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Blackjack math question?

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Blackjack math question?

Unread postby Govbarney » Fri Mar 04, 2011 12:00 pm

Ok , maybe someone here can help settle a argument for me that I do not have the math skills to settle on my own.

A friend of mine argues that you can win at black jack in the long run by using a Progressive Betting System (i.e. every time you lose you double the bet, so when you win you will get all your money back). I don’t believe this is possible because the house has a 51% advantage on every hand played. My argument is that progression will never overcome a Negative Expectation. Who is right?
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Re: Blackjack math question?

Unread postby Love child of shawn kemp » Fri Mar 04, 2011 12:49 pm

This type of betting is known as a Martingale strategy. It is an inherently flawed method of betting. Vegas has table limits on betting and while this is not done to specifically stop this type of betting it will certainly hinder it due to the exponential nature of doubling your bet after each loss when following this strategy. For example, you start playing $5 on a $100 table limit. After just five hands lost in a row, you will exceed the table limit and not be able to recoup all of your losses if you win. There are some websites out there that can go into headsplitting mathmatical detail as to why this won't work too.
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Re: Blackjack math question?

Unread postby RickNashEquilibrium » Fri Mar 04, 2011 12:59 pm

EDIT: I saw Kemp's post and that is the obvious restriction when it comes to casino gambling. My little treatise below speaks to the nature of how one can be a "winner" IE more lucky than good. He is right though, the math is headsplitting. If you think of the swings in blackjack and how much betting you need to wager in the long run in order to hit a target $ amount in winnings, the total is astronomical.

Your thinking is absolutely correct. First, lets look at the skill of card counting. Even the best card counter in the world still needs a large enough bankroll when playing higher stakes to withstand large amounts of short-term losses. Card counting tightens the gap in terms of expectation in the long run by allowing the player to make the statistical best decision given all known variables, however, as you put it the house still has an advantage every single hand.

The progressive betting style falls into the same mold. You could double your bet every single time and come out a huge winner. The caveat is that you would have to quit at some point while ahead. Think of it this way: if you started with $10 and wanted to double your bet every single time until you won $5,000, you would have to wager in total a bare MINIMUM of $10,230 (starting with $10 and winning 7 hands in a row (10=>20=>40=>80=>160=>320=>640=>1280=>2560=>5120)

As with all types of gambling, the key is having a big enough bankroll while not playing outside of your means. The reason some people are successful gamblers is self control, money management, and the willingness to take a big risk when the implied odds of losing are lower when there are more knowns than unknowns (a similar theory applies in poker when making/calling a bet with only a draw). The big key really is hitting a winning streak when the player is acting as a risk taker IE progressively betting more. A player will ALWAYS lose in the long run, but with enough great money management and luck, a player can stretch that timeline well beyond their lifespan especially if their bankroll is big enough.
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Re: Blackjack math question?

Unread postby Govbarney » Fri Mar 04, 2011 1:18 pm

Yeah its the "headsplitting mathamaticle detail" I have found on other sites I cant rap my head around.

So is what you are saying is that yes it is mathematically possible to beat the houses edge, with this system in the long run , however due to table limits and the time it would take it would be impractical?
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Re: Blackjack math question?

Unread postby RickNashEquilibrium » Fri Mar 04, 2011 1:28 pm

Govbarney wrote:Yeah its the "headsplitting mathamaticle detail" I have found on other sites I cant rap my head around.

So is what you are saying is that yes it is mathematically possible to beat the houses edge, with this system in the long run , however due to table limits and the time it would take it would be impractical?


More or less. Technically, you are not beating the houses edge you are just betting big enough each time that at some point, a hand you would win would be so large, it would probably dwarf any losses in the past given a normal distribution of losing. That's the theoretical application. In terms of practicality you are spot on. Real world casinos cap how much you can bet. A billionaire could wipeout a casino if he was willing to wager it all with the guarantee the casino would cover any/all bets. He'd have to get lucky, but it would be entirely possible.
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Re: Blackjack math question?

Unread postby motherscratcher » Fri Mar 04, 2011 1:46 pm

RickNashEquilibrium wrote:EDIT: I saw Kemp's post and that is the obvious restriction when it comes to casino gambling. My little treatise below speaks to the nature of how one can be a "winner" IE more lucky than good. He is right though, the math is headsplitting. If you think of the swings in blackjack and how much betting you need to wager in the long run in order to hit a target $ amount in winnings, the total is astronomical.

Your thinking is absolutely correct. First, lets look at the skill of card counting. Even the best card counter in the world still needs a large enough bankroll when playing higher stakes to withstand large amounts of short-term losses. Card counting tightens the gap in terms of expectation in the long run by allowing the player to make the statistical best decision given all known variables, however, as you put it the house still has an advantage every single hand.

