Quitting while ahead
1) You leave if you win the first bet
2) You leave if you are at anytime 1 unit ahead (after commissions)
3) You leave after 100 hands/ spins
Could someone explain how to calculate the probabilities of possible outcomes?
If this example is impracticle feel free to change the hands/ spin limit.
I have previously calculated outcomes for a small limit of hands/spins and am interested to see the differences.
However: the only "even chance" games you will ever find are Blackjack with counting, or Craps with dice setting (or some sort of temporary promotion). If you can do that, then why bother making the game even? Play it with the edge in your favor. Bet higher in favorable decks; work on your dice shooting and get that SRR down.
All other games pay short of true odds. Play every day, and that house edge will catch up with you. Some betting strategies can chance how wins and losses cluster. Some might even cut that house edge. None will cancel it, and if you track your wins and losses, the sessions you lose will begin to drag down the sessions you win. It's called a random walk with a negative bias.
Knew somebody who tried number 3, didn't make a blind bit of difference to his daily outcome.Quote: Walkinshaw30tSay you go to the casino once everyday and play an even chance game by the following rules:
1) You leave if you win the first bet
2) You leave if you are at anytime 1 unit ahead (after commissions)
3) You leave after 100 hands/ spins
Could someone explain how to calculate the probabilities of possible outcomes?
If this example is impracticle feel free to change the hands/ spin limit.
I have previously calculated outcomes for a small limit of hands/spins and am interested to see the differences.
1 month
Quote: zenith27i had thought of that idea..i would just wait for a 5-streak player hands and bet on banker in baccarat. I would invest 10k as my bankroll and win limit is 1k with loss limit 5k..after win, i could go home and comeback tommorow. thats 30k a month.means tripple your investment in
1 month
Simulate that over 10 million hands and let us know what you come up with.
Assume a country where people want to have a boy. Every couple begets babies until one of the following rules:Quote: Walkinshaw30tSay you go to the casino once everyday and play an even chance game by the following rules:
1) You leave if you win the first bet
2) You leave if you are at anytime 1 unit ahead (after commissions)
3) You leave after 100 hands/ spins
Could someone explain how to calculate the probabilities of possible outcomes?
If this example is impracticle feel free to change the hands/ spin limit.
1) Stop procreating once you have a boy.
2) Stop procreating after [insert number ] girls.
Result: the proportion of girls and boys in the population will remain exactly the same (50/50 if we assume equiprob).
So your hypothetical player will end up with as many losses as wins.
silly
Learning can be fun
Sally
1) example: you go to a movie with your date for a couple of hrs. (Cost $40) Leave with good experience. If you have $100 in your wallet, than basically that's what you intended to spend for the night and not much more. So your date doesn't want the extra bag of licorice, or smarties, or the extra large, extra butter popcorn... that makes you ahead (good feelings) even though you spent the $40, you still go home with $60 of what you intended to spend.
2) you go to the casino with "so much money" Subtract the "house edge" and leave the casino with "what you can afford to lose" equal to your feelings for cost of entertainment. Same deal as the movie night. You went there with what you expect to spend. You can never call it a bad night at the casino if you lose what you came to spend. Even though the house edge is present, there are many times you will eventually win (it's inevitable) and does not mean you have to "leave when your up", it means leave when you are satisfied with your entertainment for the day.
Just to clarify a few things:
I was suggesting unlimited bankroll (though can say 200 units if a number is required) with no stop loss
No time limit- only stopping after 100 bets resolved OR
Stopping immediately after winning 1 unit more than starting bankroll
I can imagine these parameters may be hard to simulate
I guess the main points I would like to know are:
Average loss if win goal isnt reached within 100 hands
Probability of loss
Probability of win
You are assuming flat betting of 1 unit per round right?
Yes that is correct flat betting.
Cheers
Quote: Walkinshaw30tOk great, for baccarat.
Yes that is correct flat betting.
Cheers
Player bets and six decks ok?
Quote: endermikePlayer bets and six decks ok?
