DJGenius
DJGenius
Joined: Mar 5, 2010
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November 20th, 2022 at 7:40:58 PM permalink
Apologies I'm sure this issue has been addressed in the past. Searching "betting systems" with "advantage" brings up lots of stuff very different from what I'm asking here.

I'm asking about a hypothetical situation where the player has a small mathematical advantage, for example somewhere between 0.50% and 0.75%

Would a betting system like the d'Alembert (increase 1 unit after a loss, decrease 1 unit after a win) increase profits, since you know in the long run you will actually win more than you lose?

Or would it be basically exactly the same as if you had bet the average bet size from your d'Alembert progression and just bet flat the whole time?

Does it make any difference at all? Seems like the d'Alembert would be more volatile.

Any help appreciated!
"The Quest stands upon the edge of a knife. Stray but a little, and it will fail, to the ruin of all." - Elf Queen Galadriel, teaching Frodo about the importance of blackjack basic strategy.
SOOPOO
SOOPOO 
Joined: Aug 8, 2010
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DJGeniusDietercamapl
November 20th, 2022 at 7:55:46 PM permalink
Quote: DJGenius

Apologies I'm sure this issue has been addressed in the past. Searching "betting systems" with "advantage" brings up lots of stuff very different from what I'm asking here.

I'm asking about a hypothetical situation where the player has a small mathematical advantage, for example somewhere between 0.50% and 0.75%

Would a betting system like the d'Alembert (increase 1 unit after a loss, decrease 1 unit after a win) increase profits, since you know in the long run you will actually win more than you lose?

Or would it be basically exactly the same as if you had bet the average bet size from your d'Alembert progression and just bet flat the whole time?

Does it make any difference at all? Seems like the d'Alembert would be more volatile.

Any help appreciated!
link to original post



Without answering your question directly I’ll try and help. If you find a situation where you consistently have a small advantage, like card counting in BJ, hole carding in a few games, certain promo opportunities, etc…. You should learn the Kelly Criterion. It will help you figure out how much to bet, way better than any system like Dalembert.

My answer assumes you actually have a bankroll that you can define.
DJGenius
DJGenius
Joined: Mar 5, 2010
  • Threads: 8
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November 20th, 2022 at 8:15:03 PM permalink
Quote: SOOPOO

Without answering your question directly I’ll try and help. If you find a situation where you consistently have a small advantage, like card counting in BJ, hole carding in a few games, certain promo opportunities, etc…. You should learn the Kelly Criterion. It will help you figure out how much to bet, way better than any system like Dalembert.

My answer assumes you actually have a bankroll that you can define.
link to original post


Thanks!
"The Quest stands upon the edge of a knife. Stray but a little, and it will fail, to the ruin of all." - Elf Queen Galadriel, teaching Frodo about the importance of blackjack basic strategy.
100xOdds
100xOdds
Joined: Feb 5, 2012
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November 21st, 2022 at 11:14:11 AM permalink
Quote: SOOPOO

Quote: DJGenius

Apologies I'm sure this issue has been addressed in the past. Searching "betting systems" with "advantage" brings up lots of stuff very different from what I'm asking here.

I'm asking about a hypothetical situation where the player has a small mathematical advantage, for example somewhere between 0.50% and 0.75%

Would a betting system like the d'Alembert (increase 1 unit after a loss, decrease 1 unit after a win) increase profits, since you know in the long run you will actually win more than you lose?

Or would it be basically exactly the same as if you had bet the average bet size from your d'Alembert progression and just bet flat the whole time?

Does it make any difference at all? Seems like the d'Alembert would be more volatile.

Any help appreciated!
link to original post



Without answering your question directly I’ll try and help. If you find a situation where you consistently have a small advantage, like card counting in BJ, hole carding in a few games, certain promo opportunities, etc…. You should learn the Kelly Criterion. It will help you figure out how much to bet, way better than any system like Dalembert.