The progressive betting style falls into the same mold. You could double your bet every single time and come out a huge winner. The caveat is that you would have to quit at some point while ahead. Think of it this way: if you started with $10 and wanted to double your bet every single time until you won $5,000, you would have to wager in total a bare MINIMUM of $10,230 (starting with $10 and winning 7 hands in a row (10=>20=>40=>80=>160=>320=>640=>1280=>2560=>5120)

As with all types of gambling, the key is having a big enough bankroll while not playing outside of your means. The reason some people are successful gamblers is self control, money management, and the willingness to take a big risk when the implied odds of losing are lower when there are more knowns than unknowns (a similar theory applies in poker when making/calling a bet with only a draw). The big key really is hitting a winning streak when the player is acting as a risk taker IE progressively betting more. A player will ALWAYS lose in the long run, but with enough great money management and luck, a player can stretch that timeline well beyond their lifespan especially if their bankroll is big enough.


The way I understood progressive betting is a little different than this. I always understood it that you only increase the bet after a lost hand. I'll use an example (more for myself than anyone else as I'm sure you guys understand it better than me):

$10-minimum $500-Table Max Bet

1st hand bet $10
- Win and you are up $10 and you bet $10 again next hand
- Lose and you down $10 and you bet $20 next hand

2nd hand (after losing) bet $20
- Win and you are up $10 ($20 minus $10 loss from first hand) - Bet $10 next hand
- Lose and you are down $30 ($20 + $10 from first hand) - Bet $40 next hand

3rd hand (after losing first 2 hands) Bet $40
- Win and you are up $10 ($40 minus $30 loss from first 2 hands) - Bet $10 next hand
- Lose and you are down $70 - Bet $80 next hand

4th hand (after losing first 3 hands) Bet $80
- Win and you are up $10 - Bet $10 next hand
- Lose and you are down $150 - Bet $160 next hand

5th hand (after losing first 4 hands) Bet $160
- Win and you are up $10 - Bet $10 next hand
- Lose and you are down $310 - Bet $320 next hand

6th hand (after losing first 5 hands) Bet $320
- Win and you are up $10 - Bet $10 next hand
- Lose and you are down $630 -

And now you are well and truly fucked because you are only able to bet $500

Essentially, you will be up $10 after every winning hand.

Without table limits, an unlimited bankroll, and unlimited time; you will ALWAYS emerge a winner. It doesn't matter what the odds. %51 for the house or 99% for the house. If you can play to infinity you will ALWAYS eventually win a hand, and after every winning hand you will have $10 more than what you started with.

It's the table limits that make this impossible. In the above example, after you lose the 6th hand in a row, you are still down $130 even if you won the next (7th) hand betting the max. If you LOSE the next (7th) hand you will be down $630. If you lose the 8th hand you will be down $1,130. Then, all of a sudden you would need 113 wining hands to get back to even.

Playing to infinity, you will always have stretches where you lose 9-10 hands in a row and that makes it impossible. Of course you will also win 9-10 hands in a row occasionally theoretically, but you only increase your bankroll by $10 with each win.

So, the way I see it, playing to infinity with unlimited funds to double each consecutive losing bet it is mathematically impossible not to emerge a winner as long as the odds of winning aren't zero.

Of course those conditions don't exist anywhere so the point is moot.

That's the way I understand it anyway.
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Re: Blackjack math question?

Unread postby RickNashEquilibrium » Fri Mar 04, 2011 2:01 pm

I am only good at poker, and craps is simply a hobby so my rationale might be a bit off.
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Re: Blackjack math question?

Unread postby Govbarney » Fri Mar 04, 2011 3:42 pm

motherscratcher wrote: Without table limits, an unlimited bankroll, and unlimited time; you will ALWAYS emerge a winner. It doesn't matter what the odds. %51 for the house or 99% for the house. If you can play to infinity you will ALWAYS eventually win a hand, and after every winning hand you will have $10 more than what you started with.anywhere so the point is moot.


Acourding to the Mathematical analysis I found on wiki , you would need infinite wealth for the system to work... I have yet to meet anyone with that much money
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Re: Blackjack math question?

Unread postby motherscratcher » Fri Mar 04, 2011 4:22 pm

Govbarney wrote:
motherscratcher wrote: Without table limits, an unlimited bankroll, and unlimited time; you will ALWAYS emerge a winner. It doesn't matter what the odds. %51 for the house or 99% for the house. If you can play to infinity you will ALWAYS eventually win a hand, and after every winning hand you will have $10 more than what you started with.anywhere so the point is moot.


Acourding to the Mathematical analysis I found on wiki , you would need infinite wealth for the system to work... I have yet to meet anyone with that much money


Yes. that's why I wrote this:

So, the way I see it, playing to infinity with unlimited funds to double each consecutive losing bet it is mathematically impossible not to emerge a winner as long as the odds of winning aren't zero.

