Steve, keep posting . This lurker enjoys reading your posts and the related posts of other list members. I am seeking a sensible alternative to max-ev strategy for my own situation, and these discussions help. My problem - play 2,000 games of AA with smaller losses in the typical losing session, while maintaining a positive overall expected value. (Words intentionally avoided - average - variance - long-term.)
[Non-text portions of this message have been removed]
"Warren Trotter wrote:
Steve, keep posting . This lurker enjoys reading your posts and
the related posts of other list members. I am seeking a sensible
alternative to max-ev strategy for my own situation, and these
discussions help. My problem - play 2,000 games of AA with smaller
losses in the typical losing session, while maintaining a positive
overall expected value. (Words intentionally avoided - average -
variance - long-term.)
------
I'll comment on this, primarily motivated by the sense that my most
recent post on this topic prompted it.
I in no way intended to suggest that Steve discontinue posting. What
I expressed was the sense the the additional feedback I received from
him was best addressed privately rather than spur further discussion
in the direction our exchanges has taken.
------
Concerning your AA play goal. It's entirely rational, particularly if
AA is your best play available, even at the reduced ER when strategy
is altered. The min-loss approach that Steve has discussed is apt in
this case.
That said, it's best that you quantify the magnitude of expected
reduced loss between royals. You may well find that it falls short of
your expectations, or you find it's not sufficient to warrant learning
an alternate strategy - keeping in mind that the learning effort
likely will increase error rate/cost. If you don't possess, at ready
hand, the knowledge to perform this calculation it may be an
indication that it's not a desirable direction to take - although it's
a calculation that can easily be absorbed upon discussion.
FWIW, min-loss is more likely considered when approaching a
progressive since very strong progressives, particularly at higher
denominations, are a rarer find. This presents a playing situation in
which there's a greater expectation over any timeframe (e.g. 5 years)
that actual prog. return will significantly vary from ER. It then
becomes desirable for some to sacrifice ER in favor of greater
probability that play will adhere more closely to ER. (In case it's
not obvious, we're basically talking reduced variance from modified
strategy with only modest ER decrease.)
------
A note concerning the separate doubling/ER discussion. The ultimate
impasse will be acceptance that doubling doesn't present additional
"coin in" which would be included in the denomminator of the ER ratio.
This is unfortunately true even though a fully valid, analogous
analysis demonstrating unchanged ER can be presented in which the
"option" to double is removed but yet still fully reflects the
mechanics of the actual the double wager in machines.
Consequently, I agree with "lb" -- it's best to accept that there will
be disagreement on this and move on, and I regret belaboring it to the
extent I have.
------
So, what do you say I lay back for awhile, observe, and learn from
others ...
- Harry
run vpsm with rf=640, sf=190
"Warren Trotter" <wtrotter@e...> wrote:
My problem - play 2,000 games of AA with smaller
losses in the typical losing session, while maintaining
a positive overall expected value.
"Warren Trotter" <wtrotter@e...> wrote:
> My problem - play 2,000 games of AA with smaller
> losses in the typical losing session, while maintaining
> a positive overall expected value.
kruggerrands wrote:
run vpsm with rf=640, sf=190
I could use a bit of education here.
My understanding is that if you choose to skew play away from a single
hand to minimize intervening loss, you choose the play strategy that's
represented by a paytable when the value of that hand is set to target
a 100% ER.
For example, if you're playing a JB progressive with a RF meter at
1200 bets ($1500 for a 5-coin quarter game), min-loss strategy would
refect a RF meter at approximately 1000 bets. (I hope I've nailed
this correctly since I'm writing on the fly.)
While I've never worked out application of min-loss when the strategy
seeks to minimizing loss between two infrequent hands, in the case of
AA - the SF and RF, I would have expected that the paytable optimized
is still one representing a 100% ER.
The set values for the SF/RF you suggest present a 100.23% ER. Where
did I skid off the correct path?
- Harry
"Harry Porter" <harry.porter@v...> wrote:
kruggerrands wrote:
> run vpsm with rf=640, sf=190
The set values for the SF/RF you suggest present a 100.23% ER.
Where did I skid off the correct path?
my numbers are sorokin adjusted (min bankroll)
AA sorokin number = 0.99941069150546
sorokin adj = (1-S^Win)/(1-S), S=sorokin number
ex: instead of rf=800, rf sorokin adjusted=(1-S^800)/(1-S)=638
(above i rounded to 640)
deuces sorokin number = 0.999346831403995
joker sorokin number = 0.999463345797305
kruggerrands wrote:
my numbers are sorokin adjusted (min bankroll)
Got it. Not the "min loss" strategy goal suggested by Warren in
stating he seeks to reduce session loss, but minimizing bankroll is
the more practical goal.
I've only a passing familarity with the specifics of Sorokin
calculations. For the AA example (and let's assume .2% cb), how does
the bankroll requirement of ER optimized strategy compaire with a min
bankroll strategy? (expressed in number of bets for each case).