My answer assumes you actually have a bankroll that you can define.
link to original post


does Kelly Criterion apply to mhb slots?

i usually max bet even $200 progressives..
most of the time I lose $. occasionally, i have a hand pay.
since i dont keep track of individual plays, i have no idea if max betting is profitable.
(overall, my bank acct grows.)

would kelly help me decide on the amount to bet to be more profitable?
Craps is paradise (Pair of dice). Lets hear it for the SpeedCount Mathletes :)
DJGenius
DJGenius
Joined: Mar 5, 2010
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November 21st, 2022 at 11:27:22 AM permalink
Just in case anyone is interested I wrote a quick program to test this for myself.

The program flips a rigged "coin" which will come up heads 101 times and tails 99 times out of 200. So if my math is right, a player always betting on heads has a 1% advantage.

I set the program to flat bet 1 unit and d'Alembert bet on the same results and ran it for 100 million tosses.

The d'Alembert betting started at 1 unit and was set to increase by 1 unit after a loss and decrease by 1 unit after a win (standard stuff).

The bankroll was unlimited.

The results were as follows:

FLAT BETTING:
After 100,000,000 tosses the final balance was 1,021,998. The total amount wagered was 100,000,000 units (flat betting) so the actual player advantage was 1.021998%. The lowest balance reached by the player at any time was -170.

D'ALEMBERT BETTING:
After 100,000,000 tosses the final balance was 50,504,783. The total amount wagered was 5,020,198,669 units so the actual player advantage was 1.00603%. The lowest balance reached by the player at any time was -10879.

The player advantage in both cases approaches the theoretical advantage of 1%. I don't think the discrepency is significant. I noticed bigger discrepencies when trying it out for a smaller number of trials. I suppose I could run it for a billion trials, but there doesn't seem to be much point.

So even when you have a statistical advantage, over the long run d'Alembert betting seems pretty useless.

VOLATILITY:
The d'Alembert player had a much lower "lowest balance" but we need to take into account the difference in bet sizes. The average bet for the d'Alembert player was 50.2 units (which is why their final balance of around 50.5 million units is comparable to the 1 million units of the flat bettor).

So if we imagine that the flat bettor was also betting 50.2 units then we have some more useful data to compare.

FLAT (ADJUSTED) vs
D'ALEMBERT

Final balance:
51,304,299.6
50,504,783

Total amount bet:
5,020,000,000
5,020,198,669

Lowest balance:
-8534
-10879

So it looks like the d'Alembert was a little bit more risky, and since it doesn't produce better results, why bother?

Not sure why I decided to mess with this today, but I hope the results are of some use to someone somewhere!
"The Quest stands upon the edge of a knife. Stray but a little, and it will fail, to the ruin of all." - Elf Queen Galadriel, teaching Frodo about the importance of blackjack basic strategy.
SOOPOO
SOOPOO 
Joined: Aug 8, 2010
  • Threads: 118
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100xOdds
November 21st, 2022 at 12:55:30 PM permalink
Quote: 100xOdds

Quote: SOOPOO

Quote: DJGenius

Apologies I'm sure this issue has been addressed in the past. Searching "betting systems" with "advantage" brings up lots of stuff very different from what I'm asking here.

I'm asking about a hypothetical situation where the player has a small mathematical advantage, for example somewhere between 0.50% and 0.75%

Would a betting system like the d'Alembert (increase 1 unit after a loss, decrease 1 unit after a win) increase profits, since you know in the long run you will actually win more than you lose?

Or would it be basically exactly the same as if you had bet the average bet size from your d'Alembert progression and just bet flat the whole time?

Does it make any difference at all? Seems like the d'Alembert would be more volatile.

Any help appreciated!
link to original post



Without answering your question directly I’ll try and help. If you find a situation where you consistently have a small advantage, like card counting in BJ, hole carding in a few games, certain promo opportunities, etc…. You should learn the Kelly Criterion. It will help you figure out how much to bet, way better than any system like Dalembert.

My answer assumes you actually have a bankroll that you can define.
link to original post


does Kelly Criterion apply to mhb slots?

i usually max bet even $200 progressives..
most of the time I lose $. occasionally, i have a hand pay.
since i dont keep track of individual plays, i have no idea if max betting is profitable.
(overall, my bank acct grows.)

would kelly help me decide on the amount to bet to be more profitable?
link to original post



I’m not the expert…. But I think Kelly will work if you know your edge, your bankroll, and usually most difficult, the variance. Or standard deviation of? Anyway, if it’s a high variance game, like the lottery, you will need a ginormous bankroll to take advantage of a small edge. In your example, the slightly off coin, Kelly would work very well. Probably easier for to just read about it on WOO than for me to try and explain it.
Mental
Mental
Joined: Dec 10, 2018
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DJGenius
November 21st, 2022 at 3:39:57 PM permalink
Quote: DJGenius

Apologies I'm sure this issue has been addressed in the past. Searching "betting systems" with "advantage" brings up lots of stuff very different from what I'm asking here.

