I finally got my Frugal poker program. (1 day b4 i'm going to
Vegas..LOL)
In Frugal's 9/6 JoB strategy, it prefers a 4 to a Royal over a Full
house.
But in Wizard of Odds page, it picks Full house over 4 to a RF.
Which should i use?
Frugal's JoB strategy different than Wizard of Odds strategy?
Both are correct. It isn't possible to hold a full house which permits
the possibility of 4/royal.
The 4/royal draw has higher EV.
···
On Saturday 20 December 2003 08:47 pm, David wrote:
I finally got my Frugal poker program. (1 day b4 i'm going to
Vegas..LOL)In Frugal's 9/6 JoB strategy, it prefers a 4 to a Royal over a Full
house.But in Wizard of Odds page, it picks Full house over 4 to a RF.
Which should i use?
> I finally got my Frugal poker program. (1 day b4 i'm going to
> Vegas..LOL)
>
> In Frugal's 9/6 JoB strategy, it prefers a 4 to a Royal over a
Full
> house.
>
> But in Wizard of Odds page, it picks Full house over 4 to a RF.
>
> Which should i use?Both are correct. It isn't possible to hold a full house which
permits
the possibility of 4/royal.
The 4/royal draw has higher EV.
duh..banging head against wall. next i'll be dropping 4 quarters in
the $1 slot machines and wondering why it doesn't work 
···
--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x> wrote:
On Saturday 20 December 2003 08:47 pm, David wrote:
How can you have both???
···
On Sun, 21 Dec 2003 03:47:53 -0000, you wrote:
I finally got my Frugal poker program. (1 day b4 i'm going to
Vegas..LOL)In Frugal's 9/6 JoB strategy, it prefers a 4 to a Royal over a Full
house.But in Wizard of Odds page, it picks Full house over 4 to a RF.
Which should i use?
vpFREE Links: http://www.west-point.org/users/usma1955/20228/VP/Links.htm
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"I finally got my Frugal poker program. (1 day b4 i'm going to
Vegas..LOL) In Frugal's 9/6 JoB strategy, it prefers a 4 to a Royal
over a Full house.
But in Wizard of Odds page, it picks Full house over 4 to a RF."
To which Steve Jacobs responded:
"Both are correct. It isn't possible to hold a full house which
permits the possibility of 4/royal."
Steve, that only true for "traditional" video poker games.
(shameless self-plug here) Have you tried Sigma's Ten Card Stud
Game? At ten cards on the draw, a full house and a 4 to the royal
flush is not an impossible event.
Cheers.
···
--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x> wrote:
On Saturday 20 December 2003 08:47 pm, David wrote:
ten_seven_vp wrote:
snip
Have you tried Sigma's Ten Card Stud
Game? At ten cards on the draw, a full house and a 4 to the royal
flush is not an impossible event.
snip
Is this a VP game that is, or will be, available in casinos? If so, can you please provide a more complete description -- how it's played, paytable, typical denominations, etc.
Thanks.
Bill Velek
ten_seven_vp wrote:
snip
> Have you tried Sigma's Ten Card Stud
> Game? At ten cards on the draw, a full house and a 4 to the royal
> flush is not an impossible event.snip
Is this a VP game that is, or will be, available in casinos? If
so, can
you please provide a more complete description -- how it's played,
paytable, typical denominations, etc.Thanks.
Bill Velek
[Assuming you ignore my shameless self-promotion] It's the same game
as "Ten Seven Poker" but renamed "Ten Card Stud Poker" so players
would know it is not a draw poker game (in my previous example, you
would keep the full house as you can't improve on the 4 to the RF).
There's a hidden secret* to the "deal 10 initial cards, player
discards 3 cards and have computer choose 5 cards randomly from the
7 remaining card" concept -- assuming Sigma got the royal flush
consolation prize right, then the player should not face royal flush
droughts based on a concept called "royal flush equivalency." I'll
have more detail once the math has been completed. People like
Steve Jacobs or other VP Guru can explain it best. For now, try to
picture playing a multi-line video poker game with lower variance
than you are used to. How much lower variance, again, the math is
still being worked on.
* [While TCSP doesn't **appear** to suffer from the covariance
effect like IGT's N-Play, TCSP doesn't have the ability to be
flopped a royal flush and have the RF be the winning hand on every
line. TSP was designed to suppose to solve one of the biggest
headaches in video poker: the variance. Also, don't get me wrong,
the game can also be designed with sky-high variance just like multi-
strike vp.]
···
--- In vpFREE@yahoogroups.com, Bill Velek <billvelek@a...> wrote:
If I've understood your reply correctly, then it sounds like "Sigma's Ten Card Stud Game" might not be an entirely random VP game; I'll clarify my concern at an appropriate place, below. And although you had mentioned Multi-Strike as an example of how variance can be increased for an existing game, your method to move in the other direction, and reduce variance, raises some questions for me.
