scobee 1: Effects of Co-variance and Overbetting Your Bank

[scobee 1]

I have had some astounding results recently by implementing some playing strategies I really cannot afford. Although I attribute most of my success to good luck, I also have run a series of BJRM sims that suggest that I am increasing the DI of my available games significantly when I play two hands the majority of the time, instead of conservatively staying within a fraction of the full Kelly criterion with one box that most recommend. I have been winning at approximately 4X my expected value, which has doubled my actual playing bankroll twice in 350 hours over the past few months. I realize that the longer I play, the more likely I will revert to the mean of my EV. Since this would predict more losses than wins in my immediate future, I have decided to postpone playing for a couple of months while I evaluate my playing records and do further research and practice. I seriously doubt that I can sustain my current 80% session win rate while playing at a 16% ROR. Here is what I have done...

The most common game for red chip players here in the midwest is simply unplayable. Crowded conditions and low EV meant that I was often playing with a SCORE of 25-35 with red chips. Even so, I was able to occasionally take trips to better locales and build my bankroll. Soon enough, with some outside contributions and a little help from creative accounting, I found myself playing to a $10K bank instead of the original $1K actual/$5K theoretical that I started advantage play with. I am now playing to a $15K bank with a $25 unit.....sometimes a $10-15 unit if possible. Even though my ROR hovers from 9-16%, I am comfortable that if I take a plunge in profits I will be able to renew my assets.

Since the games at low level tables suck, I recently started playing higher limit games. This started with DD games in Vegas, where a smaller spread would allow me an advantage. Now that I am back in the midwest, only 6D games are readily available. My typical rules would be S17, DA, DAS, S3X, no RSA, and being able to play table minimums on two boxes. Pen varies from 4.5 to 5/6, but usually I can find 5/6. I refuse to play crowded conditions or early shuffled games. Occasionally I will be playing RSA and LS, but let's leave that out of the equation for now. I use the hilo count and Snyder's High/Low Lite indices instead of the catch 22. Either set of indices would be an aid in analysis. My preferred strategy is to come off the top with 2 boxes of $25, dropping to one when the count reaches TC-1. At TC-2, I try to sit out or leave the table. As the TC rises to +1 and above, I continue to play two boxes and at each floored point, increase my bet. This would mean two boxes of $50@ +1, 2X$75@+2, 2X$100@+3, etc. with my maximum bet being 2X$200@ >+4. My question is how helpful is co-variance in neutral counts and how much additional risk am I taking on by increasing my spread over two hands given that my total BR remains the same? I am shooting for a ROR of 5% ideally, but have to limit my theoretical unit to $25 so as to be able to play under optimal conditions and maximize my SCORE. Some casinos require that I have two boxes of $50 for my minimum bet off the top. Any help would be appreciated in evaluating what my needed bankroll would be and how variations on this theme might limit my risk and/or optimize my EV while keeping variance manageable. What would a reasonable trip bankroll consist of? If I travel with 20 maximum bets as my trip bank, what are the chances I will tap out in a five hour session?

I understand that I am quite fortunate to have not yet lost half my bankroll while playing underfinanced, and this is the mitigating reason for my impending hiatus. Any suggestions as to optimal bankroll would be appreciated, or advice on changes to this strategy in keeping me viable. I am committed to maintaining the $25 unit in my game, so interpretations in that direction would be appreciated. I also utilize white rabbit and grasshopper techniques whenever possible, but cover considerations with home casinos require that I limit this to special occasions.

Thanks for any insights...

scobee

[Don Schlesinger]

> Since this would predict more losses than
> wins in my immediate future, I have decided
> to postpone playing for a couple of months
> while I evaluate my playing records and do
> further research and practice.

That statement makes no sense at all. Do you think the cards are preparing to "punish" you for your past wins? Do you figure they "know" that you owe them some money? Don't fall into the classic "maturity of chances" fallacy. When a fair coin falls heads 8 times in a row, do you figure more tails are coming, so they can "catch up"? In short, if you are playing properly, you are NEVER due for more losses than wins.

