Multiple Hand VP Games

[futrend]

<futrend@yahoo.com> Subject: Multiple Hands

"Is there any reason to play multiple hands in video poker? Does it
depend a little upon the type of game (wild cards or not)? Do serious
players only play one hand at a time and increase the size of their
bet if they want more dollars at risk? I notice the payoff schedules
sometimes change depending upon the number of hand played. What is
the reason for the house using this tactic? I am interested in any
information or opinions on this subject."
   
Thanks to those who have responded to my multiple hands question. I
am relatively new to this board and have learned to appreciate and
respect all the information received. I understand and accept the
idea of reduced volatility (short term) because some hands may
payback at least a few coins even if the original is washout.
    Originally I thought playing multiple hands was a big advantage.
I only thought of the potential benefit of holding and multiplying
strong hands. Most responses to a similar question posted about a
month ago inferred there was not a long term advantage to play
multiple hands. The logic expressed was that you also multiplied
your poor hands, not disregarding the fact that some of these poor
hands can end up earning some coins. In fact if you need to discard
all 5 cards, you still have a potential to be dealt a really strong
new hand and the more hands played in the game the greater this
chance. I do understand and have experience the excitement of
holding a real strong hand before pushing the "deal" button. This
also has caused similar disappointments when 4 to a royal comes up
empty after 4 or 9 more chances.
    I am inexperienced and this is the reason for posing the multiple
hand question again. However, I want to share some information that
I have gathered. Personal experiences at this time leans towards the
possibility that it is maybe a distinct disadvantage to play multiple
hands. I thought maybe this is why machines manufacturers are
willing to have a better pay schedule on some multiple hand games.
However, I would think this machine advantage can eventually be a
problem and thus a return back to poorer pay schedules on very high
multiple hand games (maybe 20 and higher).
    I want to share some limited personal experiences. I have been
learning and practicing JoB and Deuces Wild on Frugal VP. I have
been practicing and playing both 5 and 10 hands (thus 25 or 50 coins
versions). At the same time I am also running a personal calculator
and monitoring the result if only 1 hand or 5 coins was played on the
same hands. Granted, my play is not perfect since I do make a few
mistakes. However I have improved significantly and usually have
earned over 99.5% of the possible EV. Up to this point in time, my
playing results have caused me to think that multiple hands is a
financial disadvantage. I realize the increased opportunity of Royal
Flushes and have actually obtain about 4 in those multiple hands.
One time I was dealt the flush in my playing hand. In absence of a
royal flush, and that has been the case most of the practice hours, I
usually have had decidedly poorer results with both the 5 and 10 hand
versions. Without a RF, my winnings should be a multiple of greater
than 5 or 10 times and my losses should be less than 5 or 10 times.
Gentlemen, up to this point the opposite has been true. I have
significantly less winnings or greater losses on those runs playing
multiple hands (assuming the 5 or 10 multiple of coins played).
These trials are more than a few sessions long. I save the my single
hand results in order to pick up where I have left off. More hands
need to be played, but the trials have been in the many thousands of
hands at this point in time. I have also experienced less short term
volatility, as suggested by some of you, but significant longer term
volatility with the multiple hands. This would result from
multiplying too many very poor hands. This appears to more than
offset those hands that are less volatile (in the short run) than the
dealt hand. At times my winnings surge ahead, or losses are reduced
quickly when strong hands are multiplied. However, given enough time
the multiple hands seem to return again to a financial disadvantage
over the 1 hand option..
    I have posted the question because of my limited experience and
knowledge. I started to become suspicious when I saw higher pay
schedules for the greater number of hands. Usually no change with 3
hands but better pay schedules with 5 hands. I also found it curious
that a Deuces Wild was not offered in a 5 hand version on the same
machine that offered 3 and 5 had JoB and a 3 hand Deuces Wild. I was
wondering if that was because wild card games might be a better
choice for multiple hand games and thus manufacturers are a little
more reluctant to offer as many multiply hand wild card games with
better pay schedules. I am just thinking and reading your responses
to learn more about this and other video poker concepts

Thanks, Bob

···

Date: Thu, 08 Jul 2004 04:26:50 -0000 From: "futrend"

[rockofjello333]

There are a couple of things you should realize. First, your data,
however carefully correlated, are almost certainly derived from too
small a sample size to have real statistical meaning. The fact of the
matter is, you SHOULD have posted results that were either
significantly BETTER, OR significantly WORSE than "expected". What was
NOT at all likely to happen, was that the result came out the way it
"should" have. This is a function of what we call "The Law of Large
Numbers".

