The Anti-Martingale Strategy
Let's say that a table game has a 3 percent house edge, a $5 minimum and a $1000 maximum bet. You would have to win 8 times in a row before you reach the table maximum. Supposing that I had the bankroll to do it, how many hands (spins, rolls, tosses, twirls, etc) would it take to reach a %75 probability of having an 8 game winning streak?
I will play that many hands and if I don't get my streak, then I'll assume that it just wasn't in the cards.
Quote: s2dbakerSupposing that I had the bankroll to do it, how many hands (spins, rolls, tosses, twirls, etc) would it take to reach a %75 probability of having an 8 game winning streak?
For 75% it's 1093 hands. The 3% HA advantage hurts you pretty badly. It would be 704 if there was no HA.
Try something a little less ambitious. Lay a 6 or and 8 in craps, and try to win 6 times in a row. The HA is much lower, and the 75% probability will occur in 160 bets resolved. Use $10 as your initial bet instead of $5 if the jackpot of 32*$5 is too small for you to feel good.
BTW, anti-martingale is just as meaningless as martingale.
Quote: s2dbakerMy RNG came up with 1094 but I noticed an interesting thing. I counted the number of trials and stored it in a table. The most frequent number of trials to win 8 in a row is 8 trials. The longest I went without 8 in a row is 8331 trials. I'll let this run all night and see if it normalizes.
Well the difference between 1093 and 1094 theoretically is 75.006% and 75.038% so I'm not surprised that the simulation would miss it by that much.
Your second observation is not an artifact. Ask your self the much simpler question of how many trials do you expect to play before you win? Assume a 50/50 game initially.
The answer is
half the time you expect to win on 1st trial;
1/4 the time you expect to win on 2nd trial;
1/8 the time you expect to win on 3nd trial;
...
On average you expect to win on the 1+1/2+1/4+1/8+...= 2nd trial
But most of the time you will in one trial. That last fact won't change for a house edge.
It's basically the same reasoning for a streak of 8 wins. It will take 1093 trials to get a 75% average, but the majority of times when it happens will be the first 8.
silly
BTW, it ran all night and eventually settled at 1093. One unlucky run went 14,677.
I do believe the verdict is in, the Anti-Martingale is the suck!
Quote: s2dbakerI do believe the verdict is in, the Anti-Martingale is the suck!
It doesn't so much suck as it doesn't matter. Casinos like people who have betting strategies because it keeps player playing despite losses, because they think the strategy will pay off in the end.
But at least you can gauge what to expect. If you want to start with a larger amount (SAY $50) and intend to play until you have a streak of 4 wins, now you know that is expected to take 30 trials if there was no house edge. If you add a small house edge like laying a 6 or and 8, the number of trials moves up to 31. But if you add a larger house edge, the expected number of trials is now 34.5 .
But the expected number of trials will to get this streak of 4 wins will vary widely. But HA advantage is going to matter a lot if you play repeatedly. They didn't invent that term grindhouse for nothing. The HA just grinds away at you.
Which is why I don't understand the Chinese fascination with Baccarat. If you are going to grind away all day, why not play craps with full odds. The probability of doubling your money before going bankrupt is much higher than Baccarat.
You say that a lot, and I agree with it. Last time I was in Vegas, I took $1,000 to the craps table at Casino Royale and my friend matched it. We played $5 craps with 100 times odds. We were either going to walk away rich or go broke very quickly. Guess what happened? (I'm still here :p).Quote: pacomartinBut the expected number of trials will to get this streak of 4 wins will vary widely. But HA advantage is going to matter a lot if you play repeatedly. They didn't invent that term grindhouse for nothing. The HA just grinds away at you.
Which is why I don't understand the Chinese fascination with Baccarat. If you are going to grind away all day, why not play craps with full odds. The probability of doubling your money before going bankrupt is much higher than Baccarat.
Quote: edwardyou could try 2 double up 7 times in 250 trials, or why not 350 trials
The lower the number of trials the lower the probability of a run of a specific length.
the mean wait time for run7 is ~371 trials(the median is always lower)
and the std dev is almost the same ~365
added: formulas:
mean wait time ((1/p^n)-1)/(1-p) [One should be familiar with this one]
variance: Var(N) = 1−(p^(1+2r)−qpr(1+2r)/q^2p^2r
Sequences, Patterns and Coincidences page7
It is that possibility of a long wait time that will kill a marty especially when p <= 0.5
Quote: pacomartinI don't understand the Chinese fascination with Baccarat. If you are going to grind away all day, why not play craps with full odds. The probability of doubling your money before going bankrupt is much higher than Baccarat.
