I respectfully disagree with a portion of what you state.
While I obviously agree with the part of your post that considers
Double-Up to be a seperate game from VP, I disagree with the part
that says because Double-Up is a 100% game that it makes no
difference to EV.
I think we may be confusing a few terms. I agree that in the end
you will have (on average) the same number of coins in your bucket
whether you play Double-Up or not, but this means that your net
win/loss does not change. I'm not sure of the official term for
this... Net win/loss....Return on Investment....etc...
However, by choosing to play Double-Up, you are playing more games
(assuming you keep the number of VP hands constant as we have so far
in our examples), thus you are risking more while winning/losing the
same, which creates a new percentage.
Perhaps a new example will illustrate this better:
You and your buddy have 2 hours before you need to head to the
airport. A hand of VP takes 10 seconds (600/hr). A hand of Double-
Up takes 10 secons (600/hr). (Note: the math will work with any
rate/hr, even if the two games don't have the same rate. I'm just
trying to keep the algebra as simple as possible for this example)
So, you sit down at a 9/6 JOB machine and start playing. Your buddy
does the same. You decide to forgo the double-up option
completely. Your buddy decides to play it after every High Pair
(again, the math will work if he chose to play EVERY hand double-up,
but I'm using a realistic option here).
After 2 hours, you would have played 1200 hands, putting in 6000
coins and miraculously the machine played right to theoretical
numbers and you have 5976 coins. You've lost 24 coins.
Your buddy on the other hand will play 980 VP hands and 220 Double-
Up hands (using an assumption of approx 22.5% of all hands end in a
High pair). He will pump 4900 coins into VP and 1100 coins into
Double-Up. Again, miraculously both games paid out on their
theoretical averages. From VP he will have 4880 returned. From
Double-Up he will have 1100 coins returned. A total of 5980 coins.
You both wagered 6000 coins. You both played 1200 total games of
chance (and skill). Why did your buddy wind up with 4 more coins?
Your EV was 99.6. His was 99.66%
This isn't due to rounding or anything like this. It's a weighted
average 980 occurrences of 99.6 and 220 occurrences of 100.0 (this
works out to be 99.73 a smidge higher because in reality yoru buddy
would have won 4880.4 coins from VP, but you can't get back .4 of a
coin so I dropped it)
If I were to use 6/5 JOB for this example, the difference between
you and your buddy would become a lot more obvious than 4 coins.
You'll wind up with 5730 coins and your buddy with 5779. You with a
payback of .955 (5730/6000) and your buddy with 96.31666.
Elliot
I thank both poster for their insights regarding the double up
option
on VP machine, both authors are very knowledgable VP writer. I am
a
very new VP player, but after think about the postings I concluded
(for what it worths) that double up does not increase the EV. The
VP
game and the double up are 2 different game and not one hand.
They
are independent of each other. However this is not the reason
that
double up does not increase the EV. Becasue if double up pay out
less 100% in the long run, it will negativly impact whatever VP
game
you play ;Vice versa, if double up is a positive game (over 100%),
then it will improve whatever VP game EV you are playing. However,
because double up is a even (exactly 100%) game, that means in a
long
run, the amount of money you double up (it doesn't matter you
double
up everything even RF or just High card pair) the EV will come out
the same. So what double up does is just increase the standard
variation but not the pay out and there is no advantge to neither
the
player or the casino.
I hope this help.
--- In vpFREE@yahoogroups.com, "Elliot Frome" <compuflyers@p...>
wrote:
> I'm a novice at this cutting and pasting someone else's post and
> then replying, so forgive me if I mess it up a bit.
>
> > Let's extend your example to higher paying hands. Suppose you
> insert
> > five coins, and you get a flush. The payoff is 30 coins. You
> choose
> > to Double Up. By your definition, you have now wagered a total
of
> 35
> > coins. You have a 50% probability of receiving 60 coins, else
you
> > receive nothing, so that's an average of 30 coins out. By your
> > definition, that's an average of 30 coins received for a total
> > 35-coin wager, or only 85.7% payback. Does that convince you
that
> > there's something wrong with this math?
>
>
> There's a lot wrong with this math, but you haven't kept true to
my
> methodology. You wagered 5 coins and won 30. 30/5 = payback of
> 600%. you now wagered THAT 30 with a 50/50 shot of 0 or 60 for
an
> EV of 30.
>
> You then calculated an 85.7% payback by saying 30/35, but that's
not
> how I would calculate it. I would use 60/35 (30 that you won at
VP
> and an EV of 30 for Double-Up). This calculates to 171.4%
return.
>
> I never said to use an average, but a WEIGHTED average. So, a
600%
> return on a 5 coin wager and a 100% return on a 30 coin wager.