To begin with, the resulting change in variance in _Multi-Stike_ is still due to complete randomness, despite its inclusion of Free-Rides which are also themselves random; moreover, Multi-Strike's modification of the game has resulted in an increase rather than a decrease in ER, and its disclosure of percentages of Free-Rides enables development of optimum or perfect strategy. I will get to discussion of randomness later, but I'll start out with two direct questions: 1.) Is info available to develop proper strategy? ... and ... 2.) with the use of property strategy, how is long-term ER affected?
Please see additional comments, inserted below.
Thanks.
Bill Velek
···
*****
fordscks wrote:
[Assuming you ignore my shameless self-promotion] It's the same game
as "Ten Seven Poker" but renamed "Ten Card Stud Poker" so players
would know it is not a draw poker game ... snip
Sorry, but I'm not familiar with "Ten Seven Poker".
There's a hidden secret* to the "deal 10 initial cards, player
discards 3 cards and have computer choose 5 cards randomly from the
7 remaining card" concept -- assuming Sigma got the royal flush
consolation prize right, then the player should not face royal flush
droughts based on a concept called "royal flush equivalency."
This is the part that makes me wonder if this is entirely random, although it is still possible. Can you provide more detail about it? ... at least an explanation of what the feature does without getting into technical details about _how_ it does it? ... and confirm whether or not this is a random function?
This is my reasoning: I assume that the "deal 10 initial cards", above, is random ... and you have already stated that the computer's selection of the 7 remaining cards is random; the game to this point is therefore completely random on the computer's end, and the only non-random part -- the 3 discards by a player -- is beyond the control of the computer and has no effect on how the computer selects the final 5 cards. To this point, once a paytable is provided, we can develope perfect strategy and compute the precise statistical results. Then we apparently come to this 'consolation prize', which might or might not be random, in connection with Royal Flush "droughts", which you've suggested could still be a problem. However, with the ability to see all 10 available cards and then discarding 3, it seems to me that there would be substantially more attempts at the Royal (presumeably every time you would ever have been able to be dealt or draw a Royal, including many, many times when you would never attempt to draw to a Royal. Of course, after the computer randomly discards 2 cards, you will only get to keep the Royal once in every 21 attempts. But you also have the same consideration with all other hands; hold a Full House plus 2 extraneous cards, and you'll keep the Full House only once every 21 attempts. So after thinking about this logically for a while, this is what I'm wondering. You mention the consolation prize to fix droughts re Royals, which suggests to me that perhaps this new game gives even fewer Royals than in a regular game. After all, if it gives the same number of Royals, then it is likely to work out giving about the same number of everything else (I'll explain in a minute), and that would mean that the variance would be the same except as it might be affected by the 'consolation prize'; and it if gives more Royals, then I can't imagine why you'd be taking any steps to address possible Royal droughts. So let's assume for a minute that this game ends up paying for fewer Royals than normal; this would be due to you're wanting to keep 5 particular cards out of the remaining 7, and only succeeding 1/21 times. Seems to me that the same rationale would also apply to any other other 5 out of 7 card combinations that you would want, such as Full House, Flush, and Straight. Of course, the ratio for the number of possible Full Houses that can be made when we can see all 10 cards up-front might be substantially higher than the ratio of Royals; I won't take the time to try to figure that out right now. This does sound like an interesting game; hard to tell whether the fun factor would outweigh the frustration factor of seeing the Royal right there and then having the computer ruin it.
Thanks.
Bill Velek
have more detail once the math has been completed. People like
Steve Jacobs or other VP Guru can explain it best. For now, try to
picture playing a multi-line video poker game with lower variance
than you are used to. How much lower variance, again, the math is
still being worked on.* [While TCSP doesn't **appear** to suffer from the covariance
effect like IGT's N-Play, TCSP doesn't have the ability to be
flopped a royal flush and have the RF be the winning hand on every
line. TSP was designed to suppose to solve one of the biggest
headaches in video poker: the variance. Also, don't get me wrong,
the game can also be designed with sky-high variance just like multi-
strike vp.]
snip
fordscks wrote:
TSP was designed to suppose to solve one of the biggest
headaches in video poker: the variance. Also, don't get me wrong,
the game can also be designed with sky-high variance just like multi-
strike vp.]
Just a remark on this comment: I've pretty much satisfied myself that
the variance of multistrike is actually quite modest -- very likely in
the neighborhood of the same total wager placed on the equivalent
single-line game.
There's a little more checking and confirmation to do but I'll post
more on this later.
