachers only allowing
students to use calculators to do equations with their calculators
that they could, in a pinch, do by hand.

First we'll tackle AAA66 in DDB. I'm
assuming the 10-6-5 verity of DDB, since it's the only one slightly
over 100% return. The frequencies don't change so you can adjust them
for the other verities.

Standing Pat (AAA66) = 10.00 EV

(FH value of 10) x (Frequency of 1) /
(by total number of combinations of 1) = 10

(10 * 1) / 1 = 10


Drawing 2 (AAA) 66

We start with (AAA) there is only 1
remaining Ace in the hand rendering 1 way to get:

(AAA)A = 1

Then we need to fill in the 5th
card. After drawing the Ace from the 47 cards in the deck there are
46 left 12 of which give us bonus 4K and 34 of which give us normal 4
Aces.

(Bonus Aces Frequency of 12) x (Bonus
Ace pay of 1600) = 19,200
(Four Aces
Frequency of 34) x (Ace pay of 800) = 35,200

Total = 19,200
+ 35,200 = 54,400


Next we need to tackle Full Houses (FH)
and that's a tad harder. We need to introduce the concept of good and
bad ranks. Here Sixes are considered the bad ranks because you have
discarded two of them. All other ranks are considered “good”
because there are still 4 of them remaining in the deck.

(AAA) + (66) = 1 combination
1 x 50 = 50 EV

Then we can do a single calculation for
a good rank FH and multiply by the number of good ranks.

(AAA) + (KK) = ?

There are four Kings left in the deck
when you draw the first one and three left when you draw the second.
Since they can come in any order you then divide by 1x2 to remove
permutations.

4x3 / 1x2 = 6
So (AAA) + (KK) has a frequency of 6.
We started with 13 ranks. One of them was Aces, another was the Sixes
this left us with 11 good ranks. Therefore FH frequency with good
ranks is:

6 x 11 = 66

The EV for FH totaled is therefore:

(AAA) + Pair
(AAA) + BR = 50 EV
(AAA) + GR = 66 x 50 = 3300 EV

50 + 3300 = 3350 EV

Two calculate 3K is easier because we
can just subtract our preexisting work. Anything that isn't a FH or
4K will be a 3K. Drawing two cards there are 1081 combinations total:

47 x 46 / 1 x 2 = 1081

If we now subtract all the 4K and FH
from 1081 whatever is left will be 3K

1081 – 67(FH) – 46(4k) = 968 (3k)
968 x 15(3K pay) = 14,520 EV

Total Value of draw to (AAA) is
therefore:

4k EV = 54,400
FH EV = 3,350
3K EV = 14,520
54,400 + 3,350 + 14,520 = 72,270 EV

72,270 / 1081 = 66.8547 (EV in coins)

The value of standing pat is 50
coins. The Value of drawing to 3 Aces in DDB is 66.8547 coins. Quite
a difference. The draw is clearly better. A computer will tell you
this but there's no substitute for doing it by hand and seeing it
yourself.

I'll post the
others later.

[Tony Felder]

Wow, that's a huge difference, more so than I expected. Thanks for showing me the formula. I am just starting to play VP more seriously, about 10-12 hours a week in Detroit casino's. Have had good early results, so wan to continue to improve. Thanks for the info!!

[New2vp]

Tony, you have to watch Frank because he is a very tricky teacher.  You thanked him, but he purposely inserted a few key mistakes to see if you actually followed exactly what he was doing.  The corrections are shown below.  Now, go over this carefully to see if you really understood what he was doing and check to see if I have left any remaining mistakes.Of course, his methodology was correct, but don't let him catch you not paying attention again!So the questions posed by Tony are as
follows:

I
play mostly TDB and DDB multi-play and these are the two situations
that perplex me.