I'm asking about a hypothetical situation where the player has a small mathematical advantage, for example somewhere between 0.50% and 0.75%

Would a betting system like the d'Alembert (increase 1 unit after a loss, decrease 1 unit after a win) increase profits, since you know in the long run you will actually win more than you lose?

Or would it be basically exactly the same as if you had bet the average bet size from your d'Alembert progression and just bet flat the whole time?

Does it make any difference at all? Seems like the d'Alembert would be more volatile.

Any help appreciated!
link to original post


I am going to use a simpler system to make a few points. I assume a truncated Martingale system: you bet one unit and double to two units after a loss and then go back to one unit win or lose.

The one third of your bets will be 2 units and the rest will be one unit (on average). You will have a higher variance and a higher profit per bet compared to flat betting one unit. If you instead just bet two units every third time, you will have the same expected profit, but your variance will be slightly lower. This is because you will be betting one unit exactly 2/3rds of the time. In the Martingale case, you will be betting one unit 2/3rds of the time on average. If you run good on your one-unit bets, you will be betting less. If you run bad, you will be making more max bets. This is an extra source of variance.

If you truncate the Martingale after a bigger bet, let us say 8 units, the same principle applies. You will be betting 8 units only after a sequence incurs 3 losses to start off. If you figure out what fraction of bets end up being 8 units, you could just bet 8 units exactly that many times. You would have the same expected profit, but lower variance. The total variance and EV does not depend on what order you roll the 1/2/4/8 unit bets -- just on the fraction of bets that are at each multiple.
AxelWolf
AxelWolf
Joined: Oct 10, 2012
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DJGenius
November 21st, 2022 at 6:43:16 PM permalink
Quote: DJGenius

Just in case anyone is interested I wrote a quick program to test this for myself.

The program flips a rigged "coin" which will come up heads 101 times and tails 99 times out of 200. So if my math is right, a player always betting on heads has a 1% advantage.

I set the program to flat bet 1 unit and d'Alembert bet on the same results and ran it for 100 million tosses.

The d'Alembert betting started at 1 unit and was set to increase by 1 unit after a loss and decrease by 1 unit after a win (standard stuff).

The bankroll was unlimited.

The results were as follows:

FLAT BETTING:
After 100,000,000 tosses the final balance was 1,021,998. The total amount wagered was 100,000,000 units (flat betting) so the actual player advantage was 1.021998%. The lowest balance reached by the player at any time was -170.

D'ALEMBERT BETTING:
After 100,000,000 tosses the final balance was 50,504,783. The total amount wagered was 5,020,198,669 units so the actual player advantage was 1.00603%. The lowest balance reached by the player at any time was -10879.

The player advantage in both cases approaches the theoretical advantage of 1%. I don't think the discrepency is significant. I noticed bigger discrepencies when trying it out for a smaller number of trials. I suppose I could run it for a billion trials, but there doesn't seem to be much point.

So even when you have a statistical advantage, over the long run d'Alembert betting seems pretty useless.

VOLATILITY:
The d'Alembert player had a much lower "lowest balance" but we need to take into account the difference in bet sizes. The average bet for the d'Alembert player was 50.2 units (which is why their final balance of around 50.5 million units is comparable to the 1 million units of the flat bettor).

So if we imagine that the flat bettor was also betting 50.2 units then we have some more useful data to compare.

FLAT (ADJUSTED) vs
D'ALEMBERT

Final balance:
51,304,299.6
50,504,783

Total amount bet:
5,020,000,000
5,020,198,669

Lowest balance:
-8534
-10879

So it looks like the d'Alembert was a little bit more risky, and since it doesn't produce better results, why bother?

