Doubling bankroll with 20% flatbets odds of succeeding?
Thread Rating:
Dealer doesn't peek for BJ
Half the bet returned if doubling 11 vs 10 and dealer gets BJ
DAS
Only one split
Double on any 2 cards
Dealer stands on 17
The edge with these rules is 0.52% for the house but apparently that isn't immediately translatable to the odds of actually doubling a bankroll so i ask you guys how my scenario can be calculated into actual numbers.
https://wizardofvegas.com/member/oncedear/blog/#post1370
Incidentally If you can't be bothered to read it...
P<x/(x+x)
P<50%
If you want a more precise result that shows how much less than 50%, then there's a spreadsheet hosted by Mustang Sally.
https://goo.gl/D0pJvD
Neither solution give exact calculations for fixed percentage betting, but both give good enough ballpark.
Incidentally, on day one of my BJ career I played fixed 10% bets and went from £100 to >£6,000 which is why I still hang around messing with BlackJack. https://wizardofvegas.com/forum/gambling/big-wins/18436-my-big-win-day-at-online-live-dealer-blackjack/
If p is the probability of winning and p < 1/2, the chance of having W more wins than losses before having L more losses than wins is:
(1 - ( (1 - p) / p)L) / (1 - ( (1 - p) / p)W + L)
In your case, you want to double your bankroll with flat betting of 20% of your initial bankroll, so you want to be +5 wins before getting to -5.
The HA is 0.52%, so we "fudge" a probability of (1 - 0.0052) / 2 = 0.4974. Of course, this isn't entirely accurate, but it also doesn't take into account thinks like doubling and the 3-2 payout for a blackjack.
The result would be (1 - (0.5026/0.4974)5) / (1 - (0.5026/0.4974)10) = 48.7%
Quote: ThatDonGuyThe result would be (1 - (0.5026/0.4974)5) / (1 - (0.5026/0.4974)10) = 48.7%
20% Flatbets was a bit of a contradiction for me. I read it as 20% of Bankroll at any point in time. For that, I'm not aware of any simple formula.
Nonetheless,
Oncedear's rule of thumb says P<50% and approx 50%
TDG's formula says 48.7%
So, we tell the same story.
:o)
The important take-away is that the betting strategy does not and cannot defeat the house edge. Only good fortune can do that. But for a doubling of bankroll, one does not need much luck: It's pretty much a coin toss decision and almost as quick.
In that case, either of the answers above will surely be close enough: Somewhere in the region of 49%. It's pointless going to the trouble of calculating it to loads of decimal places, because if you give it a try, you'll either succeed or bust out with almost equal probability. Unless you intend to maybe do this as a daily or hourly exercise, in which case save yourself the trouble and just donate half a percent of your money to me.
Why do you ask this question? Do you propose to try it? Did you think maybe it would beat the house edge? ( Surely not )
Such a scheme would have value if you needed to double your money to pay a ransom on your kidnapped wife.. If the ransom was $1,000,000 and you only had $500,000. You'd be wise to do this as a one off exercise to reduce the probability of the wife being shot from 100% to about 51%. Plus you could maybe pick up some nice comps on the way. Slight downside is that you could end up with no wife and no money, Sort of like a cheap divorce.
But seriously. It's just a quick and fun way of losing money.
Ah! I wonder if comps were in your mind when proposing this scheme. Let me save you the trouble. If the value of comps is not greater than the house edge. Your scheme would not help.
Or maybe you figured that it could never go bust because you would always have 80% of 'something' left. Min wager would take care of that.
I place it less than 47% and way lower than playing Baccarat, the pass line at Craps or even playing 00 Roulette.Quote: OnceDearSomewhere in the region of 49%.
Blackjack has a horrible winning probability per hand and even worse when one uses basic Strat.
the probability to double a bankroll is about winning and BJ sucks at it
those who think otherwise can think all life long
does not change the fact
play BJ for fun
lose, win
fun
sure it can. variance rules when playing BJ without countingQuote: OnceDearAh! I wonder if comps were in your mind when proposing this scheme. Let me save you the trouble. If the value of comps is not greater than the house edge. Your scheme would not help.
for most
a lifetime of play
lesson learned
any betting system can and will easily work at BJ in a lifetime of play, except hit until bust on every hand
there are many other bets that double bankroll more often, with a higher probability and are way easier to use than BJ
I hear shaking in Palm Springs
Sally
I would suggest having this simulated by yourself. i think it wood carry more weight, like my hips and ass do.Quote: Billy1337bob20% flatbets following the fluctuation of the bankroll, yes. the bet will change the amount of money wagered depending on this.
you must have some kind of idea on the answer
you think maybe 7 or 8 or 9 times out of 10?
that seems to be BJ players thinking
i would think
i may not be right 100%
Sally
it can B calculated but lots of work, more than a few minutes, so all will pass,Quote: Billy1337bob... to the odds of actually doubling a bankroll so i ask you guys how my scenario can be calculated into actual numbers.
that is why I say simulate.
but it has to be worse than flat betting... I think was was shown B4 on other games too
example with simple bet:
pass line at craps
$200 bank
1st bet = $40
you lose cuz the bet has a greater chance to lose than win.
now bank = $160
2nd bet = $32
you win
now you won 1 and lost 1 and you bank = $192
a loser already
flat betting would still be at $200
still a contender
this sounds like a more fun math problem to solve
maybe later today B4 or AFter Baccarat at Morongo
Sally
Quote: mustangsallyit can B calculated but lots of work, more than a few minutes, so all will pass,
that is why I say simulate.
but it has to be worse than flat betting... I think was was shown B4 on other games too
this sounds like a more fun math problem to solve
maybe later today B4 or AFter Baccarat at Morongo
Sally
I agree that to build a calculated solution is too much like hard work. Not even a fun proposition.