1.
Dealt a full house of AAA66 or 77755 do you keep the full house or
toss the pair to go for the 4OAK?

2.
Dealt AAAK2 or 444K3 do you keep the kicker(as the chart says) or do
you toss both?

If we plug these hands into our
favorite VP trainer it'll pump out what draws are the best, but what
these trainers won't do is show the midget behind the curtain and the
equations used for solving this. I have always been of the mind that
for faith in VP strategies it is imperative that we only use VP
trainers as a time saver if we understand what's being done for us.
This is an equivalent policy to school teachers only allowing
students to use calculators to do equations with their calculators
that they could, in a pinch, do by hand.

First we'll tackle AAA66 in DDB. I'm
assuming the 10-6-5 verity of DDB, since it's the only one slightly
over 100% return. The frequencies don't change so you can adjust them
for the other verities.

Standing Pat (AAA66) = 10.00 EV

(FH value of 10) x (Frequency of 1) /
(by total number of combinations of 1) = 10

(10 * 1) / 1 = 10


Drawing 2 (AAA) 66

We start with (AAA) there is only 1
remaining Ace in the hand rendering 1 way to get:

(AAA)A = 1

Then we need to fill in the 5th
card. After drawing the Ace from the 47 cards in the deck there are
46 left 12 of which give us bonus 4K and 34 of which give us normal 4
Aces.

(Bonus Aces Frequency of 12) x (Bonus
Ace pay of 1600) = 19,200  X (payoff is actually 2000 for the 10-6 game that is slightly over 100% return)
(Four Aces
Frequency of 34) x (Ace pay of 800) = 35,200  X (34 x 800 = 27,200)

Total = 19,200
+ 35,200 = 54,400


Next we need to tackle Full Houses (FH)
and that's a tad harder. We need to introduce the concept of good and
bad ranks. Here Sixes are considered the bad ranks because you have
discarded two of them. All other ranks are considered “good”
because there are still 4 of them remaining in the deck.

(AAA) + (66) = 1 combination
1 x 50 = 50 EV

Then we can do a single calculation for
a good rank FH and multiply by the number of good ranks.

(AAA) + (KK) = ?

There are four Kings left in the deck
when you draw the first one and three left when you draw the second.
Since they can come in any order you then divide by 1x2 to remove
permutations.

4x3 / 1x2 = 6
So (AAA) + (KK) has a frequency of 6.
We started with 13 ranks. One of them was Aces, another was the Sixes
this left us with 11 good ranks. Therefore FH frequency with good
ranks is:

6 x 11 = 66

The EV for FH totaled is therefore:

(AAA) + Pair
(AAA) + BR = 50 EV
(AAA) + GR = 66 x 50 = 3300 EV

50 + 3300 = 3350 EV

Two calculate 3K is easier because we
can just subtract our preexisting work. Anything that isn't a FH or
4K will be a 3K. Drawing two cards there are 1081 combinations total:

47 x 46 / 1 x 2 = 1081

If we now subtract all the 4K and FH
from 1081 whatever is left will be 3K

1081 – 67(FH) – 46(4k) = 968 (3k)
968 x 15(3K pay) = 14,520 EV

Total Value of draw to (AAA) is
therefore:

4k EV = 54,400
FH EV = 3,350
3K EV = 14,520
54,400 + 3,350 + 14,520 = 72,270 EV

72,270 / 1081 = 66.8547 (EV in coins)  X (just a tiny rounding error here; this would be 66.8548, but if you incorporate the corrections from above, the new EV rounds to 63.8945)

The value of standing pat is 50
coins. The Value of drawing to 3 Aces in DDB is 66.8547 coins. Quite
a difference. The draw is clearly better. A computer will tell you
this but there's no substitute for doing it by hand and seeing it
yourself.

I'll post the
others later.

[Frank Kneeland]

The mistakes were not intentional I went off the pay table in OpVP that I have on my home computer and didn't check it against one in a casino. I have never played 10-6 DDB and wouldn't have known the difference. Thanks new2vp.Far as I knew 1600 coins was the correct pay for Aces with a Kicker in DDB.~FK