vpFREE2 Forums

Is This Your Lucky Day?

#1

I've been thinking about a way of looking at short term vs. longer
term expectations so let's run it up the flagpole and see who shoots
it down.

Let's say you played a session of 1,500 hands of FPDW. What would
your expected results be?

TABLE 1 - Expected hand frequencies for 1,500 hands of FPDW (Exact)

RF.......0.03
4D.......0.31
WR.......2.69
5K.......4.80
SF.......6.18
4K......97.41
FH......31.84
FL......24.87
ST......84.85
3K.....426.82

Of course, you can't get a fraction of a hand so Table 1 needs to be
rounded.

TABLE 2 - Expected hand frequencies for 1,500 hands of FPDW (Rounded)

RF.......0
4D.......0
WR.......3
5K.......5
SF.......6
4K......97
FH......32
FL......25
ST......85
3K.....427

So, what kind of a return would this give you?

TABLE 3 - Expected return for 1,500 hands of FPDW (Credits)

RF.........0
4D.........0
WR.......375
5K.......375
SF.......270
4K.....2,425
FH.......480
FL.......250
ST.......850
3K.....2,135
Total..7,160

In 1,500 hands, you risk 7,500 credits and expect 7,160 back for a
95.47% return. Even though you are playing a positive expectation
game, your expected short term results are a 340 credit ($85.00)
loss. In other words, you have to be lucky in order to have a
winning session. Neutral or bad luck would result in a loss.

Now let's say you played 30 such sessions. What would your expected
results be? 30 times $85.00 loss = $2,550 loss? Of course not. You
have to reanalyze the game for 45,000 hands.

TABLE 4 - Expected hand frequencies for 45,000 hands of FPDW (Exact)

RF.........0.99
4D.........9.17
WR........80.81
5K.......144.07
SF.......185.39
4K.....2,922.22
FH.......955.31
FL.......746.13
ST.....2,545.40
3K....12,804.49

Rounding to the nearest whole number.

TABLE 5 - Expected hand frequencies for 45,000 hands of FPDW (Rounded)

RF.........1
4D.........9
WR........81
5K.......144
SF.......185
4K.....2,922
FH.......955
FL.......746
ST.....2,545
3K....12,804

TABLE 6 - Expected return for 45,000 hands of FPDW (Credits)

RF.......4,000
4D.......9,000
WR......10,125
5K......10,800
SF.......8,325
4K......73,050
FH......14,325
FL.......7,460
ST......25,450
3K......64,020
Total..226,555

In 45,000 hands, you risk 225,000 credits and expect 226,555 back for
a 100.69% return. Even though each individual session of 1,500 hands
has a negative expectation, your expected results for 45,000 hands
are a 1,555 credit ($388.75) win. In other words, you no longer have
to be lucky to win, you just have to avoid being unlucky. Neutral or
good luck results in a win. Bad luck, if it's bad enough, results in
a loss.

Even though it's accurate to say that luck plays a large part in the
results of a short individual session (assuming an appropriate level
of skill), it's not accurate to extrapolate those expectations over
the long term where luck is slowly filtered out and skill combined
with choice of game become the important factors influencing results.

#2

Throw in a little standard deviation which I think is around 1% [ a little birdie told me, I didn't figure that out <g>] and you could go from a loser to a big winner in the 45000 hand run.

IMHO, I call "luck" standard deviation. Over a lifetime of VP the standard deviation is what generally will separate the winners from the losers assuming they are of equal skill levels and playing a near-perfect game.

ADR
[whispering to myself "I know I'm going to be sorry I stepped into this thread]

···

At 05:19 PM 3/10/03, you wrote:

Even though it's accurate to say that luck plays a large part in the
results of a short individual session (assuming an appropriate level
of skill), it's not accurate to extrapolate those expectations over
the long term where luck is slowly filtered out and skill combined
with choice of game become the important factors influencing results.

#3

Could this possibly be why Ive played 144,000 hand of deuces without
getting a royal flush?? If so when can I expect to get one??