It could have something to do with the number 8 being so lucky in Chinese culture.
Neither do I.Quote: pacomartinI don't understand the Chinese fascination with Baccarat.
Then again, I don't understand ANYONE's fascination with slots, Big Six, Casino War, or any side bet. But there are plenty of people that play those games.
Chinese Bac players, or Asian Bac players actually, I am one, do not "grind away" in Baccarat.Quote: pacomartinWhich is why I don't understand the Chinese fascination with Baccarat. If you are going to grind away all day, why not play craps with full odds. The probability of doubling your money before going bankrupt is much higher than Baccarat.
We follow "roads" as a trigger to bet BIG!
We bet for streaks to continue. Positive betting progressions.
Banker streaks.
Most cuss out the dealer if the Player has more and or longer streaks than the Banker during a shoe.
You a white Bac player betting for a Player win streak to continue, you will get some evil stares and some non-English words fired at you by us Asians.
It is actually very entertaining to watch.
But do not tell my Mom about this.
Boo! wheels on the ground at JFK.Quote: s2dbakerYay!! Wheels on the ground at McCarran.
Quote: mustangsallyChinese Bac players, or Asian Bac players actually, I am one, do not "grind away" in Baccarat.
You a white Bac player betting for a Player win streak to continue, you will get some evil stares and some non-English words fired at you by us Asians.
Well, since you can do the calculations, given that Main Street Station has 20X odds on a minimum of $5 bet in craps, what is the probability that you will double $2000 before going bankrupt? Do it for pass and don't pass. Now do the same thing for baccarat, with a maximum bet of $100 (you can bet on banker and nobody will root for the player).
silly
silly
pass 20x odds: p(target) 0.4854382538Quote: pacomartinWell, since you can do the calculations, given that Main Street Station has 20X odds on a minimum of $5 bet in craps, what is the probability that you will double $2000 before going bankrupt?
Do it for pass and don't pass.
dpass 20x lay odds: p(target) 0.4876891693
below has calculation and simulation results
pass 20x odds ($5 with $100 odds - stake of $2000)
[1] "bankroll target: 800, unit gain:400"
> print(formatC(data, digits=10),quote=FALSE)
data
bank 400
p(target) 0.4854382538
p(ruin) 0.5145617462
avg trials 381.7063071
Simulation of Craps Pass Line Wagers
Odds Multiplier . . . . = 20
Session Bankroll . . . = 400.00
Win goal to quit session= 400.00
No. Sessions simulated = 1000000
Starting Random seed . = 54321
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Bankroll was busted . . = 51.495% of the time ( 514946)
Win goal was met . . . = 48.505% of the time ( 485054)
dpass 20x odds($5 with 20X Lay odds - stake of $2000)
[1] "bankroll target: 800, unit gain:400"
> print(formatC(data, digits=10),quote=FALSE)
data
stake in units 400
p(target) 0.4876891693
p(ruin) 0.5123108307
avg trials 376.6013622
Simulation of Craps Don't Pass Wagers
Odds Multiplier . . . . = 20
Session Bankroll . . . = 400.00
Win goal to quit session= 400.00
No. Sessions simulated = 1000000
Starting Random seed . = 54321
------------------------------------
All bets are a single unit
------------------------------------
Simulation Results per Session
------------------------------------
Bankroll was busted . . = 51.350% of the time ( 513502)
Win goal was met . . . = 48.650% of the time ( 486498)
$2000/$100=20 betting unitsQuote: pacomartinNow do the same thing for baccarat, with a maximum bet of $100 (you can bet on banker and nobody will root for the player).
Banker bet only flay betting: p(target) 0.3685009659
Player bet only flay betting: p(target) 0.36678822
Player from
https://sites.google.com/view/krapstuff/risk-of-ruin
section 2r.
(R code for Markov chain calculations coming soon)
yes, that close in Baccarat too!
