This post explains how you can take a few pieces of data from either
WinPoker or FrugalVP, and with one subtraction, one multiplication, and
then one addition, ... determine the exact needed value of a progressive
Royal for any particular strategy change under consideration (for
example, when to start discarding a Hi-Pair against a particular 3-Royal).
To put this in context, I started to write this in response to a post on
acvpp, but decided that it might be of interest to folks on a few of the
other VP maillists, so I'm taking the liberty of cross-posting this but
I'm dropping the names of other folks for their privacy. So, ... lets
just say that _some_people_ engaged in this brief exchange on
acvpp@yahoogroups.com; I am printing the posts in what I think was their
proper sequence (if I've gotten it mixed up, I apologize):
>>> I was told according to Stanford Wong if you have three cards to a
>>> Royal and a high pair...once the jackpot reaches a certain point you
>>> discard the high pair and keep the three to a Royal which goes
>>> against the 99.54 payback strategy.
>>>
>>> Is this true? If so,at which point does this occurs.
>>>
>>> Is there any change in strategy when you are playing a high jackpot
>>> progressive 9/6 JOB machine?
>> Yes, there is a change in strategy as the progressive goes up, but I'm
>> not aware of all of it.
>> Dancer said in one article, when it reaches about $1,500 on a quarter
>> game, you shoulc hold a suited A-10.
>> You can figure it out by plugging the numbers into Win Poker.
> Regarding the 3CRF holds vs. HP, it depends on what kind of 3CRF you have
> along with any associated penalties (skip the latter point for
simplicity).
>
> For example: KQJs is a better hold than AKQs and it will take a lower
> jackpot to hold KQJs over a high pair than AKQs.
>
> Regarding holding ATs, I believe it is correct to hold ATs even when the
> jackpot is at 4,700 coins (99.85%). The actual point I do not know.
Now I'll add my comments and examples ...
First of all, theoretically a progressive Royal _could_ get high enough
that you would discard _anything_ that would preclude a Royal -- even a
dealt straight-flush -- although as a practical matter the Royal
normally would never get that high in value before being hit by someone.
Second, if you have access to either WinPoker (hereafter 'WP') or
FrugalVP (hereafter 'FVP'), it is extremely easy to figure out the
transition point where the progressive attains the necessary value to
change your strategy; you can also do the math yourself without those
programs if you know what you're doing, but I'm not going to get into
that part of it in this post. With a program like WP or FVP, you simply
create a hand that has both the 3-Royal and a High-Pair, and any other
penalty situation that you want to create for your particular scenario;
in my first example, I will not include any flush or straight penalties
because that requires that the progressive be even higher, and they
don't often occur at the same time that we are faced with a choice
between a 3-Royal and a Hi-Pair.
The math is very simple once you have the data available from one of
those programs; I'll also give directions for both programs.
For my example, I will use KQJ-h Qd 7c ... which gives me a choice
between the 3-Royal and a pair of Queens ... and this is in JoB 9/6
full-coin (just so we're all on the same page). We open either one of
our poker programs and enter that hand; in FVP you do this through the
menu-bar -- 'Perfect Play | Create a Hand' -- and in WP, you can just
open any hand while in JoB 9/6 and then go to the 'Details' screen and
substitute the cards to build the above hand. Also, just so your
figures look like mine as we go through this, the first thing to do in
FVP is to go to 'Options | Tutor Options' and set your 'Decimal
Precision' to 6 digits, and then make sure you are in Perfect Play in
JoB 9/6.
In FVP, go to 'Strategy Charts | Create a Hand' ... or in WP access a
details screen (a button is on the right-side of the screen). In either
program, construct your hand given above; in the WP details screen for
ANY hand, you can substitute cards by clicking on them to build your
hand -- a feature that I've highly recommended to Jim Wolf for his next
FVP upgrade. Then, in FVP, click on 'Perfect Stats' at bottom-left on
screen; in WP you should already be looking at the stats. These screens
should now be listing the relative ER's for the 32 different holds that
can be made on this particular hand. For those who don't have both
programs, or neither, I'll list the necessary data; both programs list
the pair of queens as the proper hold, and the 3-Roy as the second
choice, and they provide the following stats for both hands. Now, I'm
going to put this data into a 'table' in this message (something
available in Netscape), so I hope it will display properly for those
using MS Internet Explorer; if it doesn't come out looking good, it's
not all that important because the only columns that we're really
interested in are 'ER' and 'Hands' (the number of hands that can be made
on a redraw, which is 1081 when keeping three cards); here's the table ...