···

----- Original Message -----
From: "adr" <adr@basicallycredit.com>
To: <vpFREE@yahoogroups.com>
Sent: Monday, March 10, 2003 5:33 PM
Subject: Re: [vpFREE] Is This Your Lucky Day?

At 05:19 PM 3/10/03, you wrote:
>Even though it's accurate to say that luck plays a large part in the
>results of a short individual session (assuming an appropriate level
>of skill), it's not accurate to extrapolate those expectations over
>the long term where luck is slowly filtered out and skill combined
>with choice of game become the important factors influencing results.

Throw in a little standard deviation which I think is around 1% [ a little
birdie told me, I didn't figure that out <g>] and you could go from a

loser

to a big winner in the 45000 hand run.

IMHO, I call "luck" standard deviation. Over a lifetime of VP the standard
deviation is what generally will separate the winners from the losers
assuming they are of equal skill levels and playing a near-perfect game.

ADR
[whispering to myself "I know I'm going to be sorry I stepped into this

thread]

vpFREE Links:
http://www.lvcm.com/tomesims/VP/Links.html

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/

#4

Alan,

I think you're to be commended for taking the time to put together the
tables that illustrate "expected" return based on few and many hands played.

But I think that over any individual short term segment a player has NO
reasonable expectations on return. Even when many short term sessions are
factored in, the ER you describe is still only expected, not guaranteed.

The difference between short and long term have been discussed here numerous
times and opinions are all over the place, including a few who say that in
reality there is no long term. Imagine that!

My view of the luck factor is that you put yourself in a position to be
lucky by doing everything you can to increase your playing time, and by
playing with optimal strategy, so that you'll be the one sitting there if
and when the big hands hit. Other than that, over our many short term
sessions we are subject to unpredictable deviations, and it's fairly
pointless to expect anything. If our play falls anywhere near the expected
distribution, we'll be okay. If it isn't, we're sunk till next time.

lb
--JOB: about even--
--DW: about even--
---BP: about even--
--vpfree posts: about even--

···

----- Original Message -----
From: "Alan Peterson" <alan@peterson.net>
To: <vpFREE@yahoogroups.com>
Sent: Monday, March 10, 2003 5:19 PM
Subject: [vpFREE] Is This Your Lucky Day?

I've been thinking about a way of looking at short term vs. longer
term expectations so let's run it up the flagpole and see who shoots
it down.

Let's say you played a session of 1,500 hands of FPDW. What would
your expected results be?

TABLE 1 - Expected hand frequencies for 1,500 hands of FPDW (Exact)

RF.......0.03
4D.......0.31
WR.......2.69
5K.......4.80
SF.......6.18
4K......97.41
FH......31.84
FL......24.87
ST......84.85
3K.....426.82

Of course, you can't get a fraction of a hand so Table 1 needs to be
rounded.

TABLE 2 - Expected hand frequencies for 1,500 hands of FPDW (Rounded)

RF.......0
4D.......0
WR.......3
5K.......5
SF.......6
4K......97
FH......32
FL......25
ST......85
3K.....427

So, what kind of a return would this give you?

TABLE 3 - Expected return for 1,500 hands of FPDW (Credits)

RF.........0
4D.........0
WR.......375
5K.......375
SF.......270
4K.....2,425
FH.......480
FL.......250
ST.......850
3K.....2,135
Total..7,160

In 1,500 hands, you risk 7,500 credits and expect 7,160 back for a
95.47% return. Even though you are playing a positive expectation
game, your expected short term results are a 340 credit ($85.00)
loss. In other words, you have to be lucky in order to have a
winning session. Neutral or bad luck would result in a loss.

Now let's say you played 30 such sessions. What would your expected
results be? 30 times $85.00 loss = $2,550 loss? Of course not. You
have to reanalyze the game for 45,000 hands.

TABLE 4 - Expected hand frequencies for 45,000 hands of FPDW (Exact)

RF.........0.99
4D.........9.17
WR........80.81
5K.......144.07
SF.......185.39
4K.....2,922.22
FH.......955.31
FL.......746.13
ST.....2,545.40
3K....12,804.49

Rounding to the nearest whole number.

