playing black jack basic strategy, not counting cards, with surender.


assuming the house edge is 1.2%

assuming im playing to flat bet 20k every hand and every time i lose i lose 12 bets

what percent of time will i be ahead one bet. meaning if my goal was to win one bet and i would quit any time i am up 1

same as before but

2 units
3 units
4 units
5 units
6 units
7 units
8 units
9 units
10 units
11 units
12 units

Never, Blackjack is the devil... She will tell your winning for 2 hours then you bet 1/2 your money and get AA against a dealer 6 you spilt, get another ace now its pocket money, you split again get another ace... Each Ace gets a 4,3,2,6 you can't rehit them VIA house rules dealer pulls an 2 hits a ten now your out 2 times what you are up.

But I can do the math, just drinking and having fun right now (back form the bar), if you really want the correct answer,and no one else answers pm me later... I'll do it sober with explanations for each calculation and how I came up with them.

would apreciate.

To many unknowns to answer this exactly but..

Easy answer for one hand is 50-50 each hand then you toss in the 1.2% for house advantage so 48.8 you vrs 51.2dealer precards.

So the first time your ahead 1 bet/unit is 48.8 percent of the time

you a rocket scientist, i actua;y knew that one, but you didnt come close to answering my question. thats assuming you stop after just one hand. what about the times you loose 4 in a row then win 5


If there is someone really good at numbers and can convince me they are and can write a program to my specs il be happy to pay.

Look at a football 4 teamer bet meaning 4 perfect wins, .5 times .5=.25 ^4
so do that 4 times and it is .0313.

Like I said this is easy math

for the 5 time win is the same math plus one times .5

Which would be .0156 percent they win 5 times in a row.

The actual numbers are different depending the edge but 50 50 is easy math to show what I am talking about...

Also 11 beers deep, FYI

A 1.2% edge does not mean that you win 48.8% of the time. You win about 43%, lose about 49%, and push about 8%. The win/loss percentages are offset by blackjacks, doubles, and splits to get the house edge.


That's no LOL way to do a random walk calculation, and it's anything but easy math due to variable payouts. That wouldn't be the way to do it even if we had single unit wins and losses, but that case would in fact be easy. For our case, we can use a version of the risk of ruin formula using the EV and standard deviation, but I wouldn't necessarily trust it with a goal of 1 unit and bankrolls this small. I would simulate it using a BJ simulator which I have, but I'd need the number of decks and all the rules (whether BJ pays 3:2 or 6:5, whether dealer hits or stands on soft 17, what numbers can be doubled, whether double after split allowed, number of pair splits allowed, number of times you can resplit aces). Even for the risk of ruin formula I would need the standard deviation which depends the number of decks and the rules.


That's not a reason to post complete nonsense.

My BJ simulator (CVSIM) will give me the the correct percentages for unit bets won/lost/, doubles won/lost, and splits won/lost. We know how many blackjacks we win. But unfortunately, the simulator doesn't actually simulate risk of ruin; it just uses the same formula that I described above based on the EV and standard deviation (I checked it) which may not be accurate for our case. So I would have to write my own sim in R and input the results from CVSIM. This shouldn't be so bad since I wouldn't be simulating the entire game of blackjack, just a game with the correct payouts and losses.

This is actually an important problem for which many people would be interested in some tabulated results. It would also be interesting to see at what point the risk of ruin formula breaks down and by how much. The risk of ruin formula will provide a good sanity check on the simulation.

The risk of ruin formula (which may not turn out to be accurate) works as follows. We actually want to compute the risk that the house loses a 1 unit bankroll before it wins a B unit bankroll, where B is 1,2,...12. Let ror be the risk that it loses a 1 unit bankroll if it played forever (not stopping after it wins B), and r be the risk that it loses 1 before winning B. Then we have

ror = r + (1 - r)*ror^(B+1)

That is, the house's risk ror of losing 1 unit playing forever is the risk r that it loses 1 unit before winning B, plus the probability it wins B units before losing 1 unit (1-r) times the risk of ruin after that point which is the risk of losing a B+1 unit bankroll ror^B+1. Solving for r gives

r = (ror - ror^B+1) / (1 - ror^B+1)

ror is computed from the standard risk of ruin formula

ror = exp(-2*EV*1/SD²)

Where the 1 is the house's bankroll. For example, for a house edge of 1.2%, we have EV = 0.012. We'll take SD = 1.16 which is about right for a 6 deck game. This gives

ror = 0.982322209

Now if you have a 12 unit bankroll, use the equation for r with B = 12. This gives

r =~ 91.5%

So the player would have a 91.5% chance of winning 1 unit before losing 12 units according to this formula. That agrees with the number CVSIM spits out. We shall see how this compares to the simulation results, but I would still need the details.