Of course those conditions don't exist anywhere so the point is moot.
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Re: Blackjack math question?

Unread postby Bigfist » Sun Mar 06, 2011 11:56 am

The Martingale technique is a clear path to the poor house. I have personally lost 17 consecutive hands at blackjack...doing the math, if I were just trying to win five dollars, I would have at some point been over the table limit, even if the limit was 10,000 dollars. There are ways to get an edge at BJ, but that is not one of them.
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Re: Blackjack math question?

Unread postby Love child of shawn kemp » Mon Mar 07, 2011 5:58 pm

Bigfist wrote: I have personally lost 17 consecutive hands at blackjack...


Damn dude, did William H Macy sit down next to you? (movie reference)
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Re: Blackjack math question?

Unread postby Bigfist » Tue Mar 08, 2011 4:06 pm

I saw the movie.."The Cooler". Wish it had been Maria Bello sitting next to me. That would have made the 17 losses more palatable.
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Re: Blackjack math question?

Unread postby Cease » Tue Mar 08, 2011 4:32 pm

A progression I used last week in Vegas with good (fun, steady, extended play) results... The "logic" is based on streaks. Minimize losses on losing streaks, stagger aggression on win streaks. Allows to bank your 1X stake after 2nd win. From there, you are playing with house money while building stack.

Bet one unit following all losses until you win. Win, go up to 2X, then 3X on consecutive wins. 3X again, then 5X, 5X, 7X, 7X, and so on as long as the streak runs.

As a progression it's fun. Get up to 5X and 7X's, and it's enough to sweat the double down or split. Again, lose- go right back to 1X. Don't chase big losses w/ big bets that will cash your roll, be less volatile.

Any others out there with a method?

Where's the craps thread???
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Re: Blackjack math question?

Unread postby Bigfist » Sun Mar 13, 2011 11:15 am

Paging Dr. Thorp!

The problem with streaks is that one never knows when it is going to end or one is going to start. It is all retrospective, rather than prospective, data.

As Ed Thorp showed back in the early 60's, the game can be beaten with counting. His counting strategy was very basic and there have been many, many methods that have been developed since then, but they are all basically the same..bet more when the count is positive (relatively more tens and aces to be dealt) and bet low when the count is negative (relatively more low cards to be dealt).

But it sure is not as simple as all of that. Because the casinos also know how to count, and while the players can be sore losers, no player is nearly as obnoxious as the casino is when it loses. So, casinos in many places have fought back with unbeatable games..those with CSMs (continuous shuffling machines), those that break the deck early (re-shuffle when the count becomes positive), those that deal 50% out of a six deck or eight deck shoe. We even have bastardized versions of the game, such as Spanish 21, Fun 21, and others where a player blackjack pays only even money or 6/5. Even others limit player double downs to totals of hard ten or eleven, taking away the soft hand doubles.

Having said all of that, there still are good games to be found in Vegas, but you have to look.
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Re: Blackjack math question?

Unread postby leadpipe » Sun Mar 13, 2011 4:08 pm

Infinite wealth minus table limits.

Which is why it's impossible.

Counting cards AND doing it imperceptibly, and in this day and age, the second part is harder than the first, even though the first is harder than it used to be. (Thorp's book from the 60's is close to useless today)

And there's no such thing as streaks - just the math playing itself out.

You'd be suprised how many cats fashion themselves as good players and sit at a table that pays blackjack at 6/5, while there's a table in the same house paying 3/2. One of my favorite Vegas observations by the way...you know, the tool that HAS to play "third base" cause he doesn't want some hump there, yet he's playing at a 6-5 table.

If you're going to play a serious session - even at 10 dollar limits, you are better off paying for a cab ride off strip to play 3-2. You'd be suprised mathematically how few hours it would take to pay for that cab in expected value ovr 6/5.
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Re: Blackjack math question?

Unread postby waborat » Sun Mar 13, 2011 4:26 pm

Bigfist wrote:I saw the movie.."The Cooler". Wish it had been Maria Bello sitting next to me. That would have made the 17 losses more palatable.


We were in the filming of that @ The Palms playin at the crap table...

Ended up on the cutting room floor...

My wife was drooling over Ron Livingston & I was lifting my leg on Maria...

Even in real life, she's smokin
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Re: Blackjack math question?

Unread postby FUDU » Sun Mar 13, 2011 7:40 pm

Never understood the obsession with this type of debate, b/c frankly one only needs to understand the two things mentioned most often in this thread, 51% adv to the house and table limits.

This is the exact reason why table limits exist.

You want to win at black jack you need to maximize your bets on advantageous opportunities/hands.

To continue on what Lead said about fav observations, I play a lot of roulette and I love watching people obsess with the number board to see what has been coming up and what hasn't, hilarious.
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Re: Blackjack math question?