TABLE 5 - Expected hand frequencies for 45,000 hands of FPDW (Rounded)

RF.........1
4D.........9
WR........81
5K.......144
SF.......185
4K.....2,922
FH.......955
FL.......746
ST.....2,545
3K....12,804

TABLE 6 - Expected return for 45,000 hands of FPDW (Credits)

RF.......4,000
4D.......9,000
WR......10,125
5K......10,800
SF.......8,325
4K......73,050
FH......14,325
FL.......7,460
ST......25,450
3K......64,020
Total..226,555

In 45,000 hands, you risk 225,000 credits and expect 226,555 back for
a 100.69% return. Even though each individual session of 1,500 hands
has a negative expectation, your expected results for 45,000 hands
are a 1,555 credit ($388.75) win. In other words, you no longer have
to be lucky to win, you just have to avoid being unlucky. Neutral or
good luck results in a win. Bad luck, if it's bad enough, results in
a loss.

Even though it's accurate to say that luck plays a large part in the
results of a short individual session (assuming an appropriate level
of skill), it's not accurate to extrapolate those expectations over
the long term where luck is slowly filtered out and skill combined
with choice of game become the important factors influencing results.

vpFREE Links:
http://www.lvcm.com/tomesims/VP/Links.html

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/

#5

But I think that over any individual short term segment a player

has NO reasonable expectations on return.

I don't think that's quite true. What I was illustrating was that,
even in a positive expectation game, you are more likely to lose an
individual session than you are to win.

Even when many short term sessions are factored in, the ER you

describe is still only expected, not guaranteed.

No argument there.

The difference between short and long term have been discussed here

numerous times and opinions are all over the place, including a few
who say that in reality there is no long term. Imagine that!

I would agree that there really is no long term for a human being
playing a finite number of hands. However, the more hands you play,
the more you APPROACH the long term and the more likely it is that
you'll be close to expected results.

My view of the luck factor is that you put yourself in a position

to be lucky by doing everything you can to increase your playing
time, and by playing with optimal strategy, so that you'll be the one
sitting there if and when the big hands hit.

Agreed.

Other than that, over our many short term sessions we are subject

to unpredictable deviations, and it's fairly pointless to expect
anything. If our play falls anywhere near the expected distribution,
we'll be okay. If it isn't, we're sunk till next time.

While it's true that anything can happen in any one session, I
wouldn't dismiss the value of expectation. The fact remains that if
you play a negative expectation game, you will probably lose over
time and if you play a positive expectation game, you will probably
win over time. But, as you point out, nothing is guaranteed.

#6

I would agree that there really is no long term for a human being

playing a finite number of hands. However, the more hands you play,
the more you APPROACH the long term and the more likely it is that
you'll be close to expected results.<<

I think your observation is correct, but of course there is a theoretical
long term. The questions are:

1. What constitutes long term? You've seen models for 100,000 hands, a
million hands, with results falling closer to expected as the number
increases. But the math, itself, is predicated on infinite results with
each lower run measured against those results.

2. If X hands constitutes a valid sample, then where and when must those
X hands be played? Could you expect the same results playing all X hands on
one machine as playing one hand each on X different machines? My sense is
that if there's such a thing as a timeline then it belongs with the machine,
not the player, since it's the machine that deals the cards. The machine is
proactive while the player is reactive.

3. What factors determine results? I think it boils down to two things,
deviations from the normal distribution and level of expertise. Almost
invariably you will see deviations which are unpredictable. Some say they
haven't had a rf in 200,000 hands, others say they've hit three within
50,000 for example. Expertise allows you to stay in the game longer hoping
for a deviation that is profitable. It's unlikely that you will see the
normal distribution but you've got to play as if you will.

···

----- Original Message -----
From: "Alan Peterson" <alan@peterson.net>
To: <vpFREE@yahoogroups.com>
Sent: Tuesday, March 11, 2003 7:57 AM
Subject: [vpFREE] Re: Is This Your Lucky Day?