Held Hand
ER
Hands
Roy
StFl
4Kd
Full
Fl
St
3Kd
2Pr
J-Bet
FVP
Qh Qd (Hi-Pair)
7.682701
16215
0
0
45
165
0
0
1854
2592
11559
KQJh (3-Roy)
7.442183
1081
1
1
0
0
43
30
7
21
318
WP
Pair of Queens (Hi-Pair)
7.6827
16215
0 0
45
165
0
0 1854 2592 11559
KQJ-h (3-Royal)
7.4422
1081
1
1
0
0
43
30
7
21
318
Except for the greater decimal precision of FVP, you will notice that
the data is identical from both programs. Now, looking at the data on
the lines for FVP, if we subtract the ER for a 3-Roy from the ER for the
Hi-Pair, we get a difference of 0.240518, which we then multiply by
1081 because that's the number of hands possible when discarding two
cards, and we find that the Royal must therefore increase in value
259.999958, which we will round up to 260. So, when the progressive
Royal is worth 4,259 we keep the pair of Queens, but when it reaches
4,260 we start keeping the 3-Royal. We can substitute those values, one
at a time, in our programs and test them, and we see that this is
correct. ********CAUTION******** the above transition point is ONLY for
a KQJ Royal without any penalties; other combinations and/or penalty
situations will necessarily change the relative ERs, resulting in a
delta which is different than 259.999958. ALSO, if you are doing a
succession of comparisons, be careful to always reset your paytable to
normal before making your initial comparison of ERs, and also be
cautious that you don't automatically look at just the top two lines (I
just did that on a calculation, and when I checked why it didn't work, I
noticed that the 3-Royal had dropped down to the 5th line and I had the
wrong ER).
Now I'll demonstrate changing the King of hearts to an Ace of hearts,
although I'm not going to put the entire line of data down in another
table; you can just check the programs to confirm it (I started to use
WinPoker's 4-decimal figures for this because I find WP easier for this
sort of thing, but then found that it's inaccuracy doesn't work out
precisely for this hand, as is explained in the next paragraph, so I
returned to FVP for my stats).
FVP shows the ER for AQJ-h is 6.961147 and that the Hi-Pair is ER still
7.682701, for a delta of .721554 which, when multiplied by 1081 hands,
gives an adjustment value of 779.999874; the inaccuracy with WP is that
it gives an ER for AQJ-h of 7.6827 and 6.9611 for the Hi-Pair, for a
slightly higher calculated delta of .7216 which causes an adjustment of
780.0496 when multiplied by 1081. The difference is that the above calc
for FVP indicates that when the Royal is 4,779 you hold the Queens but
when it is 4,780 you hold the 3-Royal; both programs, during play,
indicate that this is correct, although WP's figures (above) suggest
that the transition point should be one coin higher.
Finally, here is a hand which adds a straight penalty: AQJ-h Qd Tc.
FVP shows the ER for AQJ-h has dropped, due to the straight-penalty, to
6.887142, for a new delta of .795559 and a new adjustment of
859.999279. That is, for that hand you would hold the Hi-Pair if the
Royal pays 4859 coins or less, but when it reachs 4860 you start holding
the 3-Royal.
I hope some of you find this useful. Now I'd like to ask a favor. I am
in the process of writing strategy charts for 'One-Eyed Jacks' Video
Poker, and I'd like to know all of the different paytables out there for
this game. So ... if you all don't mind, please let me know what they
are; I'm not necessarily interested in where they are located, although
that info might be of interest to others, so please feel free to include
that in any post. If you prefer, you can send it to me via direct
e-mail: billvelek@alltel.net. Please be sure to list the entire
paytable including a brief description of each paying hand, since there
might be variations from game to game (some might not pay for a Hi-Pair
at all, others might pay for Kings or Better, etc.).
Note to Tom Sims: Tom, I haven't been very active lately, nor long on
your list, so I don't know if this particular technique has been
discussed before; if it has not, and you think it is worthwhile, please
feel free to add this to your permanent files.
Any help will be greatly appreciated.
Thank you.
Bill Velek
Coming Soon: www.beststrategycards.com or www.2plus2is4.com (haven't
decided which name to use)
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