What's the probability?

In another post it was mentioned that in a particular game (online @ blackjack21.com) a player had managed to take an initial BR of 2000 and turn it into 12000. Just out of interest I wondered what the probability of this occuring was and therefore how often we are likely to see it.

I made some initial calculations looking at a series a max bet wins with the odd loss here and there and got an incredibly low number. I don't trust my maths so do any of you stat/probability gurus know the answer?

The game would be 15 hands, 2000 initial BR, betting range 100-1000.

Thanks in advance.

Reachy

 

It's really that high?

WOW! I didn't think the numbers would be that high. That's just under 17%. It seems amazing to me that you can increase your initial BR by a factor of 6 that often. That means you should be able to increase your BR by that much 1 in every 6 tourneys. The figure I came up with was so small it was almost off the scale. I think I came up with 0.04%!!!!

Cheers

Reachy

 

Wong cannot be used here

In this particular case, it seems to me that applying Wong’s formula, as SWOG did, produces a grossly incorrect conclusion. First of all, Wong’s formula assumes you have a 50-50 chance of winning a hand when, in fact, the percentage is more like 44%. Also, Wong was silent about the betting limit when he gave the formula. Seems to me that his formula is meant to be easy to calculate in one’s mind for an approximate answer if there is no max bet. Since Reachy stated a max bet, that limit must be factored into any calculation. In this case, that max bet makes a huge difference in the chances of achieving the $12,000 goal.

Before I get too much criticism, let me just say that I know my calculations will not yield an exact result – they may in fact be way off. I’m asking for help at the end of this post.

Let’s make a few starting assumptions:
44% = Percentage of hands a player will win
48% = Percentage of hands the dealer will win
8% = Percentage of pushes

Reachy’s scenario:
$2,000 = starting bankroll
$12,000 = ending bankroll
$1,000 = max bet
15 = Number of hands to play

Initial conclusions – note that splits and double downs are not factored in:
$10,000 must be made in 15 hands.
There will be 1 push hand (8% * 15).
That leaves 14 hands to make $10,000.
That means, at max bet, you must win 12 hands and loose 2 hands (net of 10 wins) out of 14 hands.

Formula:
(.44 * 14/12) or .5133
This calculates out to: .000088 or 0.0088%

Another way of saying this is: 1 chance out of about 11,363

Now, as I stated earlier, my math may not (actually, probably will not) yield the correct result. I am asking that one or more of the math gurus out there jump in with the right answer.

 

Ken - A few questions about the simulation

Thanks for the feedback. I figured it out the same way toolman did and came up with a similar answer.

Ken - Some questions: Which simulator did you use? I still haven't got one and I'm probably going to wait until CV4 comes out with the tournament module. Any cheap (or free) alternatives until them?

In the simulation did you use just 1 player or 5 players with the same strategy? If it was 1 then would 5 players change the odds significantly? (I'm thinking somewhere between 12.5% and 2.5% so I'll settle for 7.5%)

In a multi-player simulation where 4 players use a more conventional tournament style (whatever that is ) and one player is using the max bet strategy how often does the max bet player bust out, get in the money, and win? Is it possible with the software available to simulate this kind of thing?

Thanks in advance.

Reachy

 

If there is no 3:2 BJ, no splitting and no DD

As I mentioned earlier, my calculations were probably grossly flawed and now I see they were. Apparently this is too complex of a problem to be solved by a relatively simple formula. However, I was surprised that Ken’s simulation showed a 2.5% probability as I was expecting something much less. This led me wonder what the probability would be if there was no “bonus” for a BJ, no splitting and no DD since my original calculations did not take those advantages into account. So I ran a simulation were there is no “bonus” for a BJ, no splitting and no DD. The simulation gave me a probability of 0.20%.

The reason I’m posting this is because I was surprised that eliminating those 3 player advantages (“bonus” for a BJ, splitting and DD) resulted in the player achieving his goal only 1/12 as often as having those advantages in place.

Food for thought

PS: Nice original post Reachy. I learned a little more about this crazy game called Blackjack.

 

Which simulator?

Hi Ken, toolman - Which simulator are you using? I've just downloaded CV Data and am playing around with it but it doesn't seem to come up with the results I expected. Any tips for setting it up as a tourney simulator as it seems to be card-counting focussed.

Cheers

Reachy

 

CV Data

Reachy:

I use the CV Data simulator. If you just downloaded it you may have gotten the demo version which will not give accurate results and they say this. If you paid for the product then you have the actual product. Which do you have?

 

I did download the demo...

I thought I must be doing something wrong it was coming up with a 78% push rate!!!!

Is it worth getting the software if I only play tournament BJ? It would seem that a lot of the functionality is counting based.

Cheers

Reachy

 

Get the software

I would say that this should be one more addition to your arsenal (or in my case "toolbox" ) in your never ending battle to uncover truth, justice, and the best BJ plays.

Although there is no "tournament play" in the simulation software, with a little creativity, as Ken Smith did, you can use it to solve some tournament questions.

As far as counting, you can set up the software to just "flat bet" which bypasses all the counting related plays. There are many modifications you can make to suit your needs (including basic strategy charts, deck composition, casino rules, etc) and I guess the combination possibilities are in the many thousands.

To answer your main question "is it worth getting the software". I say absolutely. The knowledge you can gain substantially offsets the $150 (American) price. In my opinion, it's a bargain! To be sure, there are other opinions, but that's mine.

 

I think I'll buy it out of my Global winnings!!!!!

Final table on the Cruise Tourney last night!!!!

What I did was, as you said, set it up as flat bet with 15 hand sessions. That should work shouldn't it?

The cheque is in the post...

Cheers

Reachy

 

Almost

Almost.

Software will not allow a bet over $500. So set your starting bankroll at $2, objective should be $12, flat bet $1. Also, start a new session whenever you 1) reach $12, 2) Go bankrupt, or 3) Played 15 hands. This is the same as your original post except you divide each number by 1,000 for the software to accept the parameters.

Keep in mind that you probably will not come up with the same results as Ken (I could not come up with Ken's results) or I because you may have different parameters such as basic strategy chart, dealer hitting on soft 17, etc. Also, whenever you run a simulation, it is just that, a simulation. Any simulation will have slightly different results with each run. To keep the differences to a minimum, I generally do 250 million hands.

Hope this helps. It takes some time to become familiar with the software and what it can do so experiment to your heart's content.

 

Also Thumbs Down??

Good info swog. I also hope you gave THUMBS DOWN to "Blackjack 6-7-8". I hate that software.

 

Lol

I downloaded a demo of Blackjack 6-7-8 and uninstalled in within minutes!! Clearly didn't have what I wanted.

Cheers

Reachy