Imagine a coin flipped 1,000 times. Would we expect it to come up
"heads" EXACTLY 500 times? Of course not. A result something like 483
heads and 517 tails would be more like what we would expect. So we may
be "off" in our results by 3 percent or more, and not be surprised.
BUT, we WOULD be quite surprised if the 3 percent error showed up if
we flipped the coin a MILLION times, even though in this case it is
even LESS likely that we will achieve the "theoretical" result
(500,000 heads). This tells us two things:

1. You never DO get even "in the long run".
2. However, you get closer and closer to even the longer you play.

Of course, for "even" you can substitute "the theoretical result".

Second, there is no mathematical difference in the expected value of a
given play between, say, a 4-play .25 machine and a $1 single-line
machine with identical paytables. Examine, as an example, the best and
worst results---a royal flush, and a complete loser. Now, the 4-liner
will only achieve the ultimate 800-1 payout if there is a DEALT royal
(if one royal is hit the actual payoff is only 200-1); we get the
800-1 payout on the single-liner if we DRAW a royal, which is
obviously a lot easier. Similarly, it's very easy to lose the whole
bet on a single-liner, but this rarely happens on the 4-liner (even if
we draw five cards, we frequently get at least ONE paying hand). So
the net effect of the four-liner is to cut down on extreme results at
both ends of the bell curve. BUT, the net EV is the same. There is no
mathematical difference between drawing one to a flush 100 times for
$1 each and drawing one for $100.

So, the real difference between multi-liners and single-liners is that
one can play "X" dollars on multi-liners with lower volatility than on
an equivalent single-liner. This meant--and this is what has KILLED
fullpay multiline poker--that people with relatively short bankrolls
can increase their coin-in, and earn points and cashback at a
significantly increased rate, without the risk of ruin they would
experience playing a single-liner with the same total bet size. And
the casinos, since they want everyone to LOSE, HATE this circumstance
big-time.

[Steve_Jacobs]

You only get closer and closer if you express the results in terms
of percentages, and this results in the standard deviation percentage
shrinking at a rate proportional to 1/sqrt(N) where N is the number of flips.

In absolute terms, the standard deviation (s.d.) GROWS at a rate that is
proportional to sqrt(N). So, if S is the standard deviation of a single
coin flip, then the s.d. of your bankroll after 10,000 flips is 100*S,
and after 1 million flips this grows to 1000*S. When expressed as
percentages, these same numbers look like S/100 and S/1000.

Closer in terms of percentages, further away in absolute dollars.

···

On Friday 09 July 2004 01:04 am, rockofjello333 wrote:

There are a couple of things you should realize. First, your data,
however carefully correlated, are almost certainly derived from too
small a sample size to have real statistical meaning. The fact of the
matter is, you SHOULD have posted results that were either
significantly BETTER, OR significantly WORSE than "expected". What was
NOT at all likely to happen, was that the result came out the way it
"should" have. This is a function of what we call "The Law of Large
Numbers".

Imagine a coin flipped 1,000 times. Would we expect it to come up
"heads" EXACTLY 500 times? Of course not. A result something like 483
heads and 517 tails would be more like what we would expect. So we may
be "off" in our results by 3 percent or more, and not be surprised.
BUT, we WOULD be quite surprised if the 3 percent error showed up if
we flipped the coin a MILLION times, even though in this case it is
even LESS likely that we will achieve the "theoretical" result
(500,000 heads). This tells us two things:

1. You never DO get even "in the long run".
2. However, you get closer and closer to even the longer you play.