> I seriously doubt that I can sustain my current 80% session win rate while playing at a 16% ROR.

That may very well be true. But, it's different from what you implied above.

> My question is how helpful is co-variance in
> neutral counts and how much additional risk
> am I taking on by increasing my spread over
> two hands given that my total BR remains the
> same?

Increasing to two hands need not increase ROR at all, provided, for a given bank, you bet on each of the two hands 75% of what you would have bet on one single hand.

> I am shooting for a ROR of 5% ideally,
> but have to limit my theoretical unit to $25
> so as to be able to play under optimal
> conditions and maximize my SCORE. Some
> casinos require that I have two boxes of $50
> for my minimum bet off the top. Any help
> would be appreciated in evaluating what my
> needed bankroll would be and how variations
> on this theme might limit my risk and/or
> optimize my EV while keeping variance
> manageable.

What you're doing isn't bad. ROR is slightly more than 5%, however. So, you either have to increase the bank or find a way to bet less than $25 as a minimum.

> What would a reasonable trip
> bankroll consist of? If I travel with 20
> maximum bets as my trip bank, what are the
> chances I will tap out in a five hour
> session?

Virtually nil! If a top bet is 2 x $200 = $400, and you're bringing $8,000 with you to play 5 hours, you will virtually never lose that much.

> I understand that I am quite fortunate to
> have not yet lost half my bankroll while
> playing underfinanced, and this is the
> mitigating reason for my impending hiatus.
> Any suggestions as to optimal bankroll would
> be appreciated, or advice on changes to this
> strategy in keeping me viable. I am
> committed to maintaining the $25 unit in my
> game, so interpretations in that direction
> would be appreciated. I also utilize white
> rabbit and grasshopper techniques whenever
> possible, but cover considerations with home
> casinos require that I limit this to special
> occasions.

> Thanks for any insights...

Not a whole lot to add, I'm afraid. The bank is what it is, and the bet limit is fixed, as well. Just continue to avoid the negative counts. You're doing all right. Playing 2 x $200 with $15,000 of bank is not all that risky, especially if you back-count.

Don

[scobee 1]

After that lengthy series of posts on BJMath about team play, and some recent discussions with pro players, it seemed to me that with only two periods of extended losses over the past year, I am now 'due.' This may be nothing but a superstitious folktale. My hourly win rate over the course of this year is not outrageous. I am not thinking of the 'maturity of chances' so much as the average session win rate for skilled players of 55-60%. I don't expect to be punished for my good fortune, but I want to accept that this win rate may not last forever....or given the minimal correlation between skilled play and short term results, perhaps it will.

In any case, this random walk has been filled with a long positive swing for some time now and I would like to savor it through the holidays. I also want to understand the possible outcomes with a new betting schedule and the requirements of bankroll needed to sustain my play through normal fluctuations.

> What you're doing isn't bad. ROR is slightly
> more than 5%, however. So, you either have
> to increase the bank or find a way to bet
> less than $25 as a minimum.

So the plan would be to increase the bank to $20-25K to reduce the risk of ruin... and to find good $10-15 games where I can spread aggressively, whenever possible.

> Not a whole lot to add, I'm afraid. The bank
> is what it is, and the bet limit is fixed,
> as well. Just continue to avoid the negative
> counts. You're doing all right. Playing 2 x
> $200 with $15,000 of bank is not all that
> risky, especially if you back-count.

I just wanted to be sure I wasn't making some huge mistake in my calculations balancing a slightly higher ROR with a plan to maximize bankroll growth. Thanks especially for Chapters 11&12 in reference to making decisions about which games are worthwhile and how to create strategies with optimal departure points.