I'm on the fence as to whether %age wagering would be better or worse than flat betting. I'm inclined to think %age betting would have a marginally better probability because it would be possible to reach the goal in fewer, bigger bets.
Sally, I look forward to seeing the 'number' from your simulation.
Before you publish it would anyone care to have a side bet as to whether it's closer to my estimate of 49% than it is to Sally's 47%?
I really haven't sim'ed or calculated it yet.
Truth be told i don't understand these mathematical calculations at all. Really i'd just like to have some cold hard numbers in the same way that i can find bust out percentages and then run with it.
OnceDear: well my goal is to double the bankroll to begin with, after that i contemplate whether to try to do it once more. But it's dependant on the fact that i really am at a ~49% probability for every attempt because if not my interest will plummet. BJ is the most exciting game to me so if it's not the best moneywise at the same time then it's a damn shame. I don't want to trade winning prospects for excitement.
Quote: OnceDearI agree that to build a calculated solution is too much like hard work. Not even a fun proposition.
I'm on the fence as to whether %age wagering would be better or worse than flat betting. I'm inclined to think %age betting would have a marginally better probability because it would be possible to reach the goal in fewer, bigger bets.
Sally, I look forward to seeing the 'number' from your simulation.
Before you publish it would anyone care to have a side bet as to whether it's closer to my estimate of 49% than it is to Sally's 47%?
I really haven't sim'ed or calculated it yet.
He's placing it *less* than 47%. American Roulette has about 5% edge so if he's right that s!#= beyond f/^&ing terrible. Might aswell clunk away at a slot machine at that point.
Admin note: board is PG rated. Please hold off on the protanity. Thank you.
Quote: Billy1337bobHe's placing it *less* than 47%. American Roulette has about 5% edge so if he's right that shit is beyond fucking terrible. Might aswell clunk away at a slot machine at that point.
Call me sexist, but I've always had the impression that Mustang Sally is of female gender. But then again, I've varied my online personas' gender a few times over the years :o)
One thing for sure. Chucking the starting bankroll on a SINGLE even money wager like Red/Black roulette would at least expose the requisite wager to the house edge only once. Makes the probability calculation so much easier too.
Is anybody really daft enough to play American Roulette in the hope of profit?
yep.Quote: Billy1337bobThis guy "mustangsally" seems to suggest the game is really crap and the small house edge doesn't work like that in practise and short run scenario that i proposed.
in 10 hands you could easily not get
and win 1 BJ at 3 to 2.
or a double-down hand worth making.
so the short-term HE without those 2 events happening (like playting perfect Video Poker and No Royal Flushes)
in perfect proportion has to be worse than 5% or 00 Roulette, at least worse than 0 Roulette.
I am certain the Wizard of Odds can verify this
if interested
Sally
my 1st car was a new Mustang
I was popular in high school cuz that car
no more in high school and not popular no more
that car got wrecked and I now drive a Honda
Ashley Revell comes to mind. (Ashely for a boy name?)Quote: OnceDearIs anybody really daft enough to play American Roulette in the hope of profit?
played BIG (Bold Play)
on 00 Roulette downtown las Vegas (next to Greyhound Bus)
Quote: Billy1337bobSo wich one is it: ~49% or much worse? This guy "mustangsally" seems to suggest the game is really crap and the small house edge doesn't work like that in practise and short run scenario that i proposed.
Not trying to second guess what Sally would say or mean, but it both does and does not 'work like that'. In truth, on average over a reasonable number of events, sessions, or experiments, the outcome will tend to approximate to the house edge. But over one 'session' or even dozens of hundreds of sessions, the house edge is damned near irrelevant compared to the massive effect of variance. If you performed your experiment tomorrow trying to get from say $100 to $200 with a few 20% wagers, you could very likely not have any winning blackjacks or useful double down or split opportunities. You could also, quite easily have a couple or a few such great hands and fly through to your target profit.
Well you have those cold hard numbers: You have an assortment of them: Less than 47%, About 49%, less than 50%. It REALLY REALLY doesn't matter that none of the numbers are to 3 decimal places. They are all in the right ball park. Try it or don't try it. Your probability of doubling your bankroll will be less than 50%. That's for absolute certain. Doesn't mean you won't succeed. That's down to the whim of lady luck.Quote:Truth be told i don't understand these mathematical calculations at all. Really i'd just like to have some cold hard numbers in the same way that i can find bust out percentages and then run with it.
Look. I play Blackjack. I love it to bits. I even have a lifetime profit from it, mostly because I had luck on my side. The Excitement is what you make of it. Probability of doubling your bankroll is what it is. Probability of increasing your bankroll just by 10% is what it is.Quote:OnceDear: well my goal is to double the bankroll to begin with, after that i contemplate whether to try to do it once more. But it's dependant on the fact that i really am at a ~49% probability for every attempt because if not my interest will plummet.
For me too.Quote:BJ is the most exciting game to me
What destroys you is house edge. What really destroys you is exposing your money to the house edge multiple times. Whether you choose to present your money to the house edge multiple times using BlackJack, Baccarat, Roulette or whatever is totally your choice. Play what you enjoy for enjoyment.Quote:so if it's not the best moneywise at the same time then it's a damn shame. I don't want to trade winning prospects for excitement.
Lifetime house advantage= Lifetime amount staked at the table x game house edge.
The more 'action' you place: The more you expose to the house edge. The maths is not rocket science.
Play US roulette you expose money to 5.26% edge.
Play Blackjack with typical rules you expose money to 0.5% edge.
It's the total action exposed to house edge that matters.
You should intuitively be able to see which one will destroy you over the least number of games and which will let you get the max number of games under your belt before you lose your shirt.