- Harry
"Harry Porter" <harry.porter@v...> wrote:
kruggerrands wrote:
> my numbers are sorokin adjusted (min bankroll)
Got it. Not the "min loss" strategy goal suggested by Warren in
stating he seeks to reduce session loss, but minimizing bankroll is
the more practical goal.
same thing
I've only a passing familarity with the specifics of Sorokin
calculations. For the AA example (and let's assume .2% cb), how
does
the bankroll requirement of ER optimized strategy compaire with a
min
bankroll strategy? (expressed in number of bets for each case).
i'll do the no cashback example, since that's what i started with:
sorokin with 638/189 adj. strategy=0.99938991471174
10%ror bankroll, maxER strategy = 3906 bets
10%ror bankroll, minBankroll strategy = 3773 bets
this stuff can be done with a spreadsheet as long as you have some
software that will tell you the hand probabilities for the adjusted
strategies and you know the formula for sorokin number:
Prob x S^(Win+CB) summed for each hand type
oh what the heck:
AA+.2%cashback:
sorokin=0.99922792999308
10%ror bankroll=2981 bets
adjusted strategy: rf=597,sf=185,4k=39
adjusted strategy sorokin=0.99919500881707
10%ror bankroll=2859 bets
(you can repeat the adjustment again with the new sorokin number,
you'll get slightly more accuracy)
kruggerrands wrote:
oh what the heck ...
Thanks, "k"
- H.
Actually, these are not quite the same. Using a different game
(JoB 9/6 with 1300 unit payoff for royal) the 10% RoR bankrolls
come out:
10% RoR
bankroll S strategy
On Friday 02 April 2004 07:47 pm, kruggerrands wrote:
"Harry Porter" <harry.porter@v...> wrote:
> kruggerrands wrote:
> > my numbers are sorokin adjusted (min bankroll)
>
> Got it. Not the "min loss" strategy goal suggested by Warren in
> stating he seeks to reduce session loss, but minimizing bankroll is
> the more practical goal.same thing
-------------------------------------------------------------------
5515.68 0.9995826257 Min-risk strategy (aka "Sorokin", min-bankroll)
5517.75 0.9995827819 min-cost-royal (equiv. royal payoff 976 units)
5583.20 0.9995876719 TLO (True Log Optimal, Kelly approximates this)
5644.60 0.9995921560 max-EV
5644.77 0.9995921684 min-cost (best "exchange rate")
-------------------------------------------------------------------
The TLO numbers were obtained by exact optimization of expected
log bankroll. This is what Kelly betting attempts to achieve, but
the Kelly formula for bet size is an approximation. The TLO (True
Log Optimal) strategy finds the bet fraction which optimizes
geometric growth rate, then optimizes playing strategy based on
that bet fraction.
A TLO player who is constrained to play an inadequate bankroll
will change strategy in the direction of the min-risk strategy, so a
VP player who believes in Kelly principles but has an insufficient
bankroll would use a strategy somewhere between the TLO strategy
and min-risk strategy. As bankroll shrinks, the achievable growth
rate declines until the growth rate reaches 1.0, which occurs when
the bankroll is slightly less than half the optimal size. At this point,
min-risk strategy gives the optimal growth rate of 1.0. This means
that under-bankrolled players should consider switching to min-risk
strategy rather than play max-EV strategy, because doing so will
give a higher geometric rate of bankroll growth.
A TLO player who is constrained to play a unit size which is
smaller than their bankroll allows would use a strategy which is
more agressive than TLO, moving toward the max-EV strategy.
From a Kelly perspective, the max-EV strategy is only correct
for players who have such a large bankroll that they cannot find
machines with a large enough unit size to permit optimal bets.
The max-EV strategy is the most aggressive.
One more comment about log optimal play. It is important to
understand exactly what TLO/Kelly play is trying to achieve.
The goal is to get maximum growth rate, and this is not the
same as minimizing bankroll requirement. The strategy which
gives minimum bankroll requirement is the strategy that I call
"min-risk." This means that a TLO player should _not_ compare
games and/or strategies on the basis of the optimal bet size,
as this will tend to select the game/strategy with lowest risk
(which is equivalent to smallest bankroll requirement) rather
than the strategy with maximum growth rate.
For the 9/6 JoB game described above, the optimal bet
fraction for TLO strategy is 1/4493.35 units (corresponding
to a 15.67% RoR), and TLO strategy with this bet fraction
gives a growth factor of 1.00000097251. This implies that
an average of 712,741 bets are required to double the bankroll.
Using the min-risk/min-bankroll strategy allows the player to
wager 1/4437.41 units (corresponding to a RoR of 15.685%)
and gives a growth factor of 1.00000094259. This strategy
takes an average of 735,365 games to double the bankroll.
This means that the TLO strategy reduces time-to-double
by about 3% compared to the min-risk strategy.
Careful examination of the numbers I've quoted here reveals
a paradox. From the perspective of flat betting and Risk
of Ruin, the min-risk strategy minimizes bankroll requirement.
However, from the Kelly perspective, the TLO strategy
minimizes bankroll requirement. The concept of "bankroll
requirement" appears to be a relative thing which depends
on the underlying player objective, and not a distinct
concept that stands by itself.