Sorry about the table mess in my post. Yahoo says the HTML editor
should work, but I still can't figure it out.
If anyone wants to see what those tables really look like, just
email me at h_dunbar@hotmail.com.
--Dunbar
That's a very clever and simple way of looking at things, NOTI. I
don't remember seeing it formulated that way before. The
"ballpark" turns out to be quite good for longterm RoR calcs.I checked for both longterm and short-term RoR/Bankroll agreement
using
Dunbar's Risk Analyzer for Video Poker. FPDW with no cashback
agreed quite well with BP with 0.66% cashback*, especially for the
longterm. Then I thought maybe that's because the two games have
similar variance, so I looked at a big variance game, Double Double
Jackpot. (DDJ has var=38 compared to 26 and 28 for the other two
games.) I still got total agreement on longterm RoR, and just a
little
more dispersion on short-term.
Here are my results:
LONGTERM BANKROLLS for Various RoR's Comparing FPDW (no cashback)
with Double Bonus (0.66% cashback) and Double Double Jackpot (0.78%
cashback)
GAME: FPDW DB,.66% DDJ,.78% % RoR Bankroll Bankroll Bankroll 25%
2,700
2,750 2,750 20% 3,100 3,150 3,150 15% 3,650 3,750 3,750 10% 4,450
4,500
4,500 5% 5,750 5,850 5,900 2% 7,500 7,650 7,650 1% 8,850 9,000
9,000
0.5% 10,150 10,350 10,350 0.1% 13,250 13,500 13,500 0.01% 17,650
18,000
18,000
You can see there's not much difference in the 3 games if you pick
cashback the way NOTI suggested. (Bankrolls above are calculated
using
the jazbo/Sorokin polynomial risk equation.)
SHORT-TERM Results for the same 3 games as above 16 hours at 400
hands/hr, $2000 bankroll
FINAL BANK % CHANGE FPDW DB,.66%CB
DDJ, .78%CB
0 lose 100% 0% 0% 0% 1 - 399 lose 80% to 99% 0% 0% 0% 400 -
799
lose 60% to 80% 0% 0% 0% 800 - 1199 lose 40% to 60% 0% 2% 4%
1200 -
1599 lose 20% to 40% 15% 16% 17% 1600 - 1999 lose up to 20%
39% 34%
29% 2000 - 2399 win up to 20% 25% 27% 23% 2400 - 2799 win 20%
to 40%
11% 12% 14% 2800 - 3199 win 40% to 60% 6% 6% 7% 3200 - 3599
win 60%
to 80% 2% 3% 3% 3600 - 3999 win 80% to 99+% 1% 1% 1% 4000 +
double
or more 0% 0% 1%
In the short-term comparison, the game with the highest variance,
DDJ,
shows more dispersion than the other 2 games. While FPDW stayed
within
20% of the starting bankroll 64% of the time, DDJ stayed within
20% of
the starting bankroll just 52% of the time**.
My conclusion is that NOTI's Kelly fraction method is an excellent
way to find how much cashback it would take to give the same
longterm
bankroll-to-risk relationship as another game. However, it isn't
as well-suited for determining short-term (or session)
bankroll. (I
should note that NOTI never suggested it WAS useful for short-term
bankroll assessment).One final observation is to note how much difference there is
between
longterm and short-term bankroll considerations. A $2000 bankroll
is
completely adequate for a 16-hour stretch of play, but it would
not be
enough for a longterm bankroll for any of the 3 games above. --
Dunbar
* I used 0.66% instead of NOTI's 0.65% because that's the Kelly
figure I got when using variance and EV figures with more
significant
···
--- In vpFREE@yahoogroups.com, "dunbar_dra" <h_dunbar@...> wrote:
figures (from WinPoker) than the quick "26" and "28"
that NOTI used.** each short-term RoR calc consisted of 20,000 trials.