How do you calculate ER?
Calculate ER?
utln wrote:
How do you calculate ER?
Mechanically, expected return is simply the expected win for one coin
wagered (or "expected coin out" divided by "coin in", expressed as a
percent).
However, determining the expected coin out (win) for a play is a
complicated task. It's dependent upon a game's paytable and the
strategy employed in playing the game. That strategy results in an
expected distribution of winning hands from which the expected coin
out can be determined in a relatively straightforward manner.
However, determining that expected distribution is the complex task.
Additionally, it's made even more difficult since the reference to
game ER generally is a specific reference to the game strategy that
maximizes ER.
Bottom line, some type of computer software is required. The most
readily available software is Frugal Video Poker (FVP) and Winpoker.
- Harry
ER = probability x win summed for each hand type
Variance = probability x (win - ER)^2 summed for each hand type
9/6 Jacks or Better, max ER strategy:
hand_win_prob_______ER__________VAR
rf__800_2.47583E-05_0.019806614_15.80588344
sf___50_0.000109309_0.005465454__0.262499984
4k___25_0.002362542_0.059063546__1.361341371
fh____9_0.011512207_0.103609865__0.737621624
fl____6_0.011014511_0.066087065__0.275865377
str___4_0.011229367_0.044917468__0.101371844
3k____3_0.074448699_0.223346096__0.299154602
2p____2_0.129278904_0.258557807__0.130460889
pJ+___1_0.21458503__0.21458503___4.46406E-06
nil___0_0.545434673_0____________0.540470506
Sum_____1___________0.995438946_19.5146741
Bankroll (11%ror)=variance/(ER-1) bets
N0 (std.dev.=ER)=variance/(ER-1)^2 hands
Bottom line, some type of computer software is required. The most
readily available software is Frugal Video Poker (FVP) and Winpoker.
Suppose someone wants to write software such as that above? They need
to know how to do these calculations manually. Can anyone offer some
recommended reading for this? I'm not talking about a math book on
general probability, but rather something that's focused on
probability for VP.
--- In vpFREE@yahoogroups.com, "technocyberhippy" <mindfuq@z...>
wrote:
> Bottom line, some type of computer software is required. The most
> readily available software is Frugal Video Poker (FVP) and
Winpoker.
Suppose someone wants to write software such as that above? They
need
to know how to do these calculations manually. Can anyone offer
some
recommended reading for this? I'm not talking about a math book on
general probability, but rather something that's focused on
probability for VP.
I don't know of any books specifically aimed at VP math, but that may
be because it's really not a book-length subject unless you get into
very advanced subjects. The basics of computing "strategies"
(actually, simply an ordered listing of odds) is pretty simple. What
computer languages do you know? I've written calculation and
simulation programs using a combination of Excel and Visual Basic,
and I'd highly recommend that combination if you really want to get
into the nitty gritty of the numbers, but a number of tools would
work.
Whatever language you know, I'd suggest you start off by writing a
simple program to build a 52-card deck, randomly deal 5 cards, accept
discard instructions and replace the discards, then evaluate the hand
under the standard 8/5 Bonus Poker paytable. That is not a difficult
program to write by any means, and pretty much anything else you want
to do can be done by modifying that program.
Tip: I don't know how commercial programs work (I'd be curious if
anybody does) but the approach I took was assign each card a numeric
alias of 3 digits. The first two digits run from 21 to 33 and
represent ace through king (i.e., 28 = an 8) and the third digt runs
1 through 4 and is the suit. Then, when evaluation time comes, start
by sorting the hand in order by the alias number. Then you can devise
short logical tests to determine if you have each kind of hand. For
example, a flush must have the same final digit for all cards.
Another example, 4 aces must have the "214" card in the fourth
ordered spot (think about it - no other hand would sort 214 this
low). And so on.
Just plunge into it and get done what you can figure out, and if you
get stuck on anything post a specific question on the board here.
You'll find it's really pretty easy.