Boundary cases I: min spread for 1 EV?

[Kurt M. Rufa]

Hi, folks. This seems to be a perfectly lovely board and site, and I hope to be gaining the benefit of reading discussions here for a long time to come.

This may be a faq-y type of question--if so, please hook me up.

First, goals, philosophy, longwindedness:

I don't see myself ever betting much more than red-chips because the mechanics of what's going on is more interesting to me than the volume.

I'm not interested so much in counting so much to make money but rather as a technique to reduce the cost of sitting at a blackjack table. I figure that at $5 flat bet, 100 hands an hour, the $500 of action at (say) a half a percent costs $2.50. Canon on tipping as dealt on this site is $4/hr.

Now, $6.50/hr for entertainment isn't bad, and for the $2/hr in cocktail waitress one actually gets refreshing beverages, so my area of interest is in the $2.50/hour given to the casino, and the $2/hour sent the way of the dealer. I figure that my presence in the casino is relatively little marginal cost for them if I behave myself . This is important to me apropos enjoyment and relaxation. I want to be knowing in my heart that I'm completely blameless of 'abusing' them any more than someone going into a mall to window shop who buys nothing is cheating the mall.

I'm in the casino to purchase volatility with small amounts of money in a fun environment. I just don't want to pay nearly as much as they want to charge me for it.

Also, I like craps, I find craps fun, and I know full well I'm losing 7 cents when I put $5 on 'pass'. At the pinnacle of things, I'd like 2-3 hours of slight-advantage blackjack to offset an hour or so of slightly too large disadvantage craps. (Moreover, at craps I can enjoy a wider array of refreshing beverages, because I'd have to be fairly trashed not to properly bet pass, max odds, and be sure I got paid.)

So, there are a few tiers to my goals:

1) getting rid of the $2.50/hour (playing an even game)
2) getting inflow of $2/hr (tipping the dealer)
3) getting inflow of $3.50/hr (tipping the dealer and a little to buy some more relaxed, less
intellectual volatility at the craps table)

I have absolutely no illusions that I'm close to getting to any of these levels right now, but
I imagine knowing where one's headed is a good first step. Possibly more important is the notion that I'm probably not likely to be playing super-regularly - why go to all the trouble for these theoretical considerations when over my lifetime they may well be swamped by variance? (time to dig out the Chi-squared test? How many hands would it take to have 95% confidence that a time series is a result of playing at 0.1% advantage rather than minus 0.4?)

Well, I'd like to play the game as well as I know how, and in my case playing it as well as I know how is more measured by *engineering the random process* than by *maximizing the EV*. I figure most serious people do this kinda thing to some extent anyway (by Kelly betting or whatever).

Right now I'm learning basic strategy for ye olde 6 deck shoe game (RSA, DOA, DAS) that they have in Detroit (it's either that or csm, apparently, and green minimum most of the time too according to a counting ex-officemate )

Second: The main question on my mind now

On this kind of 6 deck shoe game, what is the *minimum* spread necessary to overcome the house edge, (assuming no getting up to check the bathroom whenever the count gets very bad (wonging out?)).

I really don't want to have to worry about being noticed, for various reasons, and staying in the basement with red chips seems the best way to do it. I realize the answer is going to depend on the counting system picked, too. Having read an article in the book (a collection of papers) called _Finding the Edge_, I have gained the impression that for most systems the spread is responsible for maybe 70% of the deviation in EV, and basic strategy variations the rest.

So, what kind of ballpark for the spread is needed to meet my (relatively modest) goal? What tradeoffs for counting systems and BS variations are available?

I've got a lot of other questions but the road of clue acquisition is long and twisty, with routes best plotted in real time... so I'll leave it for now at just this one.

 

[The Mayor]

Greetings, Kurt

Welcome to this board, I hope your questions will be answered by others, but I'll take a first stab.

You posed a very interesting question, "what is the minimum spread necessary to be playing an even game."

Let me begin by saying that this is a bad idea. As long as you are simply playing a break-even game, gambler's ruin is sure to wipe you out. You must play with an edge to avoid gambler's ruin. That said, if you play with the smallest of edges then even a huge bankroll will not avert gambler's ruin. You need a decent bankroll, a decent edge, and a "risk" of losing it all that you are comfortable taking. Only then can your spread be determined theoretically. And the spread will say something like "if you spread x-y then your hourly earnings are EV with a standard deviation of SD, giving you a risk-of-ruin on your bankroll of BR of ROR%"

Also let me say, that for red-chippers on a shoe game, if you spread $5 to $20, no one will even look at you. You can do it forever, and this spread certainly gives you a very slight edge. But if you "wong" (only enter shoes at a positive count +1 or higher), then you can simply flat bet and be playing with an edge! If you "wong-out" (always leave shoes that go below -1 in TC) then you can play a 2-1 spread and have an edge. These are the minimums, in my opinion, without doing the mathematics to verify them.

Again, nice to see you here,

--Mayor

 

[Kurt M. Rufa]

Re: Greetings, Kurt

I do know about gambler's ruin. Random walks on a 1D lattice are recurrent, which is why... on 2D, as well, but just barely. 3D ones are not. So if you're a drunken bear you eventually will get back home, but a drunken bird is lost forever.

I'm a continuous kind of guy, so I'd write it as a PDE; something like u_t = K u_xx + R with initial condition u0(x) = delta(bankroll) and boundary condition u(0) = 0. For R zero, sure, L1 norm of U = 0 as time goes to infinity... I'm not precisely sure how to set K and R in the right units, but I'm quite sure that the solution to a PDE like this'll give the right continuous approximation of the discrete random walk. It'd be fun to figure out the proper way to model blackjack outcomes with PDEs (if possible); I do know that in a lot of similar situations this is faster and more accurate than Monte Carlo methods (simulation).

But just as one can think of one's BJ playing as one continuous session, I can think of my bankroll as not being one fixed number. I'm not in this to make money, or have a vanishingly small risk of ruin in the long run, because in the long run I'm dead anyway. Another way to reframe my point of view is that I'm more interested in minimal volatility in the short term (smaller spread, I'd imagine) without negative drift.

It is heartening to hear that 1-4 spreads aren't considered a threat. To expand my question, I wonHow well can one do with basic strategy variations alone? I'm sure that's come up, in light of Atlantic City...

 

[The Mayor]

Basic Strategy alone

In Single Deck, you can get a marginally winning game by varying strategy alone. But in multi-deck games, strategy variations are a very small part of the game and will not bring you up to an even keel. Best to test the waters by spreading as much as you can until you start to feel the heat. Spreading is where the money is -- everything else is just fluff.

I appreciate your strong mathematics background, and encourage you to seek your answers to your purely mathematical questions at bjmath.com -- the world's top BJ theoreticians are waiting to answer you there.

Best regards,

--Mayor