- Harry
If I've understood your reply correctly, then it sounds like "Sigma's
Ten Card Stud Game" might not be an entirely random VP game; I'll
clarify my concern at an appropriate place, below. And although you had
mentioned Multi-Strike as an example of how variance can be increased
for an existing game, your method to move in the other direction, and
reduce variance, raises some questions for me.
One thing to keep in mind is that a reduction in variance isn't necessarily
a good thing. If the game is negative EV, then variance is the only thing
that gives the player a chance to come out ahead. Eliminating variance
completely would result in a game where the player loses a fixed percentage
of each wager every time the game is played.
To begin with, the resulting change in variance in _Multi-Stike_ is
still due to complete randomness, despite its inclusion of Free-Rides
which are also themselves random; moreover, Multi-Strike's modification
of the game has resulted in an increase rather than a decrease in ER,
and its disclosure of percentages of Free-Rides enables development of
optimum or perfect strategy.
I always cringe when I see the phrase "perfect strategy" because that
is a flawed notion. There isn't one "perfect strategy" which is supreme
above all others. "Optimal" is relative to the players objective, and so
the optimal strategy depends on what the player is trying to achieve.
The max-EV strategy is just one form of optimization out of myriads of
other possibilities.
I will get to discussion of randomness
later, but I'll start out with two direct questions: 1.) Is info
available to develop proper strategy? ... and ... 2.) with the use of
property strategy, how is long-term ER affected?Please see additional comments, inserted below.
Thanks.
Bill Velek
*****
fordscks wrote:
> [Assuming you ignore my shameless self-promotion] It's the same game
> as "Ten Seven Poker" but renamed "Ten Card Stud Poker" so players
> would know it is not a draw poker game ... snipSorry, but I'm not familiar with "Ten Seven Poker".
> There's a hidden secret* to the "deal 10 initial cards, player
> discards 3 cards and have computer choose 5 cards randomly from the
> 7 remaining card" concept -- assuming Sigma got the royal flush
> consolation prize right, then the player should not face royal flush
> droughts based on a concept called "royal flush equivalency."This is the part that makes me wonder if this is entirely random,
although it is still possible. Can you provide more detail about it?
... at least an explanation of what the feature does without getting
into technical details about _how_ it does it? ... and confirm whether
or not this is a random function?
It has to be random, or Nevada law would block the game from
being placed in casinos.
This is my reasoning: I assume that the "deal 10 initial cards", above,
is random ... and you have already stated that the computer's selection
of the 7 remaining cards is random; the game to this point is therefore
completely random on the computer's end, and the only non-random part --
the 3 discards by a player -- is beyond the control of the computer and
has no effect on how the computer selects the final 5 cards. To this
point, once a paytable is provided, we can develope perfect strategy and
compute the precise statistical results. Then we apparently come to
this 'consolation prize', which might or might not be random, in
connection with Royal Flush "droughts", which you've suggested could
still be a problem. However, with the ability to see all 10 available
cards and then discarding 3, it seems to me that there would be
substantially more attempts at the Royal (presumeably every time you
would ever have been able to be dealt or draw a Royal, including many,
many times when you would never attempt to draw to a Royal.
It seems likely that if the initial ten cards permit a royal, then it would
never be correct to discard one of the royal cards. Any time you have
a royal flush plus two other cards, you've got a 1/21 chance of drawing
the royal from the 7 cards. That is twice as good as a 4/royal draw on
a standard VP machine.
Of course, it all depends on the payoff schedule and the value of
the royal flush compared to other hands.
Of course,
after the computer randomly discards 2 cards, you will only get to keep
the Royal once in every 21 attempts. But you also have the same
consideration with all other hands; hold a Full House plus 2 extraneous
cards, and you'll keep the Full House only once every 21 attempts.
Right. But if you keep 4 jacks and 3 eights, every possible draw will
be at least a full house. So, the other two cards aren't necessarily
extraneous.
So
after thinking about this logically for a while, this is what I'm
wondering. You mention the consolation prize to fix droughts re Royals,
which suggests to me that perhaps this new game gives even fewer Royals
than in a regular game.
There are 15.82 billion distinct ways to draw 10 cards from a deck of 52.
For each of the 4 royal flushes, there are 1,533,939 ways to draw 5 other
cards from 47, giving 6,135,756 ways to draw a royal among 10 cards.
From this we need to subtract the 6 ways to draw two royals in the same
set of 10 cards, leaving 6,135,750 royal draws. This means we can
expect a potential royal in about 1/2578 deals, perhaps once every
3-4 hours of play. The royal cycle, assuming you never break up a royal,
is one royal every 54,145 plays.
If you play 10 lines and get dealt a royal, the probability of missing on
all ten lines is (20/21)^10 = 0.6139. So, we would expect to hit at least
one royal on about 38.6% all attempts. By offering a consolation prize
for missing all 10 royals, the motivation for ever splitting up a royal is
probably completely eliminated.