If you want max profit potential limit yourself to one wager in your lifetime. No fun in that, but still.
Quote: mustangsallyAshley Revell comes to mind. (Ashely for a boy name?)
played BIG (Bold Play)
on 00 Roulette downtown las Vegas (next to Greyhound Bus)
You just have to love or hate the outcome of that bravado.
Piddling small stakes if that was all he was worth. He should have let it roll just once more $:o)
What a fantastic and low cost Marketing bonanza that has been for that casino and for all casinos. You can't buy that much publicity for the trifling amount that Ashley walked away with.
what I do have right now is the pass line bet dataQuote: OnceDearSally, I look forward to seeing the 'number' from your simulation.
Before you publish it would anyone care to have a side bet as to whether it's closer to my estimate of 49% than it is to Sally's 47%?
I really haven't sim'ed or calculated it yet.
as I had done this some time ago
it wins at a rate of 49.29% or 244/495
so to double 5 unit Bank is easy for the math (flat betting 1 unit)
= a / (a+b)
a = (244/495)^5
b = (251/495)^5
46.47%
or exactly
864866612224 / 1861117238475
http://www.wolframalpha.com/input/?dataset=&equal=Submit&i=(244%2F495)%5E5+%2F+((244%2F495)%5E5%2B(251%2F495)%5E5)
I did not calculate betting the 20% yet (a Markov chain should do)
but the sim shows a success double rate at about 41% (at best)
a very large difference to many
now for a fun weekend with Mom and her friends and free drinks at the Casino
Sally
Quote: Billy1337bob20% flatbets following the fluctuation of the bankroll, yes. the bet will change the amount of money wagered depending on this.
Based on that criteria you can never lose everything. If you could bet any amount, even smaller and smaller fractions of a cent, and play infinitely long, eventually you will see a run that will double up your starting bankroll.
So my answer is that if you are allowed to bet an infinitesimal amount and play forever your chance of doubling your bankroll is 100%. I swear I'm not on any drugs, but I am interested in any opinions agreeing or disagreeing with that answer.
No. Not true at all. Think about it a bit harder. With each wager, you will tend towards expected value which will be the point whereQuote: TomGBased on that criteria you can never lose everything. If you could bet any amount, even smaller and smaller fractions of a cent, and play infinitely long, eventually you will see a run that will double up your starting bankroll.
EndingBankroll=StartingBankroll - HouseEdge x TotalAmountWagered
i.e You will tend towards a bankroll which is less than starting bankroll.
As you find yourself with tiny fractions of a cent, the magnitude of winning streak that you need to dig yourself out of the hole with will get greater and greater and less likely.
This is actually another of those 'messing with infinity questions' Not a bad one, but I assert that you are wrong Tom.Quote:So my answer is that if you are allowed to bet an infinitesimal amount and play forever your chance of doubling your bankroll is 100%. I swear I'm not on any drugs, but I am interested in any opinions agreeing or disagreeing with that answer.
Quote: OnceDearNot trying to second guess what Sally would say or mean, but it both does and does not 'work like that'. In truth, on average over a reasonable number of events, sessions, or experiments, the outcome will tend to approximate to the house edge. But over one 'session' or even dozens of hundreds of sessions, the house edge is damned near irrelevant compared to the massive effect of variance. If you performed your experiment tomorrow trying to get from say $100 to $200 with a few 20% wagers, you could very likely not have any winning blackjacks or useful double down or split opportunities. You could also, quite easily have a couple or a few such great hands and fly through to your target profit.
Yeah but variance still plays out in relation to house edge so it doesn't really answer anything. If there was a Roulette wheel with 10% HE and one that's 0% no one in their right mind would say those two games are equal and yet your argument would still be valid that it all comes down to luck.
Quote: OnceDearWell you have those cold hard numbers: You have an assortment of them: Less than 47%, About 49%, less than 50%. It REALLY REALLY doesn't matter that none of the numbers are to 3 decimal places. They are all in the right ball park. Try it or don't try it. Your probability of doubling your bankroll will be less than 50%. That's for absolute certain. Doesn't mean you won't succeed. That's down to the whim of lady luck.
Even with 3 decimal places it still matters. People advise against playing on slots based on those very few couple of % higher house edge and in Blackjack the same goes for 6:5 payout. I played yesterday for example and the fractions that constitute dealer not peeking on an Ace prevented me from splitting my own Aces.
And that's only fractions. If a game has 49% or under 45% house edge i would say that is a big difference right there.
Quote: OnceDearLook. I play Blackjack. I love it to bits. I even have a lifetime profit from it, mostly because I had luck on my side. The Excitement is what you make of it. Probability of doubling your bankroll is what it is. Probability of increasing your bankroll just by 10% is what it is. For me too. What destroys you is house edge. What really destroys you is exposing your money to the house edge multiple times. Whether you choose to present your money to the house edge multiple times using BlackJack, Baccarat, Roulette or whatever is totally your choice. Play what you enjoy for enjoyment.
But that's exactly the thing: the probability of doubling the bankroll "is what it is" but no one agrees *what* that is exactly. I'm not arguing against the probability or the rules of the game here that's a completly different topic.
Quote: Billy1337bobYeah but variance still plays out in relation to house edge so it doesn't really answer anything. If there was a Roulette wheel with 10% HE and one that's 0% no one in their right mind would say those two games are equal and yet your argument would still be valid that it all comes down to luck.
Sorry Bob, but what do you want? The probabilty of doubling your bankroll with the betting strategy that you propose really is what it is. It's definitely less than 50%
NO-ONE can tell you whether you will succeed or not if you go and try it.
