Thankfully I have hit 4 or 5 Royals so far this year playing mostly
Double Bonus. I can only remember one or two straight flushes all year
which pays 250. My question, if I hit the same equivalent number in
Straight Flushes shouldn't I have about 9x as many....36-45 or so???
If my thinking is correct there are 36 straight flushes and 4 Royal
Flushes in a deck. So roughly one should average 9 straight flushes
to every Royal. I know with correct play you would hold 2 card Royal
draws and wouldn't hold 2 card Straight Flush draws. I can't think
this would make the difference. In fact all 5 of my Royals were
holding 3 or 4 to the Royal, which would be similiar in Straight Flush
holds. I imagine I am missing something here and need one of you
Experts to set me straight.
Thanks in Advance
Tommy D.
Straight Flush Question for You Math Whizzes.....
For Double Bonus, it's more like 5.5 to 1 when playing proper
strategy. For Jacks or better, it's closer to 4.5 to 1.
While you are correct in stating there are 36 vs. 4, this does not take
into account the specific holds that are done as a result of the
paytables.
In similar fashion, there are twice as many straights as there are
flushes, yet flushes will occur roughly with the same frequency as the
straight.
The fact that one pays more than the other can skew how often
we 'shoot' for that hand and thus how many times we wind up with them
in a Draw Game.
Elliot
Thankfully I have hit 4 or 5 Royals so far this year playing mostly
Double Bonus. I can only remember one or two straight flushes all
year
which pays 250. My question, if I hit the same equivalent number in
Straight Flushes shouldn't I have about 9x as many....36-45 or so???
If my thinking is correct there are 36 straight flushes and 4 Royal
Flushes in a deck. So roughly one should average 9 straight flushes
to every Royal. I know with correct play you would hold 2 card Royal
draws and wouldn't hold 2 card Straight Flush draws. I can't think
this would make the difference. In fact all 5 of my Royals were
holding 3 or 4 to the Royal, which would be similiar in Straight
Flush
···
--- In vpFREE@yahoogroups.com, "tommydick1" <tommydck@...> wrote:
holds. I imagine I am missing something here and need one of you
Experts to set me straight.
Thanks in Advance
Tommy D.
tommydick1 wrote:
Thankfully I have hit 4 or 5 Royals so far this year playing mostly
Double Bonus. I can only remember one or two straight flushes all
year. My question, if I hit the same equivalent number in
Straight Flushes shouldn't I have about 9x as many....36-45 or so???
If my thinking is correct there are 36 straight flushes and 4 Royal
Flushes in a deck. So roughly one should average 9 straight flushes
to every Royal. I know with correct play you would hold 2 card Royal
draws and wouldn't hold 2 card Straight Flush draws. I can't think
this would make the difference. In fact all 5 of my Royals were
holding 3 or 4 to the Royal, which would be similiar in Straight
Flush holds.
I'll add my own perspective here to Eliot's fine reply ...
In general, what happens in the short run in vp, while driven by
longer term expectations (say, a million+ hands), is pretty much a
crap shoot. So, it's unrealistic to extrapolate from your
experience in hitting one hand type to what you might expect in another.
However, the broader question suggested by your post (the relationship
between card probabilities and hand probabilities) is important to
understand. You're already hinted at the gist of this. You just need
to take your gut understanding a step further.
As you observe, RF's are predominantly formed from 3 and 4 card draws.
This is true despite the fact that we hold 1 or 2 cards to the RF more
often simply because of the much greater chance of completing the RF
from the 3/4 card draw.
However, don't dismiss those 1 or 2 card holds. Every time a one card
hold is present, it take precedenced should a 3cd-2i sf hold also be
present. Likewise, 2RF will take precedence over most 3SF (things get
mixed up a little when the SF incl a HC, but often a high pair will
top the rest then).
The point is that in many respects, 3sf holds are disadvantaged in
most video poker variants. Thus, when you look at actual hand
distributions, there are fewer SF's than you'd expect for each RF hit
(as Eliot notes).
···
------------
Eliot alludes to the fact that paytables are the driving force in
determining the actual ratio of expected RF hits to SF's in a game.
The fact is that all paytables yield pays that are disproportionate
the the frequency with which we expect to hit a hand.
I've often toyed with an imaginary video poker variant in which we're
non-active participants, but instead selectively wager on the outcome
of the next hand of another player. (For lack of a better title, I've
loosely called this "parimutuel video poker" 
If choosing between
two hands, one of which is expected to occur only half as often as
another, when we place a bet on the less frequent hand.
Such a betting scheme, if applied to a standard 10/7 DB paytable,
would make FH's and F's standout favorites over S's, because of their
high payout relative to frequency ... that is, unless we had cause to
believe that the player's strategy would skew expectations vs. optimal
strategy, of course.
The bottom line is that because of disparate payoffs, hand
distributions differ from one paytable to the next, and therefore
there can be no extrapolations of hand frequency from theoretically
possible hands for a deck of cards.
------------
This last discussion gives rise to the question of what distributions
we might expect from a paytable in which payouts were roughly related
to expected hand frequency.
There's a game variant that is in place that appears to have addressed
this question: All American. I suspect the name was chosen because
the paytable makes a stab at an egalitarian structure of "equal pay
for equal relative frequency".
The HP and TP pay identically. The S, F, and FH do so also. The 4K
gets a comfortable boost from Jacks, and the SF (for once) has a
satisfying payback (1000 cr.) relative to how hard it is to score.
One consequence of this paytable is that the player shoots much more
aggressively for a SF, including holding 2 card SF holds. SF
frequency increases by about 25%. (Other alternate hand
considerations still keep this game from having far from the 9:1 SF to
RF ratio you speculate on.)
- Harry
Tommy
Not being a math guy, I would attack this question different from the
experts. First I would tune in to Win Poker and DB game. Then I would
click on analyze then click game. Next take note of frequency for Roy
and SF. Divide the smaller into the larger and ya got your answer for
royals to sfs. I figure for every roy we should get about 5.44 SFs. or
2 roys played should net 11 sfs, almost.
Last time I played DB I played 48047 hands. Since a royal comes about
every 48048 hands, I can't wait till I play again. First hand should be
a royal; I'm due.
However, I'm probably wrong; I ain't no math guy.
Cheers.....Jeep