So,
> if you weight the 100% 6 times greater than the 600% (there are
many
> ways to do this, but let's go with writing 100 down 6 times and
600
> once and the total is 1200% divided by 7 (6+1) and you get the
same
> 171.4%!)
>
> Nothing wrong with that math!
>
> Let's look at this a different way. You put 1 coin in VP and
you
> hit a Flush paying 5 (you're stuck on an 8/5 machine!). You now
bet
> 5 and get a Jacks or Better and you get your 5 back. What is
the
> return on your 'session'?
>
> In my eyes, I wagered 6 coins and won back 10 (5 each time).
10/6
> is 166.67%. I may have 5 times the amount of money I started
with,
> but that is not EV or payback.
>
> A computer simulation will not solve our 'dispute'. We are
> disagreeing on the calculation, not the result. In your
example,
> unless we both agree that coin in was 35 and returned was 60, no
> computer simulation will do us any good.
>
> It would appear that you are looking at the end result. I
started
> with 1 coin, I ended with 6 coins, thus a 600% return. This is
a
> correct calculation of the 'return of your money'.
>
> let's say I walk into a casino with 4 quarters in my pocket. If
I
> put 1 coin into a VP machine and play 1000 hands. The first 999
> miraculously come up High Pair and the last one comes up a
loser?
> What was my payback? 0 coins returned, 1 wagered? 0%? or I
walk
> away with 3 coins, started with 4 so it's 75%?
>
> Let's go to the old days before 'credits' on the machine, and
rather
> than playing the same 1 'coin', I start with a bucket of 1000
> quarters. I play them one at a time and for the first 999 hands
I
> get my High Pair and for the last one I get a loser. The bin at
the
> bottom now has 999 quarters. What's the return on my session?
> would ANYONE argue it's 99.9%?
>
> I realize the Double-Up option doesn't allow you this choice.
> It 'holds' the money and you decide to play or not. Once you
decide
> to 'play' you start a whole new game with it's own EV and this
EV
> must be weighted in the overall payback. Because Double-Up has
a
> 100% EV, it's easy to 'lose' it.
>
> What if Double-Up had a 99% payback stand alone? what would its
> impact to the overall experience be? It certainly couldn't have
NO
> impact to the combined game.
>
> I'm glad a 10 year old article can generate such interest!
>
> Elliot
> > Elliot Frome wrote (snip):
> > > I think the difference in our
> > >points of view come from whether we consider playing a hand
of VP
> > >followed by Double-Up as a single gambling event or two
distinct
> > >events.
> >
> > I agree with that. And since you can't Double Up until you
have
> had a
> > win (or push) on the VP game, they are not two distinct
events.
> > Linked events can not be treated as if they were independent.
Ask
> a
> > statistician.
> >
> > >If I throw 5 coins into a VP machine and hit a High Pair
returning
> > >the 5 coins, and then decide to play Double-Up, in my mind I
have
> > >played 10 coins. If I win the Double-Up and stop, the machine
> > >returns 10 coins. I consider this a return of 15 coins (5
for
the
> > >High Pair, an additional 10 for the Double-Up).
> >
> > In your mind you have played 10 coins, but in reality you have
> > deposited only five coins. You risked five coins, were given
an
> > option to get them back or to risk them again. That's only
five
> coins
> > in, not ten.
> >
> > Let's extend your example to higher paying hands. Suppose you
> insert
> > five coins, and you get a flush. The payoff is 30 coins. You
> choose
> > to Double Up. By your definition, you have now wagered a total
of
> 35
> > coins. You have a 50% probability of receiving 60 coins, else
you
> > receive nothing, so that's an average of 30 coins out. By your
> > definition, that's an average of 30 coins received for a total
> > 35-coin wager, or only 85.7% payback. Does that convince you
that
> > there's something wrong with this math?
> >
> > >If, on the other hand, you consider this to be a single
event,
you
> > >will consider it to be a return of 10 coins with a coin-in of
5.
> >
> > Exactly right. Twice the payoff with half the probability of
> receiving it.
> >
> > I suggest you write a simulation program. To simplify things,
you
> > could replace the Jacks or Better game with one that simply
> returns
> > your bet 99.54% of the time, and then Double Up with 50%
> probability
> > every time you do receive that payoff. Then compare coin in
(not
···
--- In vpFREE@yahoogroups.com, "shine_dh" <shine_dh@y...> wrote:
> --- In vpFREE@yahoogroups.com, Dan Paymar <Dan@O...> wrote:
> > action) with coin out. The payback will still be 99.54%.
> >
> > Dan
> >
> > --
> > Dan Paymar, author of "Video Poker - Optimum Play"
> > Editor and publisher of "Video Poker Times" newsletter
> > Visit my web site at www.OptimumPlay.com
> >
> > "Chance favors the prepared mind"
> > - Louis Pasteur
> >
> > [Non-text portions of this message have been removed]