Here are the results of the formula for your other values of B:

Again, these are potentially off due to the approximation used, so we need the simulation to get the accurate results.

BruceZ, you may be interested in this.
(I am always interested in the math projects that you attempt and complete.)

Here are my results from Alan Krigman's Excel worksheet that can be found here below
Excel Risk of Ruin Worksheet
edge = .005 and sd = 1.16
The webpage is interesting reading with formulas and examples.
Alan knows his stuff like you.
He also has a Survival criterion formula that I have not seen anywhere.

Happy New Year.
I still love your hat!
Sally

Oops. Above post has a typo I fixed here.
edge: -.005
sd: 1.16

Sally

His spreadsheet gives exactly the numbers that I gave and he's using the same method. In fact I made a similar spreadsheet. My numbers were for a house edge of 0.012. Yours are for 0.005. I get both sets of numbers to all the decimal places given.

So that is 2 tools (software tools I mean) that don't put any restrictions on the goal and bankroll size for these formulas. We shall see if they are right when we do the simulation.


Looks like good stuff, thanks. That survival criterion formula is the short term risk of ruin formula from Blackjack Attack. I've posted that here before. The exponential risk of ruin formula is the one I used for the problem ITT. The others make no significant difference.


Same to you. Glad you noticed.

OP, I believe that for a 1.2% house edge your rules must be single deck, BJ pays 6:5, dealer stands on soft 17, double on any 2 cards, double after split allowed, late surrender. That gives a house edge of 1.2% which we could make slightly more precise by a few hundereths of a percent if we knew how many times you can resplit pairs and aces. No other common rules would give 1.2%. If BJ paid 3:2, the edge wouldn't be nearly that bad even for an 8 deck game with the worst of the other rules. If BJ pays 6:5, we need 1 deck with the most favorable rules as given. Am I right?

If this is correct, the formula numbers that I posted earlier for 6 deck only decrease by around 0.1% or less due to the standard deviation changing from 1.16 to about 1.09.

Excellent work, as per usual, Bruce. Even with 11 beers in your system, you'd probably still nail the answer.

However, if OP seriously Martingales, I wouldn't totally assume he plays perfect basic strategy even if he says he is.

Thanks. Just to be clear, when I said the numbers only change by 0.1% with single deck, I'm just talking about the formula numbers. There's still work to be done to do a sim which will determine how accurate that formula approximation is in this case. I'd like to get the rules pinned down first, or I could proceed under my assumptions to test the formula for the case that I've assumed which would have the right edge.

It is important to know whether the OP is planning to split or double after splitting, and how many times. If this is allowed and he doesn't do it, such as when he doesn't have enough bankroll left, the house edge increases, and his chance of success changes.


He's not martingaling, he's flat betting and trying to win a single unit.

Another issue is what do you plan to do if you get down to 1 unit and get an advantageous double or split? Do you dip into your wallet for money, or do you forgo that, hence increasing the house edge? Also what do you do if you have less than 1 bet?

In this old thread, I show that the formula used in this thread agrees with a formula that more closely models blackjack, taking into account blackjacks, doubles, and splits. That formula is still approximate though, and the case considered is going from a bankroll of 500 to 6500 which is a lot different from only trying to win 1 unit as in this thread. I just include it here as a related subject. Also see Pzhon's comment in that thread about questions like these. He said:

Whoops, youre right. I also replied under the influence last night.

Interestingly, the chance of success doesn't necessarily always decrease. Sometimes preservation of bankroll is more important to long term success than a small increase in EV when the bankroll is limited. It can also be mathematically correct to double for less if this is permitted, and sometimes that would be his only doubling option.

bruce and everyone thank you for your answers i learned a lot, i actually used 1.2 to give my self a cushion for mistakes in basic strategy and stuff. i believe i could safely assume around .6 or .7