After all, if it gives the same number of
Royals, then it is likely to work out giving about the same number of
everything else (I'll explain in a minute), and that would mean that the
variance would be the same except as it might be affected by the
'consolation prize'; and it if gives more Royals, then I can't imagine
why you'd be taking any steps to address possible Royal droughts. So
let's assume for a minute that this game ends up paying for fewer Royals
than normal; this would be due to you're wanting to keep 5 particular
cards out of the remaining 7, and only succeeding 1/21 times. Seems to
me that the same rationale would also apply to any other other 5 out of
7 card combinations that you would want, such as Full House, Flush, and
Straight. Of course, the ratio for the number of possible Full Houses
that can be made when we can see all 10 cards up-front might be
substantially higher than the ratio of Royals; I won't take the time to
try to figure that out right now. This does sound like an interesting
game; hard to tell whether the fun factor would outweigh the frustration
factor of seeing the Royal right there and then having the computer ruin
it.
Ah, but that is the beauty of the consolation prize. If you see a royal
and don't break it up, you are guaranteed to come out ahead (assuming
you've played enough lines to qualify for the consolation prize). The
real frustration would come from every other "pat" hand, where you can
see them but only hit 1/21 of them.
···
On Friday 02 January 2004 02:00 am, Bill Velek wrote:
Long Detailed Post about a new type of VP game and some associated math aspects.
Steve Jacobs wrote:
> snip ... your method to move in the other direction, and
> reduce variance, raises some questions for me.One thing to keep in mind is that a reduction in variance isn't necessarily
a good thing. If the game is negative EV, then variance is the only thing
that gives the player a chance to come out ahead. Eliminating variance
completely would result in a game where the player loses a fixed percentage
of each wager every time the game is played.
True. And it would tend to make the game rather boring.
> snip ... Multi-Strike's modification
> of the game has resulted in an increase rather than a decrease in ER,
> and its disclosure of percentages of Free-Rides enables development of
> optimum or perfect strategy.I always cringe when I see the phrase "perfect strategy" because that
is a flawed notion. There isn't one "perfect strategy" which is supreme
above all others. "Optimal" is relative to the players objective, and so
the optimal strategy depends on what the player is trying to achieve.
The max-EV strategy is just one form of optimization out of myriads of
other possibilities.
I can understand your point, which is precisely why I have used (and often do so) both terms. When I use the term perfect strategy, I mean that it is mathematically perfect, i.e., no errors whatsoever in regard to relative EV's for the purpose of maximizing long-term ER. I certainly do understand that idea that some people prefer 'optimum' strategy, which typically ignores inexpensive and rare penalty cases in order to gain some simplicity for ease of mastering and to maximize play speed. Many people will therefore no doubt consider a simpler strategy which contains a few minor mathematical deviations (I won't call them 'errors' because they are deliberately made) to be 'perfect' for them. Now I suppose I could go the extra mile by elaborating and calling them "perfectly accurate" or "mathematically perfect" strategies, but that is awkward and in my opinion unnecessary.
> fordscks wrote: ...snip
> > There's a hidden secret* to the "deal 10 initial cards, player
> > discards 3 cards and have computer choose 5 cards randomly from the
> > 7 remaining card" concept -- assuming Sigma got the royal flush
> > consolation prize right, then the player should not face royal flush
> > droughts based on a concept called "royal flush equivalency."
>
> This is the part that makes me wonder if this is entirely random,
> although it is still possible. Can you provide more detail about it?
> ... at least an explanation of what the feature does without getting
> into technical details about _how_ it does it? ... and confirm whether
> or not this is a random function?It has to be random, or Nevada law would block the game from
being placed in casinos.
Well, what I thought it might consist of ... especially since the original post characterized this as a "consolation prize" ... is a uniform guaranteed payment, which would therefore not be 'random'. In other words, perhaps the program is set up to say that every time you have a five-card Royal among your 10 cards, and you lose the Royal (which will happen 20 out of 21 times because of the 2 cards randomly discarded by the computer), that you will at least still get a "consolation prize" of, let's say, 10 betting units. Or perhaps it would go a step further and only give you the consolation prize if you lost the Royal AND ALSO drew no other winning hand whatsoever. In such cases, I can't imagine that Nevada or any other gambling jurisdiction would complain unless the resulting game exceeded some state limits which prohibit games over 100%, etc.
> snip ... However, with the ability to see all 10 available
> cards and then discarding 3, it seems to me that there would be
> substantially more attempts at the Royal (presumeably every time you
> would ever have been able to be dealt or draw a Royal, including many,
> many times when you would never attempt to draw to a Royal.It seems likely that if the initial ten cards permit a royal, then it would
never be correct to discard one of the royal cards. Any time you have
a royal flush plus two other cards, you've got a 1/21 chance of drawing
the royal from the 7 cards. That is twice as good as a 4/royal draw on
a standard VP machine.Of course, it all depends on the payoff schedule and the value of
the royal flush compared to other hands.
