Betting granularity

After some research, running sims, and modifying a couple of strategies to understand this subject better, I hope I have it right.

Betting “granularity”

Here comes this awesome 11 letter word. “granularity”. According to Wikipedia: “Granularity is the extent to which a system is broken down into small parts, either the system itself or its description or observation. It is the "extent to which a larger entity is subdivided. For example, a yard broken into inches has finer granularity than a yard broken into feet."

After much reading about this on these boards and looking up the technical meaning, what exactly does it have to do with BJ?

To those who have just read through the word and all those other posts and didn’t care what it means, I guess you’ll skip this post too. To those interested keep reading. For those who can explain it better then I can, please help out. If I’m wrong in the explanation go ahead and blast me.

So when does “granularity” come into play?

Many times the word comes up when we discuss 1/2DTC, 1DTC, or 2DTC. In expanded terms this means when you convert the RC to TC. Some of us use ½ D TC conversion, 1d TC conversion, or 2d TC conversion.

The easiest way I came up to explain it is this:

Let’s say your strategy uses 1/2DTC. The current RC is 6 with 3d left to play so your TC=1. If you change to 1DTC which also requires you to double your indices, the same RC of 6 results in a TC=2.

When we run a sim using the 1/2DTC and look at all the TC’s both negative and positive generated by the sim it produces a range. Now lets say the range of all TC’s that come up greater then 1% of the time will be between TC-6 & TC+5.

Taking the 1/2DTC as an example first, for the sake of ease we can say that in the optimum betting strategy there may be 5 steps in our 1-12 spread betting strategy.
For example TC0=1u, TC+1=3u, TC+2=4u, TC+3=6u, TC+4=10u, TC+5=12u

Using the 1DTC as an example, the new range of TC’s that occur may range from TC-9 to TC+8. The optimum 1-12 betting strategy will now spread out your bet spread over a larger number of positive TC integers. For example:

TC0=1u, TC+1=2u, TC+2=3u, TC+3=4u, TC+4=6u, TC+5=8u, TC+6=9u, TC+8=10u, TC+9=12u

In this same scenario, going to 2DTC would require you to change the indices accordingly and would increase the number of steps in your betting strategy yet again.

So what does this do for us? After close review it does this: It allows us to bet closer to the true advantage we have at the time. The less jumping of bets we do as we go up each TC, which in definition “smaller parts”, prevent us from over or under betting our advantage.

So I thought, what if I set up my betting strategy by ½ TC steps. Unfortunately it did not produce the results I had expected.

My conclusions force me to admit that there are real benefits in “betting granularity”.

BJC

knee jerk reaction

ok, bjcount, i'm still kind of woozy after a few marathon bj sessions and no sleep, lol.
is this granularity thing your investigating anything like the stuff i noticed with my excel shuffler, as in the two images in the link below. ie. tc calculation exact division results to some number of significant figures vs rounding sort of thing?
http://www.blackjackinfo.com/bb/showpost.php?p=117353&postcount=18

erhh, i think the thing about considering a tc & a half, sort of stuff is supposedly the advantage between tc integral values isn't necessarily linear.

fr0g
Not sure how to interpet your graphs, sorry. Don't think it's in the same line of my interpetation.
Get some rest, hope the marathon was a winner.
BJC

still woozy, lol

is this right?
lol, i don't use 1/2DTC so i have no idea.

but wouldn't it be if your going by half decks then for 3d left to play that would be six half decks? that being the case wouldn't your TC = 2 instead of TC = 1 ? 6/(6/2) = 6 x 2/6 = 2 .

i guess i'm gonna learn something here.

Sure, the "smoother" your bets are correlated to your advantage, the better things will be from a risk of ruin standpoint. It's more about risk management rather than profit maximization.

I believe a count where the numbers are doubled, like perhaps zen or halves, will also exhibit this same behavior. In fact, Qfit attributed one strengh of an unbalance count like KO to the fact that the RCs tend to get to really large numbers, resulting in smoother (Albeit unbalanced) bet ramps.

If $33.50 was your optimal bet at TC +3, and you could actually make it, more power to ya. Practically, a certain amount of rounding may be necesessary.

fr0g

you got the six half decks right.
Using the same example above:
In 1/2DTC
If your RC is 6 and you divide by the 6 half decks your TC=1

In the 1DTC if your RC is 6 your divisor is 3 (3d left to play/1DTC) = TC=2

Similarly if your using 2DTC, if your RC=6 your divisor is 1.5 (3d/2DTC) = TC=4

BJC

please forgive my ignorance

ahh, i think i understand now. thank you for explaining.
me, i've just ever used fulls deck as a divisor. i just know me and my capabilties, lol.
and i had noticed how cvbj when true counts are set up won't allow the divisor to be a full deck for the last deck resolution when multiple deck is set up in the options stuff.
so ok, anyway i guess by going to half decks, quarter decks or even all cards sort of resolution, what it does is makes for more information, just like say you have a bunch of thermometers, one that just says hot, luke warm, cold, another that has degree's of temperature by tens of degree's and another that has degree's of temperature by one degree, ect.
so anyway i guess depending on how you resolve your tc's then the simulator makes amends for how to say bet optimally accordingly and stuff.

Here's a slightly shorter explanation of granulatiry:

http://www.advantageplayer.com/blackjack/forums/bj-main/webbbs.cgi?read=21413 (Archive copy)

-Sonny-

Thanks Sonny..

I'm finding through sims the SCORE is moving but not as anticipated. Here is what I have so far in my final trials. I started with poor games and will do a few on better including some w/ wonging. MathProf has a way with numbers to better explain my results (GC).

4.5/6d, DAS, LS, S17, play all, $10 unit, 500 million hands each sim (all bets were in rounded $10 units no fractional bets)

The first one was based on the playing and betting strategy I use in real casino play. I use RPC with RA modified indices and 1/2DTC conversion. Using CVCX it generated the optimum betting ramp for this strategy in full integer TC steps.

In the second sim, using CVCX, I generated the optimum betting ramp using the same playing strategy as above but this time used a Half TC betting ramp.

In the third sim I doubled all the indices from the playing strategy above and used CVCX to generate the optimum betting ramp for full integer TC betting ramp. This time instead of 1/2DTC conversion, I used 1DTC conversion.

BJC

Food for thought

Try looking at the difference between 1/2DTC conversions and 1DTC conversions using half-deck estimations.

-Sonny-

All sims are run using 1/2 deck estimation (resolution as cvdata puts it).

BJC