Walkinshaw30t
Walkinshaw30t
Joined: Apr 11, 2013
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February 19th, 2014 at 6:20:11 AM permalink
Ok great, for baccarat.
Yes that is correct flat betting.
Cheers
Time will tell
endermike
endermike
Joined: Dec 10, 2013
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February 19th, 2014 at 6:22:57 AM permalink
Quote: Walkinshaw30t

Ok great, for baccarat.
Yes that is correct flat betting.
Cheers



Player bets and six decks ok?
Walkinshaw30t
Walkinshaw30t
Joined: Apr 11, 2013
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February 19th, 2014 at 6:25:36 AM permalink
Quote: endermike

Player bets and six decks ok?




Yep thats fine
Time will tell
endermike
endermike
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February 19th, 2014 at 6:37:50 AM permalink
Based 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
Walkinshaw30t
Walkinshaw30t
Joined: Apr 11, 2013
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February 19th, 2014 at 6:49:43 AM permalink
Quote: endermike

Based 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?
Time will tell
mustangsally
mustangsally
Joined: Mar 29, 2011
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February 19th, 2014 at 8:01:03 AM permalink
Quote: Walkinshaw30t

Ok great, for baccarat.
Yes that is correct flat betting.

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"

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
I Heart Vi Hart
Walkinshaw30t
Walkinshaw30t
Joined: Apr 11, 2013
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February 19th, 2014 at 8:51:41 AM permalink
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
Time will tell
endermike
endermike
Joined: Dec 10, 2013
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February 19th, 2014 at 9:06:17 AM permalink
Quote: Walkinshaw30t

Ok 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.
mustangsally
mustangsally
Joined: Mar 29, 2011
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February 19th, 2014 at 10:15:29 AM permalink
Quote: endermike

There are actually closed form expressions for these things. However when we are talking about any more than very simple ones...

Yes, simple even money type flat betting can be solved using the Gambler's Ruin formula (GR)
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
I Heart Vi Hart
endermike
endermike
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February 19th, 2014 at 12:49:18 PM permalink
1) 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)

(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


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