Agreed. Which is why I used the word "presumably", above. But my point was that in normal games, there are many times that we don't try for a Royal (e.g., keeping a Hi-Pair over a 2-Royal) simply because we can't see the other 3 cards needed for the Royal in the next five cards. With this new game, we would see them, and I'm sure the correct choice is to shoot for the Royal (along with the Hi-Pair, too). I just think that we would probably see Royal more often rather than less often, but I don't know how much that 1 in 21 factor will affect the number of Royals that we would ordinarily get from holding 4-Roys, 3-Roys, 2-Roys, 1-Hi-Cd, and even a complete redraw from a 'Junk' hand.
> Of course,
> after the computer randomly discards 2 cards, you will only get to keep
> the Royal once in every 21 attempts. But you also have the same
> consideration with all other hands; hold a Full House plus 2 extraneous
> cards, and you'll keep the Full House only once every 21 attempts.Right. But if you keep 4 jacks and 3 eights, every possible draw will
be at least a full house. So, the other two cards aren't necessarily
extraneous.
Yes, I see that now. I hadn't delved into this that deep yet to notice that. And of course there are lots of other times that they would not be considered extraneous either, because they would be just as valuable as other cards held. E.g., a 7-card straight, with the hope that the computer drops two cards on either end, or one on each end. In that situation, you have a 1/7 chance of keeping your straight.
> So after thinking about this logically for a while, this is what I'm
> wondering. You mention the consolation prize to fix droughts re Royals,
> which suggests to me that perhaps this new game gives even fewer Royals
> than in a regular game.There are 15.82 billion distinct ways to draw 10 cards from a deck of 52.
For each of the 4 royal flushes, there are 1,533,939 ways to draw 5 other
cards from 47, giving 6,135,756 ways to draw a royal among 10 cards.
>From this we need to subtract the 6 ways to draw two royals in the same
set of 10 cards, leaving 6,135,750 royal draws. This means we can
expect a potential royal in about 1/2578 deals, perhaps once every
3-4 hours of play. The royal cycle, assuming you never break up a royal,
is one royal every 54,145 plays.
I got the same figures but didn't include them in my initial post because I was unsure of whether the 6 'double-Royals' hands needed to be kept, eliminated, or just 'adjusted'. I was initially leaning in the direction of _including_ them, but was a bit uncomfortable with that, and so I just about talked myself into deducting 3 (half of the number of double-Royals), because it seemed to me that if you deduct all six occurrences, you are not counting any of those Royals even though you are keeping half of them (you are always keeping one or the other in each of the six instances). That was pretty much my final decision, but I wanted to do a little math, when I had time later, to try to determine an answer with greater confidence. And now you have just indicated that they should _all_ be _excluded_, i.e., to subtract the 6 ways. I'm sure you are much sharper than I am at this and are probably correct. I would appreciate if you would take the time to try to explain your decision to drop 6 instead of 3, although this might be really simple and I'm just having a brain cramp.
If you play 10 lines and get dealt a royal, the probability of missing on
all ten lines is (20/21)^10 = 0.6139. So, we would expect to hit at least
one royal on about 38.6% all attempts. By offering a consolation prize
for missing all 10 royals, the motivation for ever splitting up a royal is
probably completely eliminated.
So, are you saying that the consolation prize is available only when playing 10 play? And what is the consolation prize, by the way?
> After all, if it gives the same number of
> Royals, then it is likely to work out giving about the same number of
> everything else (I'll explain in a minute), and that would mean that the
> variance would be the same except as it might be affected by the
> 'consolation prize'; and it if gives more Royals, then I can't imagine
> why you'd be taking any steps to address possible Royal droughts. So
> let's assume for a minute that this game ends up paying for fewer Royals
> than normal; this would be due to you're wanting to keep 5 particular
> cards out of the remaining 7, and only succeeding 1/21 times. Seems to
> me that the same rationale would also apply to any other other 5 out of
> 7 card combinations that you would want, such as Full House, Flush, and
> Straight. Of course, the ratio for the number of possible Full Houses
> that can be made when we can see all 10 cards up-front might be
> substantially higher than the ratio of Royals; I won't take the time to
> try to figure that out right now. This does sound like an interesting
> game; hard to tell whether the fun factor would outweigh the frustration
> factor of seeing the Royal right there and then having the computer ruin
> it.Ah, but that is the beauty of the consolation prize. If you see a royal
and don't break it up, you are guaranteed to come out ahead (assuming
you've played enough lines to qualify for the consolation prize). The
real frustration would come from every other "pat" hand, where you can
see them but only hit 1/21 of them.
