Ummm...OK. Should I put my 75 Cents in the machine?
(Wow, I just realized how non-techie I play video poker. <G>)
···
-----Original Message-----
From: Harry Porter <harry.porter@verizon.net>
To: vpFREE@yahoogroups.com
Sent: Wed, 10 Aug 2005 19:23:53 -0000
Subject: [vpFREE] Re: Multi-strike
John wrote:
Can someone explain the math behind the 2/4/6 numbers and how they
were arrived at? They dont seem intuitive to me at all. I would
expect all paying hands on Level 1 to be worth far more, since not
getting a paying hand causes you to miss out on the next 3 levels!
I'll offer up a reply with a modestly different perspective from that
of JBQ -- but his reply is accruate.
Jumping up to Level 3, the question is how to value the potential of
advancement to, and a win on, Level 4.
For simplicity's sake, it's assumed that the ER of the base game is
100%. So, on a wager of 1 betting unit, the expected payback is 1
betting unit.
Any time a win is scored on Level 3, you'll advance to Level 4.
Again, with a 100% game, the expected payback will be 1 betting unit,
but this Level pays twice that of Level 3, so that full expected
payback is 2 betting units.
So, for each winning hand type on Level 3, the payback to use in the
paytable is the payout for each hand PLUS the 2 betting unit expected
payout from advancing to Level 4.
If you're constructing the paytable for analysis of Jacks or Better on
Level 3, you'll add 2 for each coin played to the payout of every
hand. For example, the payout used for a 5 coin wager on Two Pair
would be 10 + (2*5) = 20.
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Now, it's worthy to note that payouts for hands on Level 3 are
actually multiplied by 4. However, for purposes of analyzing the
proper strategy for Level 3, it doesn't matter whether you multiply
all payouts by 4 or simply use the base payouts for that Level. Both
produce the same result.
----------
Having reasoned out how to treat Level 3, earlier Levels can be
handled in a similar manner. When looking at Level 2, the value of
advancement with a win is 2 for Level 3 play plus, should play advance
to Level 4 with a win (or Free Ride) on Level 3, another 2 for Level 4.
We're analyzing the value of a win on Level 2 (after all, we're
establishing the proper paytable for each winning hand), so it's a
given that play will advance to Level 3. However, it's now not
certain that we'll advance to Level 4.
Here's where it's necessary to know that the Free Ride frequencies for
each level have been set at values that, when an optimal play strategy
is used (the one that is represented by the adjusted payouts
determined here - +2/+4/+6) the probability of advancement to the next
Level is roughly 50%.
So, from the perspective of play on Level 2, the relative expected
payout for a win on Level 4 is 4 times that of Level 2 (reflecting
respective payout multipliers of 8x and 2x). Again, assuming a 100%
game, the EV of Level 4 play is 1 bet, multiplied by the 4 times
greater payouts = 4. However, when a win on Level 2 is assumed, the
probability of advancing to Level 4 with a win on Level 3 is 50%.
This means that, bottom line, the value added by potential advancement
to Level 4 after a win on Level 2 is 2 betting units.
So, we augment the Level 2 payouts by adding 2 betting units for the
value of the guaranteed advancement to Level 3, and by another 2 units
(a total of 4) for the 50% likelihood of advancing to Level 4 with a
win on Level 3.
----------
Can you see where this is going to for Level 1?
In analyzing Level 1, the value of advancement to Level 2 is analogous
to the analysis of Level 2 and the value of advancement to Level 3.
We add 2 betting units here.
Similarly, the value of advancement to Level 3 in this case is
comparable to the value of advancement to Level 4 when we were
assessing play on Level 2.
That leaves valuing the potential advancement to Level 4 from Level 1.
The probability of advancing to Level 2 is a given at 100%. The
probability at continuing to advance to Level 3 is 50%. The
probability of advancement to Level 4 play is equal to the probability
that we'll advance to Level 3 and (i.e. times) the probability of
advancing to Level 4 from Level 3. A joint probability of 25%.
Because the payouts on Level 4 (8x) are 8 times that of Level 1, the
EV of a win on Level 4 is 8 (our 100% ER x the multiplier). HOwever,
the probability of the win is 25%, so the adjusted EV of potential
Level 4 play to be added to Level 1 is 8 betting units * 25% or, again, 2.
We augment the Level 1 payouts by 2 units for Level 2 advancement, and
another 2 units each for potential advancement to Levels 3 and 4. A
total of 6.
------------
+2/+4/+6 -- got it?
I apologize for the long winded explanation - I'm sure it could be
considerably condensed. Hopefully you've skimmed and caught the full
gist.
- Harry
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