data
Baccarat Banker bet only flat bet ($100 - stake of $2000)
[1] "bankroll target: 40, unit gain:20"
> print(formatC(data, digits=10),quote=FALSE)
data
stake in units 20
p(target) 0.3685009659
p(ruin) 0.6314990341
avg trials 451.8619766
simulation
36,986 out of 100,000 at least doubledgroup middle freq freq/100
--------------------------------------------------
-7.00 <= x < 7.00 0.00 5372 5.37%
7.00 <= x < 21.00 14.00 8291 8.29%
21.00 <= x < 35.00 28.00 5574 5.57%
35.00 <= x < 49.00 42.00 8691 8.69%
49.00 <= x < 63.00 56.00 8983 8.98%
63.00 <= x < 77.00 70.00 9721 9.72%
77.00 <= x < 91.00 84.00 10978 10.98%
91.00 <= x < 105.00 98.00 5404 5.40%
105.00 <= x < 119.00 112.00 0
3983.00 <= x < 3997.00 3990.00 0
3997.00 <= x < 4011.00 4004.00 6540 6.54%
4011.00 <= x < 4025.00 4018.00 4379 4.38%
4025.00 <= x < 4039.00 4032.00 6373 6.37%
4039.00 <= x < 4053.00 4046.00 6062 6.06%
4053.00 <= x < 4067.00 4060.00 5803 5.80%
4067.00 <= x < 4081.00 4074.00 5182 5.18%
4081.00 <= x < 4095.00 4088.00 2647 2.65%
> baccPlayer(2000,4000,100)#200 bet units
[1] "in money: stake:$2000,target:$4000, wanted gain of $2000, flat betting:$100"
[1] "in units: stake:20, target of 40, gain of 20, flat betting 1"
data
stake in units 20
p(goal) 0.36678822
p(ruin) 0.63321178
avg trials 431.426747
> gambler.ruin(20,20, 0.49317517, "Baccarat Player bet")
[1] "Baccarat Player bet. Stake:20, Target:40"
[1] "p(goal):0.36678822, p(ruin):0.63321178"
[1] "mean Trials:390.374, mean given Goal:390.374, mean given Ruin:390.374"
Ties omitted from mean calculations
almost forgot,
Got to add EZ Baccarat Banker results too
(very popular version at many casinos. in CA Morongo comes to mind)
20 to 40 units (double-up or go home)
p(target): 0.38659994 <<<<Yahoo!
p(ruin): 0.61340006
mean Trials: 445.49230
Hope this give some more information to those seeking it
results accurate as calculated (R code coming soon again for inspection)
so,
craps appears to have a better chance to doubleup than a higher avg bet at Baccarat
but can take longer (each game at craps is about 3.375 rolls in length)
remember at craps pass line $5 with $100 odds does not return a $100 avg bet
$5 * 1/3 + $105 * 2/3 = 5/3 + 210/3 = 215/3 = about $71.67
Sally
added: Banker bet flat betting $200 each round
$2000/$200 = 10 betting units
[1] "bankroll target: 20, unit gain:10"
> print(formatC(data, digits=10),quote=FALSE)
data
stake in units 10
p(target) 0.4159397898
p(ruin) 0.5840602102
avg trials 113.7492802
Quote: pacomartinIt doesn't so much suck as it doesn't matter. Casinos like people who have betting strategies because it keeps player playing despite losses, because they think the strategy will pay off in the end.
But at least you can gauge what to expect. If you want to start with a larger amount (SAY $50) and intend to play until you have a streak of 4 wins, now you know that is expected to take 30 trials if there was no house edge. If you add a small house edge like laying a 6 or and 8, the number of trials moves up to 31. But if you add a larger house edge, the expected number of trials is now 34.5 .
But the expected number of trials will to get this streak of 4 wins will vary widely. But HA advantage is going to matter a lot if you play repeatedly. They didn't invent that term grindhouse for nothing. The HA just grinds away at you.
Which is why I don't understand the Chinese fascination with Baccarat. If you are going to grind away all day, why not play craps with full odds. The probability of doubling your money before going bankrupt is much higher than Baccarat.
Maybe they like touching cards rather than "bones" (superstition re: death maybe)?
Quote: mustangsallyChinese Bac players, or Asian Bac players actually, I am one, do not "grind away" in Baccarat.
We follow "roads" as a trigger to bet BIG!
We bet for streaks to continue. Positive betting progressions.
Banker streaks.
Most cuss out the dealer if the Player has more and or longer streaks than the Banker during a shoe.
You a white Bac player betting for a Player win streak to continue, you will get some evil stares and some non-English words fired at you by us Asians.
It is actually very entertaining to watch.
But do not tell my Mom about this.
A couple of years ago, while playing blackjack in the High Limit pit at GNLV, the Baccarat table ran 18 bankers in a row. The player (non-Asian) rode the streak but did not increase his bet above the $100 table minimum
Quote: aceofspadesA couple of years ago, while playing blackjack in the High Limit pit at GNLV, the Baccarat table ran 18 bankers in a row. The player (non-Asian) rode the streak but did not increase his bet above the $100 table minimum
I hope that guy walked away $1700 richer... haha...
Quote: TigerWuI hope that guy walked away $1700 richer... haha...
He kept playing after the streak so, I assume he added at least $1700 at that point (well, minus commission)
