I'll lean on Norm and Gronbog for help here? My understanding is that CVData guidance is +6, so that's what I used.Originally Posted by ZenMaster_Flash
Thanks Eric. So Hilo bets almost as well as Hiopt2 when the same optimal playing strategy is used for both (9 to 144 as the same with similar win RoR and paying some extra RoR 10 to 160 bet range for Hiopt2/ASC). A much smaller difference in win rate for Hilo's wider range of advantages in each betting bin. Apparently the wider range of advantage is narrowed a lot with more accurate index play.
One more update; it came up in discussion last night to effectively ask the dual question: what if we stick with index play, but can *bet* perfectly (i.e., with perfect knowledge of our pre-deal expected return, variance, indeed the whole distribution of outcomes)?
The following table fleshes this out. The "++" markings indicate playing with the indicated strategy, but betting optimally.
At first glance, this seems to strongly suggest that playing strategy matters much more than betting strategy... with the one exception that Hi-Lo I18 with optimal betting does manage to leap-frog Hi-Lo with full indices. Thoughts?Code:Strategy | $/hr | SCORE | ROR | <=0 +1 +2 +3 +4 +5 +6 +7 +8 +9 >9 ======================================================================================= TDZ | 14.46 | 15.04 | 0.1250 | 6, 20, 57, 93, 96, 96, 96, 96, 96, 96, 96 TDZ ++| 15.90 | 17.22 | 0.1147 | 6:1:96 Hi-Lo I18 (BJA3) | 19.87 | 21.22 | 0.1182 | 7, 23, 63,102,112,112,112,112,112,112,112 Hi-Lo I18 (BJA3) | 21.35 | 21.31 | 0.1359 | 8, 23, 63,102,128,128,128,128,128,128,128 Hi-Lo I18 (Cac) | 21.51 | 21.60 | 0.1343 | 8, 23, 63,102,128,128,128,128,128,128,128 Hi-Lo full | 22.22 | 22.48 | 0.1322 | 8, 23, 63,102,128,128,128,128,128,128,128 Hi-Lo I18(BJA3)++| 23.75 | 24.72 | 0.1247 | 8:1:128 Hi-Lo full ++| 24.67 | 26.02 | 0.1214 | 8:1:128 Hi-Opt II full | 25.19 | 26.65 | 0.1205 | 8, 8, 25, 48, 71, 95,119,128,128,128,128 Hi-Opt II full | 26.86 | 26.73 | 0.1367 | 9, 9, 25, 48, 71, 95,119,144,144,144,144 Hi-Opt II full ++| 28.08 | 28.43 | 0.1320 | 9:1:144 Optimal (Hi-Lo) | 30.07 | 31.11 | 0.1262 | 9, 31, 74,118,144,144,144,144,144,144,144 Optimal (HO2) | 31.44 | 33.05 | 0.1222 | 9, 9, 30, 55, 80,105,129,144,144,144,144 Optimal (HO2) | 33.18 | 33.14 | 0.1357 | 10, 10, 30, 55, 80,105,129,155,160,160,160 Optimal (opt.) | 34.90 | 35.40 | 0.1315 | 10:1:160
My unsolicited opinion:This is the best thread to ever appear on this forum.
I await commentary by TARZAN. His respect for Eric Farmer is paramount,
and for years he has waited for Eric Farmer to verify his strident (central)
canon ~ that P.E. is the primary metric worthy of our (collective) focus.
With this overarching principle I have always agreed; and it has led
me to the enhancement of my Hi-Opt II play via the inclusion of
Playing Adjustments for both Aces and Sevens, in keeping with the
marvelous chapter #5 of "The Theory of Blackjack" by the redoubtable
Peter Griffin, Ph.D. on "Multivariate Card Counting Systems."
Neither are looked at in a vacuum. That is playing strategy affects optimal betting. That said it is interesting that for Hilo, betting is so weak that Hi-Lo I18 with optimal betting does manage to leap-frog Hi-Lo with full indices. Hilo is supposed to be strong for betting but that is BC not betting accuracy. The width of the advantage bell curves around each advantage estimate for each betting bin says Hilo doesn't bet that accurately which this seems to confirm. I believe BC says how accurate your betting bin advantage estimates are but says nothing about the range and SD around the average advantage for each bin. Betting accuracy addresses both. Optimal betting (++) bets 100% accurate. The other thing to weigh into that is it is also affected by playing accuracy so it also says that the gain to full indices from the I18 may not be that much. The truth as to why, Hi-Lo I18 with optimal betting does manage to leap-frog Hi-Lo with full indices, lies somewhere in the combination of these statements (betting accuracy and playing gain from I18 to full indices). How much is due to either component is not clear.
ericfarmer,
I would interested in seeing what effects using risk-adverse indices would yield. If it's not too much trouble, even just seeing the hi-lo I18 results would be appreciated.