I strongly assert that your probability of success is closely related to the house edge on the game that you play GIVEN THE SAME 20% WAGERING STRATEGY. Thus I suggest that with that betting strategy with double zero roulette, your probability of success would be much, MUCH worse than a typical 3:2 Blackjack game, simply because house edge is SO much worse. Maybe there are craps wagers or Baccarat wagers where your probability would be better. But Probabilty of success won't be better than 50%.
40%, 45%, 47%, 49% ? Stick a wet finger in the air or sim it or calculate it or even try it for yourself. If you try it once, then win or lose, you'll be none the wiser as to the probability you just exposed yourself to.
6:5 payout blackjack sucks. The house edge chomps away at your bankroll with every bet you take, and on average you would need to make more bets to attempt to reach goal with such a sucky game.Quote:Even with 3 decimal places it still matters. People advise against playing on slots based on those very few couple of % higher house edge and in Blackjack the same goes for 6:5 payout. I played yesterday for example and the fractions that constitute dealer not peeking on an Ace prevented me from splitting my own Aces.
It's a big difference. but I'm sorry. So what. The maths is tricky. Simulating is less tricky. I'm not inclined to put in that effort. Maybe someone else will. But again, What do you want? Someone to say 'Do it' or someone to say 'Don't do it'? O.K. Do it. You will soon see how luck is inextricably entwined.Quote:And that's only fractions. If a game has 49% or under 45% house edge i would say that is a big difference right there.
Because the calculation is not worth the effort. Play the game that gives you the best probability subject to your own money management system. Be confident that so long as there is no probability of exceeeding your target profit, that the wagers with the lowest house edge will bear the best probability of success (ON AVERAGE). But you won't get the 'on average result' when you try it once: You will succeed or fail with an aggregate probability of 100%.Quote:But that's exactly the thing: the probability of doubling the bankroll "is what it is" but no one agrees *what* that is exactly.
TELL YOU WHAT BOB.....
Just for You, and just because it's VERY simple to do. I'll create and run a sim for single zero roulette and double zero roulette. I'll get you doubling probabilities for both those games to 3 decimal places. Someone else can do the exercise for Blackjack, because currently I'm not so inclined.
Quote: OnceDearEndingBankroll=StartingBankroll - HouseEdge x TotalAmountWagered
But with an infinite number of trials there is no 'Ending Bankroll.'
It's all about 'Tends towards' when iterating over a number of trials that approaches infinity.Quote: TomGBut with an infinite number of trials there is no 'Ending Bankroll.'
The bankroll will tend towards zero with a few fits and starts along the way.
Quote: OnceDearwith a few fits and starts along the way.
This is where my mind veers off. It doesn't take that much to see 10 wins in a row -- a one in 1347 chance of single zero roulette. It will eventually happen. Twenty wins in a row is around a one in 1.8 million shot. That too will eventually happen. Thirty wins in a row happens roughly once every 2.5 billion times. Which will also happen given enough time. And ten million wins in a row will happen at some point along the way to infinity.
I'm often wrong on these things, so if someone stronger than I am at these type of problems disagrees, they're probably right. . .
Quote: TomGI'm often wrong on these things, so if someone stronger than I am at these type of problems disagrees, they're probably right. . .
I'm probably right :o) But it was 30 years since I graduated and explaining some of this stuff is better left to the proper maths experts who know the correct mathematical proofs.
Fundemental problem with your hypothesis Tom is that those very rare events will be needed far before they are likely to happen. E.g. thirty wins in a row might well happen after you are in such a hole that you need forty wins in a row just to get your bankroll back up to a cent.
Quote: OnceDearTELL YOU WHAT BOB.....
Just for You, and just because it's VERY simple to do. I'll create and run a sim for single zero roulette and double zero roulette. I'll get you probabilities for both those games to 3 decimal places. Someone else can do the exercise for Blackjack, because currently I'm not so inclined.
OK... I promised to sim this for Roulette, because that is easy and because Bob seems to want SOME idea of how house edge impacts on the probability of doubling his money. Not yet run to the promised accuracy though.
Roulette Simulation is currently running. It's experimented half a million times for each variant of the game and hasn't yet settled out 3 decimal places. I expect that would need an overnight run ( clunky old VBA in Excel )
I used the following criteria to define the task at hand:-
Initial bankroll = $1000
Target final bankroll = $2000
Minimum stake =$1
Each wager 20% of existing bankroll rounded to the NEAREST whole $1
If there was $5 or less of existing bankroll, the next wager would be $1
Wagering on one of the even money outside bets. I chose 'Odd' and if anyone asks what the result would look like if I chose even, or black or red, I will tell them where to go.
To give absolutely the best probability of doubling bankroll, I made it impossible to exceed the target profit. So each wager had a maximum value capped at
Max wager = ($2000-(existing bankroll)).
As expected, the US rules Roulette with its house edge 0f 5.26% gave a crappy 34.7% probability of doubling bankroll using that strategy. That's pretty probably +/- 0.1%
European single zero rules (No en-prison rule) with its house edge of 2.7% gave a less crappy 41.5% probability of doubling bankroll using that strategy. Probably +/- 0.1%
Oh yeah. And for good measure I took out the zero and it gave me a not at all crappy probability of 50.0%
Good old VBA in Excel.
Quote: mustangsallyway lower than playing Baccarat, the pass line at Craps or even playing 00 Roulette.
I just sim'ed it for 00 roulette using his 20% scheme. It sucked big time P=34.7%%. Single zero roulette was pretty crappy too. Can't yet be bothered to sim it for BJ
Ah, but variance is our friend. Don't dismiss those occasional Blackjacks, good doubles or good splits. Low house edge is low house edge is GOOD. Even variance is good 'cos therein lies the fun. If you sim this kind of betting scheme with Blackjack, then often the sim will have rubbish streaks of losses. but in your gazillion experiment runs, some, rather many, will be boosted by good double or split opportunities or BlackJack wins. The sim exercise must not dismiss those good runs which all go towards the average.Quote:Blackjack has a horrible winning probability per hand and even worse when one uses basic Strat.