Thanks, Steve. This has been a very interesting discussion for me. You speak like you are already familiar with this game, but I sort of got the impression from fordscks' comment: "assuming Sigma got the royal flush consolation prize right") ... that this game might not even be release yet; is your insight just because you're a 'VP Guru'? ... or have you seen or played the game?
Cheers.
Bill Velek
···
On Friday 02 January 2004 02:00 am, Bill Velek wrote:
Long Detailed Post about a new type of VP game and some associated math
aspects.
>Eliminating
> variance completely would result in a game where the player loses a fixed
> percentage
> of each wager every time the game is played.True. And it would tend to make the game rather boring.
Agreed. The main point is that reducing variance isn't automatically
good for the player. It is good only when the game if favorable.
> > snip ... Multi-Strike's modification
> > of the game has resulted in an increase rather than a decrease in ER,
> > and its disclosure of percentages of Free-Rides enables development of
> > optimum or perfect strategy.
>
> I always cringe when I see the phrase "perfect strategy" because that
> is a flawed notion. There isn't one "perfect strategy" which is supreme
> above all others. "Optimal" is relative to the players objective, and so
> the optimal strategy depends on what the player is trying to achieve.
> The max-EV strategy is just one form of optimization out of myriads of
> other possibilities.I can understand your point, which is precisely why I have used (and
often do so) both terms. When I use the term perfect strategy, I mean
that it is mathematically perfect, i.e., no errors whatsoever in regard
to relative EV's for the purpose of maximizing long-term ER. I
certainly do understand that idea that some people prefer 'optimum'
strategy, which typically ignores inexpensive and rare penalty cases in
order to gain some simplicity for ease of mastering and to maximize play
speed. Many people will therefore no doubt consider a simpler strategy
which contains a few minor mathematical deviations (I won't call them
'errors' because they are deliberately made) to be 'perfect' for them.
Now I suppose I could go the extra mile by elaborating and calling them
"perfectly accurate" or "mathematically perfect" strategies, but that is
awkward and in my opinion unnecessary.
You are making a fine distinction between computer-perfect and
human limitations that make a simplified strategy a more practical way
to play. That is much different than the distinction that I'm making.
What I'm saying is that there are a vast number of different ways to
create a computer perfect strategy, and only one of those computer
perfect strategies seeks to maximize EV. As a counter-example,
players who wish to maximize the probability of turning an $X
starting bankroll into a $Y final bankroll would be significantly
better off using a strategy which minimizes risk. Another strategy
maximizes the average number of dollars in the players pocket
when playing until a royal jackpot is hit.
> It has to be random, or Nevada law would block the game from
> being placed in casinos.Well, what I thought it might consist of ... especially since the
original post characterized this as a "consolation prize" ... is a
uniform guaranteed payment, which would therefore not be 'random'. In
other words, perhaps the program is set up to say that every time you
have a five-card Royal among your 10 cards, and you lose the Royal
(which will happen 20 out of 21 times because of the 2 cards randomly
discarded by the computer), that you will at least still get a
"consolation prize" of, let's say, 10 betting units.
How is that not random? In fact, how is that any different than being
dealt 3/kind on an ordinary machine, and keeping all 3 to guarantee
a payback of at least 3 units? It is paying on an event that isn't tied
to a specific poker hand, but it is still based on a random outcome
an is still completely defined in a mathematical sense, so that we are
not prevented (in theory) from computing an EV for the game.
Or perhaps it
would go a step further and only give you the consolation prize if you
lost the Royal AND ALSO drew no other winning hand whatsoever.
That is still random.
In such
cases, I can't imagine that Nevada or any other gambling jurisdiction
would complain unless the resulting game exceeded some state limits
which prohibit games over 100%, etc.
Agreed. There are certainly ways to define payoffs in ways that a
gambling jurisdiction would complain, but I don't you've given any
examples that fit into that category.
> There are 15.82 billion distinct ways to draw 10 cards from a deck of 52.
> For each of the 4 royal flushes, there are 1,533,939 ways to draw 5 other
> cards from 47, giving 6,135,756 ways to draw a royal among 10 cards.
