--- In vpFREE@yahoogroups.com, "rockofjello333" <rockofjello333@y...>
wrote:
So here's my solution: Make the royal flush worth no more than any
other straight flush. Put the 2% payback thus lost back into some
other rare (but not as rare) hands, such as: (Using 9/6 JOB as a
base)
Double the straight flush to 500 coins
Pay 25-1 for a "sequential" straight
Award 25-1 for finishing with four to a royal (losing hand)
On one-card flush draws, catching the right color, wrong suit
refunds
the bet (drawing to a spade flush, you catch a club)
Randomly appearing feature: "X"'s are wild for this hand only with
standard paytable still in effect
If anybody wants to bother, I'd be curious to see what the EV effect
of any or all of these modifications would be.
Calculating the exact EV changes would be difficult because each
paytable change opens the possibility of strategy changes, so you
have to run the reulting paytable through a game analyzer. This is
made especially difficult in many of the examples you give because
you are introducing new pay hands that are not already built into the
tables that programs like WinPoker use. It would involve going back
to the original 134,459 unique hands table to determine the
probability of each of 32 possible draws (4.3 million probabilities
to calculate). I have a rough draft of some software that would do it
but it takes 4 days to run, plus some set-up time. So far the only
thing I have run is a standard 52-card deck with no wild cards and
just the traditional pay hands, but my intention is to make it
flexible enough to run any imaginable scenario including all the ones
you mention here.
However, I love the ideas, and I've thought of some of the same
things and other stuff along the same lines. It's part of the reason
I'm developing this particular software. Even without the software,
however, we can make a start with back-of-the-envelope and rule-of-
thumb type calculations.
Your object, of course, would be keep overall game EV about the same,
so the discussion below is in terms or what you could trade off for
approximately equal returns.
First, on decreasing the royal value and paying for 4-to-a-royal.
Let's say the odds of getting 4-to-a-royal is 1/47th the odds of the
royal itself (*). In DB, a royal of 4000 coins is worth 1.67% of your
overall return. So, if strategy changes were not possible, you could
cut the royal back to 1650 coins and pay 50 coins for each 4-to-a-
royal (1650 + 47*50 = 4000). Now, that would likely change perfect
strategy quite a bit, so you'd have to cut back payouts to make up
for gains possible through strategy changes to keep the game EV the
same. But it sure looks like you could still have the royal paying
1000 coins and 4-to-a-royal paying 35-50. Personally, I would like
that game as it makes royals more like 4OAK's, where there already
are intermediate payouts for getting part of the way there (high
pairs and 3OAKs). And it would substantially reduce variance.
(*)Note: I used to think the ratio of 4-card "scares", where the 5th
card could have been drawn, to actual royals was 47:1. I'm not so
sure this is true any more based on records I have kept of my play,
but I don't have a better number to suggest and it's possible that
I've been drawing an unusually high ratio thus far. Anyhow, let's say
the 47:1 ratio is correct. You'd have to adjust the number for a few
more cases where the 5th card is not possible (i.e., you hold 2 Kings
and draw TJA of one of the suits), or exclude these from the hands
eligible for payment. The above calculations assumed the latter but
that is going to be hard to explain in 4 words or less, so the former
would probably be the way to go
For the sequential straight, one of every 60 straights should be
sequential either forward or backwards. In DB, straights pay 25
coins - cut that to 20, and you have 320 you could pay for a
sequential (60*25=1500;59*4+320=1500). Strategy change opportunites
here would be fewer, so 250-300 coins seems a reasonable final answer.
Or, pay 25:1 (125 coins) and take the cost out of the royal and leave
regular straights at 25 coins. This might be done for a cost of about
1500 coins on the royal: 1.50% of DB hands are straights, if we pay
125 for sequentials that means we need 0.50% total return
(0.015/60*100/5=0.050), which is 30% of the 1.67% ER of the royal in
DB, or 1200 coins. Suppose strategy gains require another 300 coins
to offset, that leaves 2500 you could pay for the royal.
Finally, right color, wrong suit on a 4-card flush draw would happen
about 1.50-1.63 times more often than a successful fill, depending on
the discard, so you could take 1 off successful flushes and probably
cover it (since not all flushes come from 4 card draws).
Alternatively, taking it from the royal might cost 3500 coins on the
royal, which is probably too much so not a good way to go. Flushes
are 1.52% of DB hands, say 60% come from drawing to 4 cards (that was
a SWAG), so you need .0152*.6*1.5*1 = 1.37% total return. The royal
is worth 1.67%, so taking off 1.37% leaves 0.30% or 723 coins. Reduce
for strategy gains and you might have 500 left over.
Note: these are all rough calcs, not extensively checked since this
is just blue sky type speculation - hopefully if I made any errors
somebody will catch them and give us the correct calculation.
The random wild cards idea is the one that I, personally, like least.
I mean, yeah that sounds great, but the overall game still can't
yield more than about 100%, and it seems like this feature would have
a very high cost on the regular paytable if it happens with any
frequency. Or it will be as rare as a sub-jackpot hand and will still
have a substantial chance of resulting in zero payout. So this would
be a real volatility booster. However, based on the latest new game
releases (multi-game, 50-plays, etc), this idea may be the most
likely to happen since VP players as a group seem to be notoriously
optimistic.
The other changes sound better to me, especially anything having to
do with reducing the value of the RF and spreading that gain over a
larger number of smaller hands.