Yep thats fine
(results probably good to at least 3 sig figs)
Prob of winning (quitting with 101): .9028
Prob of pushing (quitting with 100 after 100 hands): .0009
Prob of losing (quitting with less than 100 after 100 hands): .0963
Avg loss, given you quit with less than 100 after 100 hands: 11.64
Avg expected return on this strategy (starting with 100 units): 99.78
Quote: endermikeBased on 1,000,000 independent attempts (about 80 seconds run time):
(results probably good to at least 3 sig figs)
Prob of winning (quitting with 101): .9028
Prob of pushing (quitting with 100 after 100 hands): .0009
Prob of losing (quitting with less than 100 after 100 hands): .0963
Avg loss, given you quit with less than 100 after 100 hands: 11.64
Avg expected return on this strategy (starting with 100 units): 99.78
Ok great thanks, pretty impressive results!
Would it be too tricky to find results for banker bets?
Or for higher number hand limit?
Flat betting does not give one the best chance (highest probability) of hitting a win goal according to the math experts starting with the paper by Dubins, Lester E.; Savage, Leonard J. (1965). "How to gamble if you must"Quote: Walkinshaw30tOk great, for baccarat.
Yes that is correct flat betting.
when playing against a house edge (-ev) one must bet Bold
that is to bet exactly what is needed to hit your win goal or everything trying
by flat betting one can lose the first bet and never recover to show a 1 unit profit, no matter how large your bankroll and how many lifetime bets you make.
That is the function of the house edge. The random walk with a negative drift concept.
This (bold play) can be exactly and easily calculated in Excel or using a program
and with an even money bet, if losing the first 1 unit bet, your next bet should bet 2, lose that your next bet would be 4 and so on
sounds like a Marty. and it is. Bold Play trying to win just 1 unit
with your max 100 bets
Player at Bac
I show flat betting has a 90.728631% of success by the 100th bet (8 deck) this is verified by a transition matrix
Using just a 9step Marty (max bet of 2560 at a 10min table and a 2001unit bankroll)
we can increase that hit rate to 99.779341%
sounds good huh
yes, that high, but a large hit if you do not win one time in the 9step marty.
and that probability is just for one attempt.
to win 313 times in a row without a loss is a coin flip 50/50 (99.779341%^313)
a loss would be 511 units.
"How to gamble if you must"
there are a few other papers about this concept of Bold Play
and my calculations and simulations show these math guys to be correct.
of course the average bet will now be higher and that seems to point to a higher expected loss
when played many many times, but your win rate is way higher.
more for the interested in those papers
Have fun!
Sally
Quote:
more for the interested in those papers
Have fun!
Sally
Thanks
That is quite interesting but a little un practical for my intended purpose.
I will be sure to read up on it never the less!
Cheers
Quote: Walkinshaw30tOk great thanks, pretty impressive results!
Would it be too tricky to find results for banker bets?
No, once the code is written running it is as simple as me turning Matlab on and using different inputs. Should gambler quit when they are a full unit ahead or is .95 of a unit sufficient?
[Side note: MSally is correct about flat betting not being the best way to ensure quitting ahead. I really like the topic of random walks (which is what the flat betting problem is in math terms) and hence am more than happy to mess around with things like this]
There are actually closed form expressions for these things. However when we are talking about any more than very simple ones we need to resort to computers to solve the closed forms to any accuracy, so I normally just simulate them since then I don't have to worry about recasting the problem and then solving it analytically.
Yes, simple even money type flat betting can be solved using the Gambler's Ruin formula (GR)Quote: endermikeThere are actually closed form expressions for these things. However when we are talking about any more than very simple ones...
It has been around since the 1600s
Problem with that formula is is does not at all factor in time or the number of trials.