To each his own. With low edge of Blackjack, I can get more action for my dollar than roulette. ( I don't play craps, or baccaslap so no comment on those)Quote:those who think otherwise can think all life long does not change the fact.
i think something is wrong with your simQuote: OnceDearAs expected, the US rules Roulette with its house edge 0f 5.26% gave a crappy 34.7% probability of doubling bankroll using that strategy. That's pretty probably +/- 0.1%
European single zero rules (No en-prison rule) with its house edge of 2.7% gave a less crappy 41.5% probability of doubling bankroll using that strategy. Probably +/- 0.1%
Oh yeah. And for good measure I took out the zero and it gave me a not at all crappy probability of 50.0%
Good old VBA in Excel.
edit: I did not see at 1st you were hitting the target exactly
none of my sims or calcs were doing that.
see at end then...
results are too high
for pass line at craps i use 2 different programs and still get 41% success rate
0 Roulette can not beat craps
here is the R code I used
just the value of w needs to be changed
and this code does not roundup the bet
my other code did
w <- 244/495
s <- 1
f <- 0.2
nextBet <- function(m) {
if(m >= 2000) 0
else m*f
}
oneNight <- function() {
m <- 1000
b <- nextBet(m)
while(b >= 1 & m >= b) {
if(runif(1) < w) m <- m + b*s
else m <- m - b
b <- nextBet(m)
}
m
}
score <- function() {
n <- 1e5
x <- 0
for(i in 1:n)
if(oneNight() >= 2000) x <- x+1
x/n
}
print(score())
and results
R version 3.1.2 (2014-10-31) -- "Pumpkin Helmet"
Copyright (C) 2014 The R Foundation for Statistical Computing
Platform: x86_64-w64-mingw32/x64 (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
Natural language support but running in an English locale
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> w <- 18/37
> s <- 1
> f <- 0.2
>
> nextBet <- function(m) {
+ if(m >= 2000) 0
+ else m*f
+ }
>
> oneNight <- function() {
+ m <- 1000
+ b <- nextBet(m)
+ while(b >= 1 & m >= b) {
+ if(runif(1) < w) m <- m + b*s
+ else m <- m - b
+ b <- nextBet(m)
+ }
+ m
+ }
>
> score <- function() {
+ n <- 1e5
+ x <- 0
+ for(i in 1:n)
+ if(oneNight() >= 2000) x <- x+1
+ x/n
+ }
>
> print(score())
[1] 0.37406
> w <- 18/38
> s <- 1
> f <- 0.2
>
> nextBet <- function(m) {
+ if(m >= 2000) 0
+ else m*f
+ }
>
> oneNight <- function() {
+ m <- 1000
+ b <- nextBet(m)
+ while(b >= 1 & m >= b) {
+ if(runif(1) < w) m <- m + b*s
+ else m <- m - b
+ b <- nextBet(m)
+ }
+ m
+ }
>
> score <- function() {
+ n <- 1e5
+ x <- 0
+ for(i in 1:n)
+ if(oneNight() >= 2000) x <- x+1
+ x/n
+ }
>
> print(score())
[1] 0.30578
> w <- 244/495
> s <- 1
> f <- 0.2
>
> nextBet <- function(m) {
+ if(m >= 2000) 0
+ else m*f
+ }
>
> oneNight <- function() {
+ m <- 1000
+ b <- nextBet(m)
+ while(b >= 1 & m >= b) {
+ if(runif(1) < w) m <- m + b*s
+ else m <- m - b
+ b <- nextBet(m)
+ }
+ m
+ }
>
> score <- function() {
+ n <- 1e5
+ x <- 0
+ for(i in 1:n)
+ if(oneNight() >= 2000) x <- x+1
+ x/n
+ }
>
> print(score())
[1] 0.4107
>
Sally
follow up
so an easy Markov chain solves this
maybe I post it after I remove some code to make Google happy
I used your parameters
success results:
pass line
0.455545783
0 roulette
0.417834822
00 roulette
0.350807058
without hitting exactly the double target
(going over double is OK - always betting 20% of bank)
i gets
pass
0.421683684
0roul
0.384078393
00roul
0.318252408
will check sun nite
Quote: mustangsallyi think something is wrong with your sim
edit: I did not see at 1st you were hitting the target exactly
none of my sims or calcs were doing that.
So does your edit mean you don't see my sim as wrong?