> But I think that over any individual short term segment a player
has NO reasonable expectations on return.

I don't think that's quite true. What I was illustrating was that,
even in a positive expectation game, you are more likely to lose an
individual session than you are to win.

> Even when many short term sessions are factored in, the ER you
describe is still only expected, not guaranteed.

No argument there.

> The difference between short and long term have been discussed here
numerous times and opinions are all over the place, including a few
who say that in reality there is no long term. Imagine that!

I would agree that there really is no long term for a human being
playing a finite number of hands. However, the more hands you play,
the more you APPROACH the long term and the more likely it is that
you'll be close to expected results.

> My view of the luck factor is that you put yourself in a position
to be lucky by doing everything you can to increase your playing
time, and by playing with optimal strategy, so that you'll be the one
sitting there if and when the big hands hit.

Agreed.

> Other than that, over our many short term sessions we are subject
to unpredictable deviations, and it's fairly pointless to expect
anything. If our play falls anywhere near the expected distribution,
we'll be okay. If it isn't, we're sunk till next time.

While it's true that anything can happen in any one session, I
wouldn't dismiss the value of expectation. The fact remains that if
you play a negative expectation game, you will probably lose over
time and if you play a positive expectation game, you will probably
win over time. But, as you point out, nothing is guaranteed.

vpFREE Links:
http://www.lvcm.com/tomesims/VP/Links.html

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/

#7

WE play 1500-2000 hands 5 or 6 nites a week. Playing 1500 hands
ANYTHING can happen. It is much to short a period for ANY math to be
valid. We have never had a lsing year in the 6 years we live here, but
many many losing 1500 hand nites. You can not predict any expectation
on this small a sampling.

···

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#8

WE play 1500-2000 hands 5 or 6 nites a week. Playing 1500 hands

ANYTHING can happen. It is much to short a period for ANY math to be
valid. We have never had a lsing year in the 6 years we live here,
but many many losing 1500 hand nites. You can not predict any
expectation on this small a sampling.

Actually, you can. Don't forget that the math is at work on every
single hand. While nobody can say, "The next time you play, you're
going to win $X." Someone who analyzed the game could say, "You have
an X% chance of winning your next session" or "The probablility that
you'll lose more than $100 is X%" and if you examined the results
from all your sessions of the past 6 years, you'd see that the
distribution is pretty close to what the math would predict.

#9

1. What constitutes long term? You've seen models for 100,000

hands, a million hands, with results falling closer to expected as
the number increases. But the math, itself, is predicated on
infinite results with each lower run measured against those results.

The royal flush is the mortal enemy of the long term. Every time you
hit one (IF you hit one), it changes your return dramatically.

2. If X hands constitutes a valid sample, then where and when must
those X hands be played? Could you expect the same results playing
all X hands on one machine as playing one hand each on X different
machines? My sense is that if there's such a thing as a timeline
then it belongs with the machine, not the player, since it's the
machine that deals the cards. The machine is proactive while the
player is reactive.

It doesn't matter where and when you play. The expected results
don't change. The actual results may be different but you can't know
that in advance nor can you know what would have happened if you had
moved to another machine.

3. What factors determine results? I think it boils down to two

things, deviations from the normal distribution and level of
expertise. Almost invariably you will see deviations which are
unpredictable. Some say they haven't had a rf in 200,000 hands,
others say they've hit three within 50,000 for example. Expertise
allows you to stay in the game longer hoping for a deviation that is
profitable. It's unlikely that you will see the normal distribution
but you've got to play as if you will.

A word here about "normal distribution." VP results do not give you
a true normal distribution. Because of bonus hands like the royal,
you are more likely to have a losing session than you are to have a
winning session but you are more likely to have a big winning session
than you are to have a big losing session.

#10

The royal flush is the mortal enemy of the long term. Every time you
hit one (IF you hit one), it changes your return dramatically.

I'm not sure what point you're making here or below, where you say...