Regards,

scobee

[scobee 1]

I appreciate Don's comments, but I was kinda hoping to get some discussion about playing two hands at what would be a comfortable level.....if you were informed by sims that only one hand was your preferred Kelly. I know it is common practice to spread to two hands in higher counts, and that DD' has suggested that two hands at table minimums is one way to eat small cards. My confusion is about what you sacrifice to ROR when you play two hands off the top and during neutral TC's in relationship to what you gain from co-variance. Let's say that rather than betting $50 off the top as a minimum, you played 2X$25 instead as your minimum. What difference would it make to your EV and variance? It would seem to lower variance but not affect EV. Help me out here, guys. Conversely you could theoretically double your betting level and not double your ROR.... so that the co-variance would give you a smaller SD in relationship to your EV. Can someone explain if this phenomenon would provide a better plan of attack or am I just chasing rainbows?

scobee

[Don Schlesinger]

> Let's say that rather
> than betting $50 off the top as a minimum,
> you played 2X$25 instead as your minimum.
> What difference would it make to your EV and
> variance? It would seem to lower variance
> but not affect EV. Help me out here, guys.

As I imagined, you seem to know all the answers, so there simply is no more to say. It lowers your variance to bet the same total amount on two hands instead of one. It does little or nothing to your EV.

> Conversely you could theoretically double
> your betting level and not double your
> ROR....

Also true. Or, you could bet optimally by upping your total bet to 150% of the one-hand wager, while keeping ROR the same. I actually think you know as much about this as we do! :-)

> so that the co-variance would give
> you a smaller SD in relationship to your EV.

The precise description is that the ratio of EV to variance would increase.

> Can someone explain if this phenomenon would
> provide a better plan of attack or am I just
> chasing rainbows?

See, that's the question we can't answer. You tell us! Do you want the same EV and less variance (lower ROR); do you want more EV, more variance, but the same ROR; or, do you want something in between the two?

There is no "right" answer to the above.

Don

[scobee 1]

At first blush, I thought I was getting my wrists slapped for being an eager but inattentive student. Fortunately, I realize that Don is an excellent teacher and that I was just being told to be more specific. So again, I am grateful for your responses and now understand that maybe I 'kinda/sorta' have a handle on what is happening here after all.

> I actually think you know as much about this
> as we do! :-)

What I know is what I have been taught. You and John Auston have made this easy enough for even a precocious monkey to improve EV.... as long as he is a disciplined monkey who can read, operate a keyboard, and add +1 or -1 for hours in smoky, distracting conditions... and a primate who will walk on negative shoes while dragging his hands on the floor.

> The precise description is that the ratio of
> EV to variance would increase.

Improving EV requires that variance grows concurrently is how I read this. Chiseled in mathematical granite, yes?

> You tell us! Do you want the same EV and
> less variance (lower ROR); do you want more
> EV, more variance, but the same ROR; or, do
> you want something in between the two?

> There is no "right" answer to the
> above.

Ah, you have placed your acupuncture needle exactly on my pressure point. I have been very fortunate in the beginning...save for a very bad beat in June when I lost my first meager bankroll entirely on one long weekend. I think what I am looking for is a way to use that $25 unit I have grown into most effectively in terms of ROR. I would like to consider the two boxes my hedge against not really having the BR yet to be maxing out at $300. So I bet $400 instead and oddly enough, it is the same ROR with greater EV. "Le plus ca change, le plus le meme chose." I have experienced the comfort and impatience of a 1-4 spread playing only in positive counts....wonging in at TC+2 and staying as long as the true remains >-1. That is a beautiful strategy, but limited by crowded boats and attentive critters most of the time. So I guess now what I want is a lower ROR than 13.5% with a game that I can play as a white rabbit. So my answer would be I want a higher EV and more variance, but the same (albeit a lower 5%) ROR...accomplished by adding to my bank.

Anyway, now I am ruminating and wasting bandwidth. Your advice and subtle encouragement is welcome, so I will take it to the Risk Manager and figure out what I am looking for exactly so that I do not become just another exasperating student who refuses to listen to the answer the first time it is given.