>
> >From this we need to subtract the 6 ways to draw two royals in the same
>
> set of 10 cards, leaving 6,135,750 royal draws. This means we can
> expect a potential royal in about 1/2578 deals, perhaps once every
> 3-4 hours of play. The royal cycle, assuming you never break up a royal,
> is one royal every 54,145 plays.I got the same figures but didn't include them in my initial post
because I was unsure of whether the 6 'double-Royals' hands needed to be
kept, eliminated, or just 'adjusted'. I was initially leaning in the
direction of _including_ them, but was a bit uncomfortable with that,
and so I just about talked myself into deducting 3 (half of the number
of double-Royals), because it seemed to me that if you deduct all six
occurrences, you are not counting any of those Royals even though you
are keeping half of them (you are always keeping one or the other in
each of the six instances). That was pretty much my final decision, but
I wanted to do a little math, when I had time later, to try to determine
an answer with greater confidence. And now you have just indicated that
they should _all_ be _excluded_, i.e., to subtract the 6 ways. I'm sure
you are much sharper than I am at this and are probably correct. I
would appreciate if you would take the time to try to explain your
decision to drop 6 instead of 3, although this might be really simple
and I'm just having a brain cramp.
We drop 6 hands because there were 6 cases that were counted twice
in the original number. They were counted one time for each of the
suits that allowed a royal, and since these 6 hands consists of two
royals of different suits, they were counted twice.
> If you play 10 lines and get dealt a royal, the probability of missing on
> all ten lines is (20/21)^10 = 0.6139. So, we would expect to hit at
> least one royal on about 38.6% all attempts. By offering a consolation
> prize for missing all 10 royals, the motivation for ever splitting up a
> royal is probably completely eliminated.So, are you saying that the consolation prize is available only when
playing 10 play?
I believe so, but I'm not sure.
And what is the consolation prize, by the way?
Good question. Probably some fraction of the payoff for a royal.
Actually it is guaranteed to be _some_ fraction, but hopefully it would
be a large enough fraction that it would seem like a mini jackpot. If
it is larger than the payoff from any other hand, then that would
probably justify never splitting up a royal. I think the biggest
"guaranteed payoff" would be hands like 4/kind + 3/kind that
guarantee a full house. So, to me it would seem like a ripoff if
the consolation wasn't at least better than getting this biggest
guaranteed payoff, which would be (full house payoff) * (number
of hands played).
> Ah, but that is the beauty of the consolation prize. If you see a royal
> and don't break it up, you are guaranteed to come out ahead (assuming
> you've played enough lines to qualify for the consolation prize). The
> real frustration would come from every other "pat" hand, where you can
> see them but only hit 1/21 of them.Thanks, Steve. This has been a very interesting discussion for me. You
speak like you are already familiar with this game, but I sort of got
the impression from fordscks' comment: "assuming Sigma got the royal
flush consolation prize right") ... that this game might not even be
release yet; is your insight just because you're a 'VP Guru'?
or have you seen or played the game?
I haven't seen/played the game, but I received a few details in email.
I'm not sure how much of that detail I'm allowed to disclose. I wasn't
asked to _not_ disclose, but wasn't given permission either, so I'm
not really sure what I can/can't say. I got the impression that this
might not be out yet, and that some details (such as size of consolation
prize) haven't been decided.
Given that there are 15 billion starting hands, I'd be curious to know if
this game has ever been analyzed completely, even by those who
created it. I wouldn't be surprized if it has only been simulated and
never completely analyzed to find a computer-perfect strategy.
···
On Friday 02 January 2004 07:07 pm, Bill Velek wrote:
Steve Jacobs wrote:
On Friday 02 January 2004 07:07 pm, Bill Velek wrote: ... snip ...
> ... . When I use the term perfect strategy, I mean
> that it is mathematically perfect, i.e., no errors whatsoever in regard
> to relative EV's for the purpose of maximizing long-term ER. I
> certainly do understand that idea that some people prefer 'optimum'
> strategy, which typically ignores inexpensive and rare penalty cases in
> order to gain some simplicity for ease of mastering and to maximize play
> speed. ...
snip
... That is much different than the distinction that I'm making.
What I'm saying is that there are a vast number of different ways to
create a computer perfect strategy, and only one of those computer
perfect strategies seeks to maximize EV. ...
snip
Okay. I see what you mean now. But of course, when we include the fact that there are different strategies for different goals or different priorities, then the argument that this is a reason to not call a strategy "perfect" ... because it is only perfect when striving for maximum ER ... well, that argument applies equally to any and all adjectives describing a strategy, including the use of the terms "correct" strategy, "optimum" strategy, and "best" strategy, etc. -- because the particular strategy for maximum ER most likely won't be the right one for the alternative goals you've suggested. Technically, you are absolutely correct; however, for ease in communication, I think that we can probably agree that the most commonly used strategy is for maximum ER, and therefore the most commonly used reference for "best", "correct", "optimum", or "perfect" strategy is the one for maximum ER. Sort of like a "default" meaning, and we can probably also further confirm the meaning from the context of what is said.
snipped my explanation re why I had asked whether the "consolation prize" is random; i.e., that I thought that it might be a constant, as opposed to random.
How is that not random?