Here it is: Rough and ready vba
Dim spin As Integer
Dim odd As Boolean
Dim initialbank As Integer
Dim bankbefore As Integer
Dim wager As Integer
Dim bankafter As Integer
Dim success As Boolean
Dim failure As Boolean
Dim successct As Long
Dim failurect As Long
Dim percentagesuccess As Double
initialbank = 1000
bankbefore = initialbank
For i = 1 To 500000
Application.ScreenUpdating = False
If i Mod 100 = 0 Then Application.ScreenUpdating = True
success = False
failure = False
bankbefore = initialbank
While Not (success) And Not (failure)
DoEvents
spin = Int((38 - 1 + 1) * Rnd + 1)
'Debug.Print spin
If spin Mod 2 = 1 And spin < 37 Then
odd = True
Else
odd = False
End If
'Stop
wager = Int(bankbefore / 5 + 0.5)
If wager = 0 And bankbefore > 0 Then wager = 1
If wager + bankbefore > 2 * initialbank Then wager = 2 * initialbank - bankbefore
'Stop
If odd Then
bankafter = bankbefore + wager
Else
bankafter = bankbefore - wager
End If
bankbefore = bankafter
' Stop
If bankafter >= 2 * initialbank Then success = True: successct = successct + 1 ': Stop
If bankafter = 0 Then failure = True: failurect = failurect + 1 ': Stop
'Stop
Wend
Range("o6").Value = i
Range("p6").Value = successct
Next i
Stop
End Sub
There's a line in there spin = Int((38 - 1 + 1) * Rnd + 1)which limits the spin to either 36,37, or 38. edit to suit. I use 37 to represent 0 and 38 to represent 00 and just discount those two results as odd but count them in denominator. By substituting the 38 with 37 I limit the wheel to 37 possibilities. Make it 36 for a no zero wheel. Of course it doesn't matter that they are not numerically zero because neither is treated as odd or even in the If spin Mod 2 = 1 And spin < 37 Then
Quote:I used your parameters
success results:
pass line
0.455545783
0 roulette
0.417834822
00 roulette
0.350807058
without hitting exactly the double target
(going over double is OK - always betting 20% of bank)
i gets
pass
0.421683684
0roul
0.384078393
00roul
0.318252408
Short of letting those sims run for longer, we pretty much concur on the probability for the two roulette variants. You amply demonstrate that not disallowing the possibility of going over the win target will result in a lower probability of achieving win target. For others, who wonder why:, That's because if it's possible to go over win target, you must allow the possibility of having a higher than necessary final wager and that high wager might lose, setting you back further than you needed to be set back and increasing your probability of failure, as well as exposing more than essential action to the house edge.
Sally. Glad we agree on the roulette results give or take a bit of rounding (you ran only 1e5 experiments. I observed 5e5 andsuch low sample still has the result flailing about at the decimal fraction). I'm not familiar with your code, but it looks pretty easy to include the restriction to max bet as a simple if statement.
your sim results look rightQuote: OnceDearThanks Sally for taking the trouble to sanity check my numbers.
So does your edit mean you don't see my sim as wrong?
I first ran a sim just to see where my calculations should be.Quote: OnceDearSally. Glad we agree on the roulette results give or take a bit of rounding (you ran only 1e5 experiments.
here is my transition matrix (the exact target one) in Excel in Google
https://goo.gl/OJcSni
I do not expect many to understand it (Don, BruceZ will, the Wizard should)
but if I can do this and I had help, 99% of the world's population can do it too
the transition matrix self populates
i think that method is clever using a simple IF statement
some hate using Excel and at times I use R
but I need to see the matrix
took me long time to get it (learn the process)
but this matrix about 2 minutes to complete
also
it is 1.3MB so B careful open in a smartphone to view
mine can't
answer in cell GX101
value of p
can B changed in cell GW1
sheet will calculate after hit enter
not online, must download to your device
i never seen calculations for fraction betting versus flat betting
we did it
Sally
Some people just run these sims like they are preparing a bowl of Cheerios for breakfast ;-)
I got a sim I'd like run, BJ of course.
Sumptin' like a dozen different bet sizes, 'bout twenty if/then statements.
Lil more complicated than that.
Might be willing to pay a couple bucks if I got something I could play around with, meaning the bet sizes and the if/then statements.
I've looked a bit and haven't found anything in the marketplace 'off the shelf' that looks like it meets the criteria.
And I am too lazy ( or stupid, or both ) to learn how to put it together myself ( not even sure it can be done, or should be done ;-)
I thought there would be a market for such a program. Some dumb dumb re-invents a square wheel everyday ;-)
They usually don't roll well... Octagons are better, but still bumpy.
This might be a project for OhDear ( OK, Sally scares me a little ).
PM if interested. Just post here if you want to laugh at me. I'm used to it.
Cool. Took several minutes to knock up. It's first incarnation was just a spreadsheet with half a dozen columns but too slow to watch over.Quote: mustangsallyyour sim results look right
Quote:here is my transition matrix (the exact target one) in Excel in Google
https://goo.gl/OJcSni
I do not expect many to understand it (Don, BruceZ will, the Wizard should)
Very cool indeed. I wasn't familiar with Markov Chains or transition matrices. Reading up now. Excel rocks!
Quote:i never seen calculations for fraction betting versus flat betting
we did it
Sally
We did indeed, independently and quickly, even arriving at the same result: YAYyyy us.
Useful when investigating Kelly betting probabilities.
Now..... Should we be inclined to do the sim for Blackjack? I think I'd like to prove that Blackjack would give better probability than your craps bet.
I'm probably conceding that my 49% was too high and now pitching closer to 47% as a prediction/guesstimate.
$:o)
Run. Tee-hee Create!Quote: TwoFeathersATLDamn
Some people just run these sims like they are preparing a bowl of Cheerios for breakfast ;-)
Quote:I got a sim I'd like run, BJ of course. Sumptin' like a dozen different bet sizes, 'bout twenty if/then statements. Lil more complicated than that.
Might be willing to pay a couple bucks if I got something I could play around with, meaning the bet sizes and the if/then statements.
PM me if you are serious. I'm already inclined to extend this exercise for Blackjack. Would probably take a few hours.
Quote:I've looked a bit and haven't found anything in the marketplace 'off the shelf' that looks like it meets the criteria.
And I am too lazy ( or stupid, or both ) to learn how to put it together myself ( not even sure it can be done, or should be done ;-)
This might be a project for OhDear ( OK, Sally scares me a little ).
Might be. Sally is pretty impressive with the old maths stuff. I reckon either of us could do off the wall real life stuff with Excel that would seriously impress.
I used this page to learnQuote: OnceDearVery cool indeed. I wasn't familiar with Markov Chains or transition matrices. Reading up now. Excel rocks!
http://www.zweigmedia.com/RealWorld/Summary6b.html
BJ can be done also with the matrix solution when the probability distribution is known.Quote: OnceDearNow..... Should we be inclined to do the sim for Blackjack? I think I'd like to prove that Blackjack would give better probability than your craps bet.
I'm probably conceding that my 49% was too high and now pitching closer to 47% as a prediction/guesstimate.
$:o)
most get that from a sim
and yes, Kelly betting for sports versus flat betting
2 camps and both think they are the best method
haha
at least 4me it is fun
Sally
Thanks.Quote: mustangsallyI used this page to learn
http://www.zweigmedia.com/RealWorld/Summary6b.html
Interesting, use the non-sim method using a transition table, but first use a sim to get underlying probability distribution. I'd be inclined to get the probability distribution from the wizards excellent strategy derivation workbooks.Quote:BJ can be done also with the matrix solution when the probability distribution is known.
most get that from a sim
I don't know if you've seen them or his video derivation of BS, but excellent, simple and extremely elegant. https://www.youtube.com/watch?v=jCF-Btu5ZCk He's shared a variant to me that applies different rules. Deriving probabilities is an interim step within the workbook. I created a derivative workbook which does not involve infinite decks and which was composition dependent.
Kelly betting for bankroll growth, for sure.Quote:and yes, Kelly betting for sports versus flat betting
Quote:At least 4me it is fun
Fun rocks. Winning/losing/playing all parts of the same fun. Being in the game is the fun. As my Dad used to say. If you are playing the game and enjoying it, then you've already won.
Martingale: Fun. Flatbetting: Fun.
When it's not fun. Stop. Losing and not stopping is not fun!
If you are playing just for profit, that's a different set of rules. Is working 9-5 fun? For some.
Wrangling with probability derivation can be fun too and doesn't cost bankroll.
Quote: OnceDearOK... I promised to sim this for Roulette, because that is easy and because Bob seems to want SOME idea of how house edge impacts on the probability of doubling his money. Not yet run to the promised accuracy though.
Roulette Simulation is currently running. It's experimented half a million times for each variant of the game and hasn't yet settled out 3 decimal places. I expect that would need an overnight run ( clunky old VBA in Excel )
I used the following criteria to define the task at hand:-
Initial bankroll = $1000
Target final bankroll = $2000
Minimum stake =$1
Each wager 20% of existing bankroll rounded to the NEAREST whole $1
If there was $5 or less of existing bankroll, the next wager would be $1
Wagering on one of the even money outside bets. I chose 'Odd' and if anyone asks what the result would look like if I chose even, or black or red, I will tell them where to go.
To give absolutely the best probability of doubling bankroll, I made it impossible to exceed the target profit. So each wager had a maximum value capped at
Max wager = ($2000-(existing bankroll)).
As expected, the US rules Roulette with its house edge 0f 5.26% gave a crappy 34.7% probability of doubling bankroll using that strategy. That's pretty probably +/- 0.1%
European single zero rules (No en-prison rule) with its house edge of 2.7% gave a less crappy 41.5% probability of doubling bankroll using that strategy. Probably +/- 0.1%
Oh yeah. And for good measure I took out the zero and it gave me a not at all crappy probability of 50.0%
Good old VBA in Excel.
Well in that case it's better with just a single bet. But then again with BJ you could bet 50% instead and get the chance to double down or 25% to split and double 2 times. But splitting occurs even less seldom than doubling and for those splits to be good to double at is even less likely.
Quote: Billy1337bobWell in that case it's better with just a single bet. But then again with BJ you could bet 50% instead and get the chance to double down or 25% to split and double 2 times. But splitting occurs even less seldom than doubling and for those splits to be good to double at is even less likely.
Yes. Indeed.
I've answered that self same question in another of your very own threads, 2 months ago. I covered off the whole 50% and doubling/splitting thing there.
yep. the math greats from the 1600s knew that tooQuote: Billy1337bobWell in that case it's better with just a single bet.
here is a table that shows the % chance to double a unit size bank
just flat-betting
all will be under 50% due to the house edge (the casino short-pays the player on a win)
the exception is the fair 50/50 game
| unit bankroll | 50/50 coin flip | Bacc Player | pass line | 0 roul evens | 00 roul evens | Blackjack |
|---|---|---|---|---|---|---|
| 1 | 50.00% | 49.318% | 49.293% | 48.649% | 47.368% | ? |
| 2 | 50.00% | 48.635% | 48.586% | 47.299% | 44.751% | ? |
| 3 | 50.00% | 47.954% | 47.880% | 45.954% | 42.163% | ? |
| 4 | 50.00% | 47.273% | 47.175% | 44.614% | 39.617% | ? |
| 5 | 50.00% | 46.593% | 46.470% | 43.282% | 37.126% | ? |
| 6 | 50.00% | 45.914% | 45.767% | 41.960% | 34.702% | ? |
| 7 | 50.00% | 45.237% | 45.066% | 40.650% | 32.355% | ? |
| 8 | 50.00% | 44.561% | 44.367% | 39.352% | 30.093% | ? |
| 9 | 50.00% | 43.888% | 43.670% | 38.069% | 27.924% | ? |
| 10 | 50.00% | 43.217% | 42.976% | 36.803% | 25.853% | ? |
| 11 | 50.00% | 42.548% | 42.284% | 35.555% | 23.886% | ? |
| 12 | 50.00% | 41.882% | 41.595% | 34.326% | 22.023% | ? |
| 13 | 50.00% | 41.219% | 40.910% | 33.118% | 20.267% | ? |
| 14 | 50.00% | 40.559% | 40.228% | 31.931% | 18.618% | ? |
| 15 | 50.00% | 39.903% | 39.550% | 30.768% | 17.074% | ? |
| 16 | 50.00% | 39.250% | 38.875% | 29.628% | 15.633% | ? |
| 17 | 50.00% | 38.601% | 38.205% | 28.513% | 14.293% | ? |
| 18 | 50.00% | 37.956% | 37.540% | 27.424% | 13.051% | ? |
| 19 | 50.00% | 37.315% | 36.879% | 26.361% | 11.901% | ? |
| 20 | 50.00% | 36.679% | 36.223% | 25.325% | 10.840% | ? |
one can see the trend!
BJ data to follow
of course,
can ONE player really tell the difference between a 49.3% chance of winning and a 47.3% chance of winning?
1000 marbles in a box
493 are green
draw green and WIN!!
another game!
1000 marbles in a box
473 are green
draw green and WIN!!
hahaha
Sally pretty
I can tell
yes, I seen. I think that method would still require a computer to cycle thru all possible hands (lots) to get the probability distributionQuote: OnceDearI don't know if you've seen them or his video derivation of BS,
The Wizard has resorted to simple sims for his data in the past
as has others (like teliot to mention 1+0)
even easy stuff like unit results {-2, -1, 0, 1, 1.5, 2} would be an extreme exercise in calculations for 6 and 8 deck games for the average computer.
my Dell is above average
i say that is why no one has shown they have done just that.
I will soon sim that game and see what I get
I B rusty on sims as baseball takes almost all my attention
I love to watch teams score runs!
Sally
Quote: OnceDear
Now..... Should we be inclined to do the sim for Blackjack? I think I'd like to prove that Blackjack would give better probability than your craps bet.
I'm probably conceding that my 49% was too high and now pitching closer to 47% as a prediction/guesstimate.
Do you base this on comparing the difference 2.7% HE made for Roulette and then comparing that to Blackjack having a 2.18% edge over 0-Roulette? That would be very good and assuming that it works we've concluded a point where it can't get any better, a best case scenario. It can on the other hand get worse and that's dependant upon how exactly those BJ's, splits and Double Downs should be factored in.
If the 1.5, 2, 3 and 4 unit wins can NOT be factored in in a short term run like 20% flatbetting then it's looking pretty hopeless for Blackjack. If they can then BJ is only about equal to one spin of 0-Roulette anyway - pretty dissappointing considering how much better the theoretical odds are.
Pretty much. I assert that the game with the lowest edge, will ON AVERAGE have the best probability of succeeding with your system, with the proviso that it is NEVER possible to bet enough to go over target. I've yet to prove it to myself, to you, or to Sally. I may be wrong. Time and a complex simm will tell.Quote: Billy1337bobDo you base this on comparing the difference 2.7% HE made for Roulette and then comparing that to Blackjack having a 2.18% edge over 0-Roulette?
Quote:...that's dependant upon how exactly those BJ's, splits and Double Downs should be factored in.
If the 1.5, 2, 3 and 4 unit wins can NOT be factored in in a short term run like 20% flatbetting then it's looking pretty hopeless for Blackjack. If they can then BJ is only about equal to one spin of 0-Roulette anyway - pretty dissappointing considering how much better the theoretical odds are.
I do assert that ON AVERAGE, over a decent number of trials, those 'good hands' must not be discounted.
However, I also agree that absolutely minimum number of bets would be best chance, because that exposes you to minimum of "action x house edge"
The information ought to have a prominent place on the Wizard of Odds website aswell.
Quote: Billy1337bobWell i can't force anyone nor do i want to but i really think someone in the know should put in the effort and make those calculations a reality. It's dynamite information on the same level as knowing basic strategy actions , what could possibly be more important to a game than knowledge about the actual probability of winning money? It's by very definition the best question that could be asked.
The information ought to have a prominent place on the Wizard of Odds website aswell.
I intend to do it, just to test my own assertion. But I don't place much value on it. Do you? How much $$$ for my time and effort ?
The knowledge won't swing -ev to +ev.
Quote: OnceDearI intend to do it, just to test my own assertion. But I don't place much value on it. Do you? How much $$$ for my time and effort ?
The knowledge won't swing -ev to +ev.
I could offer you a ton of money but since i know you're such huge idealist and all about the cause you'd reject them anyway. It would break your heart into pieces accepting such money.
Quote: mustangsallyBlackjack has a horrible winning probability per hand and even worse when one uses basic Strat.
I've come to understand that knowing basic strategy decreases the HE. How can it decrease your winning probability?
On a side note, the comments re: variance ring true with me. Three weeks ago I'm playing heads up with the dealer and had the best shoe I've ever played, perhaps losing only 5 hands in the entire shoe! I played BS and flat betted the whole time and more than doubled my session bankroll in a single shoe! (I promptly colored up and left the table.)
Very considerate of you. Thanks.Quote: Billy1337bobI could offer you a ton of money but since i know you're such huge idealist and all about the cause you'd reject them anyway. It would break your heart into pieces accepting such money.
Quote: theoriemeisterThis line from Sally piqued my interest:
I've come to understand that knowing basic strategy decreases the HE. How can it decrease your winning probability?
I've struggled with that prospect too. As I see it so far, THE AVERAGE probability of hitting win goal would increase by playing BS properly, but the variance would also increase as you get more doubling and splitting. Increased variance and increased potential to overshoot the target would mean that you'd have to take the counter measure of capping your bets more often. Smaller bets gives rise to more bets and more exposure to the house edge.
Until I write my simm, I'm uncertain whether Sally's assertion is correct. I am of course prepared for the opportunity to say 'Wow Sally was right' but I'd need to triple check my facts for saying she was wrong, and I haven't single checked yet.