Regards,

scobee

[Don Schlesinger]

> At first blush, I thought I was getting my
> wrists slapped for being an eager but
> inattentive student. Fortunately, I realize
> that Don is an excellent teacher and that I
> was just being told to be more specific. So
> again, I am grateful for your responses and
> now understand that maybe I 'kinda/sorta'
> have a handle on what is happening here
> after all.

Yeah, you're doing rather well.

> Improving EV requires that variance grows
> concurrently is how I read this. Chiseled in
> mathematical granite, yes?

Sometimes. Improving EV via the play of two hands instead of one, if done optimally, increases EV and variance by exactly the same percentage, so that the ratio of EV to variance remains constant, thereby keeping ROR unchanged.

But, improving EV does not require that variance grow, too. Consider adding surrender to a game that didn't have that rule. EV grows while variance decreases! Special thing, that surrender rule! :-)

> I think what I am looking for is a
> way to use that $25 unit I have grown into
> most effectively in terms of ROR. I would
> like to consider the two boxes my hedge
> against not really having the BR yet to be
> maxing out at $300. So I bet $400 instead
> and oddly enough, it is the same ROR with
> greater EV.

Right.

> "Le plus ca change, le plus
> le meme chose."

Not quite right! :-) "Plus ca change, plus c'est la meme chose." (Accents missing. Cedilla under the "c" in "ca" and circumflex over the first "e" in "meme.")

> So I guess now what I want is a lower ROR than
> 13.5% with a game that I can play as a white
> rabbit. So my answer would be I want a
> higher EV and more variance, but the same
> (albeit a lower 5%) ROR...accomplished by
> adding to my bank.

Right again. Or, alternatively, lowering the size of your starting unit, which, I know, you don't want to do.

Don

[scobee 1]

> Not quite right! :-) "Plus ca change,
> plus c'est la meme chose." (Accents
> missing. Cedilla under the "c" in
> "ca" and circumflex over the first
> "e" in "meme.")

I forgot my cedilla and circumflex in a Paris courtyard near Napoleon's Tomb. There are no accent grave or aigu needed in your quote.

Years ago I tried to live there, and the French never let up on me for being American. I was kind of proud that I got the gender right for 'le plus' but I completely botched the phrase.

"The more things change, the more they remain the same." Is how I think of it.

Is there an ES game in Monte Carlo? I would love to beat the French after all these years.

scobee

[Norm Watenberger]

Plus ?a change, plus c'est la m?me chose

[Don Schlesinger]

> I forgot my cedilla and circumflex in a
> Paris courtyard near Napoleon's Tomb. There
> are no accent grave or aigu needed in your
> quote.
Right.

> Years ago I tried to live there, and the
> French never let up on me for being
> American.

You'll find that things have changed dramatically in recent years. Many friends that have made trips to Paris for the first time have come home raving about how well they were treated and about how cordial and friendly the French were to them. Many some things DO change!

>I was kind of proud that I got the
> gender right for 'le plus' but I completely
> botched the phrase.
What gender? There is no article in front of "plus."

> "The more things change, the more they
> remain the same." Is how I think of it.
Correct.

> Is there an ES game in Monte Carlo? I would
> love to beat the French after all these
> years.

No such luck.

Don

P.S. Check the change in your title. :-)

[Don Schlesinger]

> Plus ?a change, plus c'est la m?me chose

You'll have to teach me how to do that.

Don

[Norm Wattenberger]

It's not how I did it; but you could get a French keyboard and set French as your language. I used to have French set as a secondary Windows language. This puts a button on the tool bar that let's you quickly switch between languages. I did this to test the international number format and international dates code in CVBJ and CVData. Had to remove it as I had a problem writing the new CVBJ manual. Every time I clicked on a paragraph that had 'Casino V?rit?' in it, Word would see the accents and cleverly assume that the document was in French, switch the keyboard to the French character set (resulting in nonsense) and try to load the French dictionary.

Never did like computers

[scobee 1]

Plus ?a change, plus c'est la m?me chose

I wish I could find those accents on my keyboard....in the interests of accuracy.

V?rit? means truth, I read somewhere recently.

:-)

Very timely, Norm.