VP results do not give you
a true normal distribution. Because of bonus hands like the royal,
you are more likely to have a losing session than you are to have a
winning session but you are more likely to have a big winning session
than you are to have a big losing session.

Theoretical long term results include a proportional distribution of rfs
along with everything else. If you're saying that short term results won't
give you a normal distribution, then okay. Otherwise, wha? And what's this
thing about the rf being the enemy of long term? Doesn't compute.

It doesn't matter where and when you play. The expected results
don't change. <<

This is firmly a matter of opinion, but here's an analogy. If you were
without water in the desert and you came across two water fountains a couple
of miles apart, and were told that each fountain goes on for 10 seconds an
average of every 125 hours, would you run back and forth between the two of
them hoping one will turn on while you're there, or would you camp out at
one of them and hope for it to turn on? Obviously, odds are you're dead meat
either way, but is there an advantage to one approach over the other?

#11

That all depends on the water. Is the water drinkable at both fountains? Are there ice cubes at either "fountain"? Can we throw coins in the fountain, make a wish, and it be granted? Are either of these fountains at or near a rest stop on the I-15 to LV?

ADR

···

At 08:46 PM 3/12/03, you wrote:

If you were
without water in the desert and you came across two water fountains a couple
of miles apart, and were told that each fountain goes on for 10 seconds an
average of every 125 hours, would you run back and forth between the two of
them hoping one will turn on while you're there, or would you camp out at
one of them and hope for it to turn on?

#12

Theoretical long term results include a proportional distribution

of rfs along with everything else. If you're saying that short term
results won't give you a normal distribution, then okay. Otherwise,
wha? And what's this thing about the rf being the enemy of long
term? Doesn't compute.

For a very good explanation of the normal distribution as it applies
to VP, see: http://www.jazbo.com/videopoker/curves.html

As far as the Royal Flush being the enemy of the long term, consider
this: let's say you played 800,000 hands of $.25 FPDW
($1,000,000 coin-in) and had a return of exactly 100.76%. Your
profit would be $7,600. On the next hand, you hit a royal. Your
profit is now $8,600 -- an profit increase of 13% on one hand. Use
the same scenario after 8,000,000 hands and your profit increase
after hitting a royal would still be 1.3%. How can you say you've
reached the long term if one hand can still make that much of a
difference?

It doesn't matter where and when you play. The expected results

don't change.

This is firmly a matter of opinion, but here's an analogy. If you

were without water in the desert and you came across two water
fountains a couple of miles apart, and were told that each fountain
goes on for 10 seconds an average of every 125 hours, would you run
back and forth between the two of them hoping one will turn on while
you're there, or would you camp out at one of them and hope for it to
turn on? Obviously, odds are you're dead meat either way, but is
there an advantage to one approach over the other?

OK, I'll bite. If you run back and forth between fountains, you run
the risk of being caught between fountains or at the wrong fountain
when one of them turns on. If you stay at one fountain, you're
guaranteed to get its water when it turns on. This is not to mention
the wasted energy expended running back and forth.

Now, back to VP. Since all VP machines are just computers which deal
random (or pseudo-random) hands, given the same game and pay table,
one is not inherently better or worse than any other. Therefore,
expected results -- no different. Actual results if you had chosen
machine A vs. if you had chosen machine B -- not knowable.

#13

How can you say you've

reached the long term if one hand can still make that much of a
difference?<<

I see your point, but I don't recall anyone saying that the long term had
been reached, unless I missed something in a previous post. Most analysis of
long term are amalgams of many samplings, with a prediction that results
will fall within a certain range, but even some results within those ranges
result in a loss. For most players, measuring results against long term
models is really pointless. So in that sense, I agree with you, which is
why I mentioned earlier that in the short term there are NO expectations (if
I recall, the sample mentioned was 1500 hands).

  >> Actual results if you had chosen

machine A vs. if you had chosen machine B -- not knowable.<<

Right, not knowable. But just for the sake of argument, if both events (the
fountains and the machines) are truly random, and logic dictates a certain
action in one case, why wouldn't logic dictate the same action in the other?

lb