I currently use RA indices for more than just the I18 but am fully willing to re-sim the appropriate index set if it's not published anywhere.
This is a worthwhile project.
I use Risk Aversion, even though I have an almost ZERO R.O.R.
There is a gap in my BJ knowledge that needs filling.
Can we see a table of playing indices indicating the delta -
(metric indicating rate of change).
I know that there are (significant) differences for various hand matchups.
True risk aversion is a function of critical fraction of bet to BR size. There is not a one size fits all risk averse index for any play. Read BJA3 pp. 370-378. The table on page 378 shows the effect of bet relationship to BR on risk aversion but reading those few pages until you understand the math will help clear things up.
The odds are with 0 RoR there are no risk averse indices and you should use EV maximizing indices. That said, I play to less than .01% RoR but I still use some risk averse indices. To me an extra penny in EV is not worth twice the risk whether the play has a risk averse index for my ratio of BR to bet size or not, at least for bigger bets.
Last edited by Three; 01-22-2017 at 10:48 AM.
Eric's research always has no agenda. That is why he gets respect from almost everyone. He is interested in answers. He is looking into the absolute ceiling for perfect play and betting. The application is to see how close one can come using various approaches. The traditional systems results are well known. Just how much is left on the table and what avenues can recover some of it is illuminated. Then the non-traditional approach that can break through the ceiling for the additional approach falls somewhere at or below the absolute ceiling for optimal play and optimal betting. The question can be answered as to what is the real value for approaching the unattainable absolute ceiling, playing more accurately than traditional approaches or betting more accurately. If you abandon the linear approach for using count tags 1.0 BC is no longer the ceiling because BC has no meaning. The value of the count tags are no longer static for determining bets. The tags never change but they are not used in a linear fashion so the bets would look like the count tags are changing. In other words count tag and cards removed are no longer indicative or predictive of the recommended bet for your approach. The same is true for PE where PE of 0.70 is said to be the linear ceiling but nonlinear approaches to information gathered are said to have PE in the .9's.
I don't think you understand the point of what he is doing. It isn't about comparing counts. It is about understanding counts individually and how you might strive to increase your counts performance by non-traditional additions like side counting for PE gain where the count tag for the side counted card varies by hand match up. Or non-traditional methods for sizing bets that make BC meaningless because bet size is not linearly related to the count tags you assign for gathering information due to the way you use the information gathered. Much talk has been made about the gain or lack thereof for non-traditional approaches. Eric has established the absolute ceiling of perfect play and/or perfect betting is worth the effort but the effort will only attain a portion of that. The question is, will that portion also be worth it? Those that practice such systems believe it is. At some point we may see some statistics to show just how much of that difference between the traditional approach ceiling and the absolute perfect play and/or betting ceiling the non-traditional approaches of gathering and using information can capture.
Well, isn't everyone's RoR technically never zero anyways? We just paraphrase '0 RoR' as negligible or virtually zero however, not matter how big your bankroll is there is still the theoretical possibility (albeit beyond rare--mind numbingly unlikely) that you can lose enough bets to go bust. Unless the casino decides that their next mailer they send will be for "100% loss rebate: lifetime duration; any number of bets; all bets qualify" then you'll never literally be at 0 RoR. A physicist once told me that it's theoretically possible for atoms to randomly arrange themselves such that you fall through a wall you're leaning against, but again, mind numblingly improbable and for all intents and purposes, impossible.
This is a good point. As Tthree points out, the only "new" entries in the tables presented here are those for optimal play. I only included the others (fixed/basic total-dependent strategy, Hi-Lo, Hi-Opt II, etc.) for two reasons:
First, including fixed/basic TDZ establishes a "baseline" of *lowest* reasonable performance, which with the optimal performance at the other end, gives us a normalizing yardstick between which we can evaluate any other strategy. (This is something I tried to do back in 2013 as described here, where in that case I focused solely on *playing* efficiency, basically since betting efficiency was beyond the capability of my CA at the time. This is something that Don asked about regarding this latest analysis, so following is a table of flat-bet EV for each strategy, as well as a corresponding conversion to what I have proposed is a "better PE": )
The second reason is just sanity checking: *because* performance of these systems can be evaluated via other means, I had better be able to reproduce those figures using my algorithms, implementation, and analysis approach. Once that consistency was verified, that gives us confidence that the *new* results, namely *optimal* strategy performance-- which is evaluated using exactly the same algorithms, implementation, and analysis approach, just different inputs-- are sensible.Code:Strategy | E[X] | PE =================================== TDZ | -0.4655% | 0.000 Hi-Lo I18 (Cac) | -0.4080% | 0.292 Hi-Lo I18 (BJA3) | -0.4001% | 0.333 Hi-Lo full | -0.3792% | 0.439 Hi-Opt II full | -0.3413% | 0.632 Optimal | -0.2688% | 1.000
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