Perhaps the word was poorly chosen. I was merely trying to find out whether the "consolation prize" is awarded only occasionally, on a random basis, sort of like a Free Ride in Multi-Strike ... or if it was, instead, given _everytime_, which I perceived to be more like a reliable _constant_ as opposed to an occasional, and therefore 'random', awarding of the prize. I was only drawing the distinction so folks would understand what information I was asking for, so that I could fully understand the feature. I guess I didn't do a very good job, but then these email posts are written very quickly.
snip
> I'm sure
> you are much sharper than I am at this and are probably correct. I
> would appreciate if you would take the time to try to explain your
> decision to drop 6 instead of 3, although this might be really simple
> and I'm just having a brain cramp.We drop 6 hands because there were 6 cases that were counted twice
in the original number.
Yep, it was a brain cramp. 
snip
Given that there are 15 billion starting hands, I'd be curious to know if
this game has ever been analyzed completely, even by those who
created it. I wouldn't be surprized if it has only been simulated and
never completely analyzed to find a computer-perfect strategy.
Yes, and it sounds like creating an accurate strategy will be a bitch without writing a computer program ... plus I can't see how WinPoker or FrugalVP would help much along those lines, either.
Nice discussion. Thanks.
Cheers.
Bill Velek
like "Sigma's Ten Card Stud Game" might not be an entirely random VP
game; I'll clarify my concern at an appropriate place, below."
[I'm really not here to self-promote the game, but instead to answer
a bona fide question].
The game is random because the deck is using a standard deck of 52
playing cards (wait until we add jokers!!). The machine randomly
deals 10 cards as the initial hand. After the player discards 3
cards to form a "7 card basket", then the machine again randomly
choose 5 from this "7 card basket" to form each final hand (again,
drawing from the same "7 card basket" as many times as needed).
There is no "draw" feature in this game because you are starting out
with ten cards, which is the most cards you will see in any
tradition 5 card video poker game with a draw feature (discard all
and draw 5 new cards).
The consolation prize is simply a reward for missing the royal
flush, since each line has a 1 in 21 shot for the royal flush. The
parallel in traditional video poker would be offering an extra pay
line such that if one flopped 4 to the royal and fails to convert to
a royal flush after the draw, then the game pays 10 to 1 as a
consolation (if you see this feature in a video poker game, then you
know where it came from :-0. Right now, there is no such "extra pay
line." And having such extra pay line does not make the game less
random (altho you will be rewarded 46 times out of every 47 tries
*in addition* to whatever winning hand you happen to finish with,
i.e. a high pair, flush, etc). The hidden feature or secret is that
the consolation prize is not mentioned in the payline, but in the
help section (please don't ask me why). Lastly, the game is random
because the appropriate gaming authorities have approved the game
and the manufacture is a legit manufacturer.
"I will get to discussion of randomness later, but I'll start out
with two direct questions: 1.) Is info available to develop proper
strategy? ... and ... 2.) with the use of property strategy, how is
long-term ER affected?"
A1 If you have an video poker analyzer that can a game with 15.8
billion+ starting hands, I can't see why you couldn't given the game
randomly deals out ten cards at a time.
A2. Your EV is dependent on the strategy you use just like any other
video poker game. If you understand probabilities, you can
calculate the royal flush cycle (the consolation prize, as I
understand it, does not alter the royal flush cycle).
The current games is mentioned in Strictly Slots where Bob Dancer
comments about new games from the Gamo Expo -- or check out games in
www.sigmagame.com (where the game is stilled listed under Ten Seven
Poker).
<SNIP>
···
--- In vpFREE@yahoogroups.com, Bill Velek <billvelek@a...> wrote:
If I've understood your reply correctly, then it sounds
fordscks wrote:
snipped stuff regarding randomness of Sigma's Ten Seven Poker / Ten Card Stud Game
I just visited the Sigma site -- http://www.sigmagame.com/ -- and notice that the lower right corner of the screen has a couple of yellow-button with red-lettering: "Door" and "Power" ... and a much smaller dark red square of some sort that I can't make out.
What is the function of these buttons?
Thanks.
Bill Velek
I just visited the Sigma site -- http://www.sigmagame.com/ -- and
notice that the lower right corner of the screen has a couple of
yellow-button with red-lettering: "Door" and "Power" ... and a
much
smaller dark red square of some sort that I can't make out.
What is the function of these buttons?
Thanks.
Bill Velek
I provided a link so you can see a representative pay table in the
event you wanted to figure out the EV for this type of game (keep in
mind the consolation prize when you do your analysis; as I was told,
the original consolation prize was 200 coins and has since been
increased). The motif is outdated as I previously mentioned. As
for your hardware question, may I suggest you contact Sigma and
inquire about their "Dallas" platform.
···
--- In vpFREE@yahoogroups.com, Bill Velek <billvelek@a...> wrote: