Doubling Down only generates a grand total winning of 1 unit for your lifetime?

[gambler516]

What is the difference in winnings between doubling down with 10 versus 9 and just hitting with 10 versus 9. I do not know the odds of winning this situation but the total winnings would be a factor of the percentage, right? If you win 51% of the time and you double ever time then your winnings are a grand total of 2 units; if you do not double every time then your winnings are a grand total of 1 unit. Am I not correct in this assesment? Seems like almost a moot point, with very little gain. Would love a better explanation of why you double in these types of situations.

[Bodarc]

You always make the play that maximizes the expected return or minimizes the expected loss. It is called basic strategy and should not be deviated from unless called for by your count index. With a 10 V 9, you have an advantage so the correct play is to put more money on the table which is what doubling down does. Don't question basic strategy. Just memorize it and play it faithfully. BTW every hand you play is just 1 win or 1 loss for your lifetime.

[hitthat16]

You double 10 vs 9 because the math and simulations say to.

[bigplayer]

The Zen Index to not double 10 vs 9 is only -2 (so don't double at -3 or lower). That means the decision is sensitive to positive and negative counts. If you've got a bottom bet out and the count is neutral or negative you won't affect your overall win rate by a significant amount. When the count drops to -3 not doubling down is the right play. When the count goes up, however, you're leaving real money on the table by not doubling down and this is magnified by the fact that you've got a big bet on the table when the decision is a very correct one.

[SiMi]

Hey, 516!

I think this is a great question because it shows you are REALLY thinking about what you're doing! I'm guessing you are referring to Basic Strategy and wondering why it says to DD on 10 vs. 9, right? I do not know the odds of winning this particular hand but when I have questions like this, I go to Stanford Wong's Professional Blackjack, Appendix E since I've used it for years and I know right where the tables are located (in the back). It's also in App. A of Blackjack Attack 3 and there's also a web page on the Wizard of Odds web site that has the info for the Expected Value for all hands in various games:

http://wizardofodds.com/games/blackjack/appendix/1/

also at:

http://wizardofodds.com/games/blackjack/appendix/9/

The Wizard shows the Expected Value for Hitting a generalized 10 vs. 9 as 0.117 while the EV for DD is 0.144. So, if we subtract the DD EV from the Hit EV, we get 0.144 - 0.117 = +0.027. This means the DD play will return, over time, 0.027 MORE of your initial bet than Hitting. So, OVER TIME, you will come out ahead if you DD in this scenario (using Basic Strategy and NOT index play variations).

Thus, +0.027 of your initial bet is the "difference in winnings between doubling down with 10 versus 9 and just hitting with 10 versus 9" which is what you asked.

If you managed to bet $100,000 over a long time in this particular scenario, then the math says you would win $2,700 MORE by DD every time than if you Hit every time. The more you play and bet, the more it matters.

I hope this helps!
SiMi

[hitthat16]

The Zen Index to not double 10 vs 9 is only -2

Isn't it -4? According to Snyder's Zen count indices?

http://blackjackforumonline.com/cont...nt_Indices.htm

[SiMi]

Hello, moses!

The Wizard of Odds website has the results of a 30 billion 'hand' simulation of BS BJ with specified rules which shows a mean of -0.003 and a standard deviation of 1.14.

http://wizardofodds.com/games/blackjack/appendix/4/

This means your EV is -0.003 (a little less than 1/2 of 1 %) and you will win or lose 1.14 units more or less than that mean value on average on each outcome using BS. It would be interesting to run the sim WITHOUT DD on 10 vs. 9 (and other close hands) to see what the SD turns out to be. As you say, it would be less. Probably, someone has done that and I'm just missing it...

BTW, it seems to me the table is a bit screwy because it refers to '30 billion HANDS' of Blackjack but the results are all stated in terms of outcomes per ROUND and the total outcomes exceed 30 billion. So, something seems wrong. If you ran a sim for 30 billion ROUNDS you would end up with EXACTLY 30 billion results based on rounds (-8 to +8 as he's set it up). If you ran the sim for HANDS, your results would not be stated in terms of outcomes that reflect the NET result of multiple hands per round. So I'm not sure exactly what's going on, but the table is VERY interesting to study.

Best!
SiMi

[MJGolf]

Just to quote Julian Braun from "How to Play Winning Blackjack" at page 42 when you hit 10 against a 9, you win 56 hands and lose 44 out of 100 but if you double, you will lose more hands, winning 54 v losing 46 for a net gain of 3 in his chart (or 4 on a calculator) bucks.

While it's a small margin gain and a close call, it's still positive to double v hit this hand in the long run over time. Basic strategy only. His index is -2 for multi deck, too.

[Three]

BTW, it seems to me the table is a bit screwy because it refers to '30 billion HANDS' of Blackjack but the results are all stated in terms of outcomes per ROUND and the total outcomes exceed 30 billion. So, something seems wrong. If you ran a sim for 30 billion ROUNDS you would end up with EXACTLY 30 billion results based on rounds (-8 to +8 as he's set it up).

In data representation numbers that are to a certain number of significant digits imply a range. Saying 30 billion hands the range is 29.5 billion to 30.499999999 billion. To say 30.0 billion the range is 29.05 billion to 30.049999999 billion. To say 30.00 billion the range is 29.005 billion to 30.004999999 billion. All of theses are accurate representations of 30,002,127,012. Only when you get to 30.000 billion does the result fall outside the accuracy limits of the number presented (29.0005 billion to 30.000499999). This does not include the sample size of 30,002,127,012.