Unread postby Cease » Sun Mar 13, 2011 7:45 pm

Counting cards is nearly impossible for the novice player (like me) with modern shuffles. After a couple of shoes, you can see and feel high and low cards coming (at least you think you can). Beyond feel, you are stuck with against math, luck and being able to walk away. Best bet is not playing at all, but why go and not play?

Found myself a table paying 6-5 on blackjack, most single deck tables are like this. Vacate these tables immediately. Dealer was trying to talk me into doubling down my blackjacks against bust cards at 6-5 tables to get more money in play. Interesting thought, but I layed off.
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Re: Blackjack math question?

Unread postby waborat » Sun Mar 13, 2011 8:03 pm

Cease wrote:Counting cards is nearly impossible for the novice player (like me) with modern shuffles. After a couple of shoes, you can see and feel high and low cards coming (at least you think you can). Beyond feel, you are stuck with against math, luck and being able to walk away. Best bet is not playing at all, but why go and not play?

Found myself a table paying 6-5 on blackjack, most single deck tables are like this. Vacate these tables immediately. Dealer was trying to talk me into doubling down my blackjacks against bust cards at 6-5 tables to get more money in play. Interesting thought, but I layed off.


6/5 tables, hitting soft 17 & 6+ deck shoes have ruined BJ...

Gawd, remember the days of single/double decks w/ nice penetration?

Move your foot to the right or left when low & high cards would come out and your % of walking away a winner went waaaaaaaay up...

Order free drinks, get a comped lunch and you were always profitable
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Re: Blackjack math question?

Unread postby motherscratcher » Sun Mar 13, 2011 8:15 pm

Dealers hit on soft 17? I didn't know that.

Also, I'm assuming that drinks will not be free in Cleveland. They are only free in Vegas, right?
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Re: Blackjack math question?

Unread postby FUDU » Sun Mar 13, 2011 8:22 pm

motherscratcher wrote:Dealers hit on soft 17? I didn't know that.

Also, I'm assuming that drinks will not be free in Cleveland. They are only free in Vegas, right?


Free drinks in Vegas?, ha that is priceless stuff moscratch.
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Re: Blackjack math question?

Unread postby motherscratcher » Sun Mar 13, 2011 8:25 pm

FUDU wrote:
motherscratcher wrote:Dealers hit on soft 17? I didn't know that.

Also, I'm assuming that drinks will not be free in Cleveland. They are only free in Vegas, right?


Free drinks in Vegas?, ha that is priceless stuff moscratch.


They're not? I was only there once. Around 2004 I think. Drinks were free while playing. Not anymore?
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Re: Blackjack math question?

Unread postby FUDU » Sun Mar 13, 2011 8:25 pm

Well they don't charge you for them, but they're not free if you know what I mean.
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Re: Blackjack math question?

Unread postby motherscratcher » Sun Mar 13, 2011 8:31 pm

FUDU wrote:Well they don't charge you for them, but they're not free if you know what I mean.


No, they are free. I remember I used to sit down at a nickel slot and put $20 in when I wanted a drink. Then I'd play for 15-20 minutes waiting for a waitress to wander by so I could order. Then I'd run through that $20 and put another $20 in. About a half hour later she'd come back with my drink. I'd cash our and take my remaining $7 and free drink, which would take about 2 minutes to drink.

See...free.

Wait.
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Re: Blackjack math question?

Unread postby FUDU » Sun Mar 13, 2011 8:45 pm

I got a free meal from a bit boss at New York New York once. Spent 10 hours at the same $5 table on a Friday night (left $400 up), then 12 hours at the table next to it the following night (down at least $200 IIRC).

Boss comes up to me and a friend and says "How's everything going tonight Don?". Being minimum 20 drinks into the night I'm completely baffled how he knows my name ( ::doh:: ). He then says "why don't you two grab a bite to eat, you gotta be hungry right, you've been playing for 12 hours and have only got up once (bathroom trip), you'll feel better later (its 4am). I say thank you but I'm OK, he replies "I'm insisting, please come with me". Put his hand on my shoulder and starts to assist me to stand up. I'm feeling a bit nervous at this point, thinking something is up, I even ask him. He laughs, says I'm just looking out for you, you've done this two night in a row in my casino, you deserve a meal for your time served.

What I did at that buffet was criminal.
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Re: Blackjack math question?

Unread postby skatingtripods » Sun Mar 13, 2011 8:51 pm

motherscratcher wrote:Dealers hit on soft 17? I didn't know that.


Not around here, but yes. Lots of tables in Vegas are this way. So are the 6/5 BJ tables. Hated it. When I was out there the start of February, I literally would walk a mile at 2 am just to get to a 3/2 table.

There's still a good amount of single/double deck out in Vegas. Pitch too. None around here.
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