paranoid android: positive count and running out of money

[paranoid android]

Say you are playing a table, the count is positive, but you only have 2 units left on your person. Which is the correct play?

1) Play 2 units? If so, I lose the ability to double or split because I'll be out of money.

or

2) Play 1 unit and maintain my ability to double and split.

I guess the question comes down to whether you can play with a positive expectation at the current count even when you don't have the ability to double/split. I'm guessing that if this is ever true, then it is only when the count is very high (but this is only a guess), so that in general, it would be better to play just one unit and maintain doubling/splitting ability. Anyone know the right answer?

[StrayFrog]

> 2) Play 1 unit and maintain my ability to
> double and split.

keeping enough money on hand for a double or split is correct.

[Pro Player]

[Mr. Lucky]

where you are so low on money that you are in jeopardy of running out. Always bring overkill into the casino. You want to be able to have not only enough left to be able to double AND split, but also be able to do it several more times with your max bet out before it's time for a shuffle.

However, to answer your question of what to do when you're down to 2 units, bet just one, preferrably less, since you might have to split and double a few times. Although a significant portion of our edge comes from BJs, a lot of it also comes from not only splitting and doubling but also insuring in high counts. If you put it all out there and take away those options, you may well still be playing at a disadvantage even in a high count.

[7up]

From Theory of blackjack
No pair splitting, -.4%
Do doubling down, -1.6%

[Parker]

> where you are so low on money that you are
> in jeopardy of running out. Always bring
> overkill into the casino. You want to be
> able to have not only enough left to be able
> to double AND split, but also be able to do
> it several more times with your max bet out
> before it's time for a shuffle.

> However, to answer your question of what to
> do when you're down to 2 units, bet just
> one, preferrably less, since you might have
> to split and double a few times. Although a
> significant portion of our edge comes from
> BJs, a lot of it also comes from not only
> splitting and doubling but also insuring in
> high counts. If you put it all out there and
> take away those options, you may well still
> be playing at a disadvantage even in a high
> count.

I could not agree more. Your session bankroll should be large enough that you never are in danger of "tapping out" for the session.

What if you are dealt a pair, and end up resplitting to four hands and doubling on several of them? This sort of hand doesn't happen very often, but when it does it can completely turn a session around (either way), and you should always be prepared for the possibility.

Furthermore, being low on funds can adversely affect your judgement in playing and betting decidsions, creating a reluctance to shove out the big bets when the count calls for it, take insurance, etc. The old timers call this "playing with scared money."

[Mr. Lucky]

> From Theory of blackjack
> No pair splitting, -.4%
> Do doubling down, -1.6%

Yes, but why bet 2 units at a 1% edge when you can bet 1 at a 3% edge and still probably have one left over for the next round at an advantage?

[Dreamer]

The edge is based on you ability to split, double down and take Insurance.
So you don`t really have a 3% edge at that count.
Even with 2 units you have a little less edge as
you cant re-split to 3 or more hands.
(you also cant DAS as well)
As already stated don`t let yourself get in this position in the first place.
Always have "back up" funds in your wallet.

D.

> From Theory of blackjack
> No pair splitting, -.4%
> Do doubling down, -1.6%

[7up]

Then where is the line?
How about at 5% edge?...2*3% better than 1*5%
about 50% of chance can bet on the next hand

[7up]

but we should also find the answer and the solution.
A real case: I was walking back home, instead of passing by the casino, I went throught it,...

[MathProf]

I once did a brief study of this problem, by doing combinatorial analysis of representative packs. I compared betting 2 units with no doubling or splitting, to one 1 unit with doubling and splitting, but no replit and no DAS. I did not find any practical pack in which it was better to bet the 2 units. I posted these results somewhere, but I can't remember where. There is an outside chance that I could dig up that data.

You can cook up a hypothetical pack in which you would be better off to bet the full amount, but I don't think it is realistic to beehive that you will see this at the table.

Now betting half your stake does not allow DAS or repslitting. But the gain from these is marginal. You will have higher EV if you bet one-half and give them up, rather than bet one-third or one-fourth.

While it is best to Never run into this situation, sometimes it cannot be avoided in practice, so it an practical problem. I originally did my study for a player who had this problem.

> Then where is the line?
> How about at 5% edge?...2*3% better than
> 1*5%
> about 50% of chance can bet on the next hand

[7up]

there must be a reason. I would like to know.
I catch an Ace for the first card several times everyday, how much should I bet if I have only 2 untis?

[MathProf]

I dug up the old data that I ran before. This was done in the Fall of 2000, about 2 years ago:

 

                 May Double/Split        May Not Double/Split  

    0   0.000     -0.62%     1.13        -2.37%     0.98 

    1   1.000     -0.11%     1.13        -1.96%     0.99 

    2   2.000      0.40%     1.14        -1.55%     0.99 

    3   3.000      0.90%     1.13        -1.16%     0.99 

    4   4.000      1.39%     1.15        -0.76%     0.99 

    5   5.000      1.91%     1.17        -0.36%     0.99 

    6   6.000      2.45%     1.16         0.04%     0.99 

    7   7.000      2.99%     1.17         0.42%     0.99 

    8   8.000      3.52%     1.17         0.79%     0.99 

    9   9.000      4.07%     1.17         1.17%     1.00 

   10  10.000      4.61%     1.17         1.54%     1.00 

Here is how you read this table.
At a TC of 10, the EV is 4.61% and SD is 1.17, if you play where you allowed to double or split, but only once. If you can't double or split, then your EV is only 1.54%, with an SD of 1.00 Note that 2*1.54% is 3.08%, which is still much lower than 4.61%.

This will change at higher true counts. At a TC of 52, the deck consists of only Aces and 10s, and so doubling will not be an issue. But this an extreme case. In practical BJ, you very seldom see counts higher than 10.

The method here was to use representative packs for the various true counts. A started with a 10 deck Shoe, and add one of each high card and removed one of each low card per TC point. I did a CA which used optimal strategy against that pack. This is only an approximation, but I believe that it is sufficiently accurate for the purposes here.





> there must be a reason. I would like to
> know.
> I catch an Ace for the first card several
> times everyday, how much should I bet if I
> have only 2 untis?