My example with a 101 unit bankroll trying to win just 1unit in 100 trials with Player in Bac (Risk of Ruin at 0)
the GR shows a probability of success at 97.1295885% (I think this is more of a limit)
and using a different formula the average number of trials = 141.24 (not a normal distribution)
a Markov chain or simple recursive calculation (using a spreadsheet) shows these probabilities with time as a factor (N=# of trials)
N=50: 87.525532%
N=100: 90.728631%
N=1000: 95.936583% (ruin now possible)
How about a 201unit bankroll and max 200 trials? (Risk of Ruin at 0) Player in Bac and same 1 unit win goal
GR shows a probability of success at 97.2959404%
the average number of trials = 326.91
probabilities with time as a factor (N=# of trials)
N=50: 87.525532%
N=100: 90.728631%
N=200: 92.991191
N=1000: 95.936583% (ruin now possible)
N=3000: 96.832522% (ruin now possible)
one could end up playing a very long time and still not hit that elusive 1 unit win
but have fun trying!
Sally
2) Based on 10,000,000 independent attempts (about 1200 seconds run time)
(results probably good to 4 sig figs)
Prob of winning (quitting with 101): .8372
Prob of pushing (quitting with between 100 and 101 after 100 hands): .0015
Prob of losing (quitting with less than 100 after 100 hands): .1613
Avg loss, given you quit with less than 100 after 100 hands: 8.05
Avg expected return on this strategy (starting with 100 units): 99.70
1 full unit?Quote: endermike1) Using flat betting on the banker and quitting when 1 full unit (or more) up or 100 hands have been played
2) Based on 10,000,000 independent attempts (about 1200 seconds run time)
Prob of winning (quitting with 101): .8372
a win on a $20 bet nets $19 after the $1 comm
I ran a 101 unit bankroll (2020) sim and stopped when the bankroll hit 2039 or 100 trials
that seems more than fair to quit after the first win.
here is the value calculated using a transition matrix for success = 88.483079%
from a quick 1 million sim I get 884,658 attempts that were successful = 88.4658%
grouped data
items: 1000000
minimum value: 1073.00
first quartile: 2039.00
median: 2039.00
third quartile: 2051.00
maximum value: 2057.00
mean value: 2015.44
midrange: 1565.00
range: 984.00
interquartile range: 12.00
mean abs deviation: 51.44
sample variance (n): 8496.01
sample variance (n-1): 8496.02
sample std dev (n): 92.17
sample std dev (n-1): 92.17
"how do you calculate this?"
either simulate and/or use a spreadsheet or a program to raise a transition matrix up to any power (number of trials)
I think the OP may too be bummed out that the probability is not closer to 99.95% or even higher.
just remember that the longer one plays against a house edge game, the less chance that player has of coming out even or ahead
in other words
the chances increase with every trial that the player will not be even or ahead no matter how many trials are completed each day
Sally
Quote: mustangsally1 full unit?
a win on a $20 bet nets $19 after the $1 comm
Yup, it means a win on the first hand isn't enough. I just had the sim pay .95 of a unit for a win and lose 1 full unit for a loss.
OK,Quote: endermikeYup, it means a win on the first hand isn't enough. I just had the sim pay .95 of a unit for a win and lose 1 full unit for a loss.
OP has now two sets of sim data for Banker bet
and I think most Bac players would disagree that
the Player bet has the higher probability of winning just 1 unit over 100 hands played than the Banker bet
even with paying the comm
I did at first
Sally
added:
my matrix shows with a 2020 bankroll betting $20 and trying to hit a target of 2040
success = 84.471064%
latest:
how about something I think would not work well at hitting a 1 unit win
Single 0 roulette
betting 2 columns (or sections) so bet 2 units to win 1
not much variance here, my first guess was yuck, but a nice win probability
It does even better than Craps Don't Pass or Pass or Player bet in Bac
I had to check it twice and sim it too.
interesting
91.549408%
100 spins max, bankroll of 201 units and target goal of 202 units
Quote: zenith27i had thought of that idea..i would just wait for a 5-streak player hands and bet on banker in baccarat. I would invest 10k as my bankroll and win limit is 1k with loss limit 5k..after win, i could go home and comeback tommorow. thats 30k a month.means tripple your investment in
1 month
varmenti?
Quote: mustangsally
Single 0 roulette
betting 2 columns (or sections) so bet 2 units to win 1
not much variance here, my first guess was yuck, but a nice win probability
It does even better than Craps Don't Pass or Pass or Player bet in Bac
I had to check it twice and sim it too.
interesting
91.549408%
100 spins max, bankroll of 201 units and target goal of 202 units
That is interesting- what was the average loss?
Quote: endermikeYup, it means a win on the first hand isn't enough. I just had the sim pay .95 of a unit for a win and lose 1 full unit for a loss.
Yes that is true, I was just thinking that if you were 1 banker win infront late in the spins the commission would have eaten up any profit
first something to compare againstQuote: Walkinshaw30tThat is interesting- what was the average loss?
recall the Player bet in Bac 101 unit bankroll and 1 unit win goal and 100 max bets
my calculated values - faster and the most accurate using a transition matrix
(verified with a simulation - slower and the least accurate)
Prob of winning (quitting with 102): 0.907286313 <<< this value is much higher when removing the time factor as I pointed out in an earlier post
Prob of pushing (quitting with 101 after 100 hands): 0.001546102 (1 in 647)
Prob of losing (quitting with less than 101 after 100 hands): 0.091167586
Avg loss, given you quit with less than 101 after 100 hands: -12.37590892 units
expected value on this strategy: -0.220995423 units
Now the Single 0 Roulette making 2, 2to1 type bets (columns or sections with prob of winning at 24/37)
Bankroll 201 and target goal at 202
Prob of winning (quitting with 202): 0.91549408
Prob of pushing (quitting with 201 after 100 hands): 0.00 <<< either lose 2 units or win 1 unit
Prob of losing (quitting with less than 201 after 100 hands): 0.08450592
Avg loss, given you quit with less than 201 after 100 hands: -13.97135554 units
expected value on this strategy: -0.18066225 units
use (y)our wings and fly!
Sally
now 3 units are required to be wagered and one can lose 3 or 1 or win 1 or 3 and actually overshoot the 1 unit win goal (301 bankroll)
that should lower the probability of at least a 1 unit win and it does to just 89.183220%
and raises the avg loss to -18.56314162 units
Sally
Quote: mustangsallywith those type of bets (combining even money bets for 18/37)
now 3 units are required to be wagered and one can lose 3 or 1 or win 1 or 3 and actually overshoot the 1 unit win goal (301 bankroll)
that should lower the probability of at least a 1 unit win and it does to just 89.183220%
and raises the avg loss to -18.56314162 units
Sally
Sorry I should have explained myself, I mean betting 1/3rd of a unit on each.
Quote: mustangsally
This (bold play) can be exactly and easily calculated in Excel or using a program
and with an even money bet, if losing the first 1 unit bet, your next bet should bet 2, lose that your next bet would be 4 and so on
sounds like a Marty. and it is. Bold Play trying to win just 1 unit
Sally
This.
Pick a game, any game that has more or less 50/50 odds - say betting black/red at the roulette wheel.
Start with $100
Bet $10. Lose. $90 left
Bet $20. Lose. $70 left
Bet $40. Win! BOOM! $110.
Walk away.
In theory, if you had say $50K and were willing to lay $1K as the initial bet you could walk away with $1K/day and call it good.
Until that day when you lost 7 times in a row...
Quote: TerribleTomThis.
Pick a game, any game that has more or less 50/50 odds - say betting black/red at the roulette wheel.
Start with $100
Bet $10. Lose. $90 left
Bet $20. Lose. $70 left
Bet $40. Win! BOOM! $110.
Walk away.
In theory, if you had say $50K and were willing to lay $1K as the initial bet you could walk away with $1K/day and call it good.
Until that day when you lost 7 times in a row...
You wouldn't even have to lose 7 in a row.
Loss 1: 1k/49k left
Loss 2: 2k/47k left
Loss 3: 4k/43k left
Loss 4: 8k/35k left
Loss 5: 16k/19k left
Now you don't have enough left to put up the next bet, but if you started with $63k you'd be able to lose 6.
Quote: BuzzardIn that case are 62 other members willing to put up1K as my partners?
Maybe, but $1K/62/day doesn't exactly pencil out to quitting your day job...
Quote: TerribleTomMaybe, but $1K/62/day doesn't exactly pencil out to quitting your day job...
Really? That's your biggest concern with this plan?