The Wizard of Odds website has the results of a 30 billion 'hand' simulation of BS BJ with specified rules which shows a mean of -0.003 and a standard deviation of 1.14.

You did the same thing here with mean of -0.00290361 being said to be -0.003 and SD of 1.1417 being said to be 1.14.

[SiMi]

Hi, T3!

Thanks for the reply. I believe I follow your point that '30 billion' has 2 significant figures so it allows for the number of outcomes to be lesser or greater than 30 billion.

My concern was more of a practical one because I've written a BJ simulator and I can tell it to run X ROUNDS of BJ. In so doing, it will split hands as needed and it will calculate the net result for each player BY ROUND (regardless of how many hands he ends up with in that round). The result of a round can be as low as -8.5 if you took insurance, lost it, split 4 hands, DD and lost them all or as high as +8 if you split and DD on 4 hands and win them all.

I will end up with slightly more hands than rounds due to splits. So, my X rounds becomes X+y hands in the end. But, when I present the results of a sim I ran, I would have to say it represents only X rounds and there would only be X outcomes to evaluate because the results are PER ROUND, not per hand. Then, and this is the important part, when I calculate probabilities based on the outcomes per round, I use X EXACTLY as the divisor for all the probability calculations - not X+y because my data are in rounds, not hands.

The only way to get a sim of exactly X HANDS would be to potentially stop a player from splitting a hand that he would normally split so as to get X hands on the nose. I don't think anyone would code a BJ simulator that way because it's not realistic and it's more work.

So, if someone presents a table of results based on PER ROUND outcomes and says that it represents 30 billion HANDS but then the totals show over 30 billion outcomes and the probabilities are all calculated on the basis of over 30 billion outcomes, I'm totally confused. Can you mix and match like that? Can you tabulate your outcomes on the basis of per round outcomes and then, because you got more than 30 billion hands, use that LARGER number for all the probability calculations? Isn't that mixing apples and oranges?

Thanks again for the input!
SiMi

[Gronbog]

Hands/rounds are often used interchangeably colloquially, in the literature and among various software programs. It can be a source of confusion. Add to this the notion of a tournament round. Most tournament rules will state that each round consists of so many hands.

[Exoter175]

What is the difference in winnings between doubling down with 10 versus 9 and just hitting with 10 versus 9. I do not know the odds of winning this situation but the total winnings would be a factor of the percentage, right? If you win 51% of the time and you double ever time then your winnings are a grand total of 2 units; if you do not double every time then your winnings are a grand total of 1 unit. Am I not correct in this assesment? Seems like almost a moot point, with very little gain. Would love a better explanation of why you double in these types of situations.

Hello Gambler, it would appear as if my colleagues have missed the "title" question, so I'll address it.


Percentages of winning/not winning each and every hand are but ONE aspect of the "whole" here in lifetime play.

Lets look at a few numbers as an example.

If I played 2,000 hours last year at 85HPH, I saw a total number of 170,000 hands. If just 1% of those hands were 10v9 doubles, I'd have seen 1,700 scenarios where this comes into question. Even with a mere 2% greater win/loss of those hands (the 51/49 split you had mentioned, assuming no ties), I'll yield 1,734 units won, 1,666 units lost a net gain of 68 units. Now lets look back at the "not doubling" aspect and assume that not doubling will always yield a stiff hand, though we know it does not, and apply the same win/loss % you had listed. I will win 867 units, and I will lose 833 units, for a net gain of 34 units.

Of course this is simple math and not "accurate" i used these numbers to help answer the title question. Which is the gaining of 1 unit in your lifetime. That is inaccurate. While the shorthand simulation you saw might suggest a gain of 1 unit, the reality of the situation is that you'll gain x2 units for every player decision that you encounter. If your base sim that you looked up based the play on 1 unit, then yes, you are looking at gaining 1 unit everytime you make that decision. Though, of course, there's a million other numbers to factor in, like variance, but in the "perfect world" like the one I just did for "ease of use", you'll see that you're going to double the amount of "won" units by choosing to make the decision to double based on your index, not gain 1 unit over your lifetime. Unless, of course, your "lifetime" play is extremely short, then yes it is feasible to only ever gain 1 unit from the decision, but we know that isn't the case here.

[Exoter175]

My chart on #10 indicates expectation on this scenario is 2015 for me. Below is a CVI recap of your 2014. Except I included 7 and 9 in the count. Assumed you play $25 table.

Hand	2-8vsA-9	Base	% units	Dealt	%Won	% Lost	%tied	Total	Won	Lost	P/L
10v9	dou	170000	0.32%	544	49.82%	41.69%	8.49%	100%	271.0	226.8	2211	54.44%
10v9	0 H1	170000	0.22%	374	50.94%	40.29%	8.77%	100%	190.5	150.7	1992	55.84%
10v9	1 H=	170000	0.11%	187	52.19%	38.79%	9.02%	100%	97.6	72.5	1253	57.36%
10v9	2	170000	0.05%	85	53.84%	36.59%	9.57%	100%	45.8	31.1	733	59.54%

Thank you Moses!