Not sure why I decided to mess with this today, but I hope the results are of some use to someone somewhere!
link to original post

This is good stuff. It shows that if you have an advantage, you have an advantage, it doesn't matter if you have a system or not. Now run the same simulation with a -1% disadvantage.
♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪
Mental
Mental
Joined: Dec 10, 2018
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DJGenius
November 21st, 2022 at 7:29:30 PM permalink
Quote: DJGenius

Apologies I'm sure this issue has been addressed in the past. Searching "betting systems" with "advantage" brings up lots of stuff very different from what I'm asking here.

I'm asking about a hypothetical situation where the player has a small mathematical advantage, for example somewhere between 0.50% and 0.75%

Would a betting system like the d'Alembert (increase 1 unit after a loss, decrease 1 unit after a win) increase profits, since you know in the long run you will actually win more than you lose?

Or would it be basically exactly the same as if you had bet the average bet size from your d'Alembert progression and just bet flat the whole time?

Does it make any difference at all? Seems like the d'Alembert would be more volatile.

Any help appreciated!
link to original post

The important point is that EV adds up proportionally to the bet size and variance adds as the square of the bet size. So, you intuition is right. For a given sum of total wagers over a given number of bets, you always minimize variance by flat betting. If betting one unit gets you one unit of variance for a certain wager, and you bet 1, 2, and 3 units, then you will incur 1*1+2*2+3*3 = 14 units of variance. Flat betting 2 units 3 times gets you 3*(2*2) = 12 units of variance. The EV is the same for both scenarios.
DJGenius
DJGenius
Joined: Mar 5, 2010
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November 22nd, 2022 at 9:33:44 AM permalink
Quote: AxelWolf

Quote: DJGenius

Just in case anyone is interested I wrote a quick program to test this for myself.

The program flips a rigged "coin" which will come up heads 101 times and tails 99 times out of 200. So if my math is right, a player always betting on heads has a 1% advantage.

I set the program to flat bet 1 unit and d'Alembert bet on the same results and ran it for 100 million tosses.

The d'Alembert betting started at 1 unit and was set to increase by 1 unit after a loss and decrease by 1 unit after a win (standard stuff).

The bankroll was unlimited.

The results were as follows:

FLAT BETTING:
After 100,000,000 tosses the final balance was 1,021,998. The total amount wagered was 100,000,000 units (flat betting) so the actual player advantage was 1.021998%. The lowest balance reached by the player at any time was -170.

D'ALEMBERT BETTING:
After 100,000,000 tosses the final balance was 50,504,783. The total amount wagered was 5,020,198,669 units so the actual player advantage was 1.00603%. The lowest balance reached by the player at any time was -10879.

The player advantage in both cases approaches the theoretical advantage of 1%. I don't think the discrepency is significant. I noticed bigger discrepencies when trying it out for a smaller number of trials. I suppose I could run it for a billion trials, but there doesn't seem to be much point.

So even when you have a statistical advantage, over the long run d'Alembert betting seems pretty useless.

VOLATILITY:
The d'Alembert player had a much lower "lowest balance" but we need to take into account the difference in bet sizes. The average bet for the d'Alembert player was 50.2 units (which is why their final balance of around 50.5 million units is comparable to the 1 million units of the flat bettor).

So if we imagine that the flat bettor was also betting 50.2 units then we have some more useful data to compare.

FLAT (ADJUSTED) vs
D'ALEMBERT

Final balance:
51,304,299.6
50,504,783

Total amount bet:
5,020,000,000
5,020,198,669

Lowest balance:
-8534
-10879

So it looks like the d'Alembert was a little bit more risky, and since it doesn't produce better results, why bother?

Not sure why I decided to mess with this today, but I hope the results are of some use to someone somewhere!
link to original post

This is good stuff. It shows that if you have an advantage, you have an advantage, it doesn't matter if you have a system or not. Now run the same simulation with a -1% disadvantage.
link to original post



Thanks for your comment. Running the program with a 1% disadvantage (house edge) results in the same. Both systems approach the expected result of -1%.

However it's worth noting that the poor d'Alembert system is forced to increase again and again (since it always increases with a negative result, and things will be trending negative here). The final result was a loss of over 501 billion dollars! So the average bet was somewhere around 500,000 units higher than flat betting. In other words it was a train wreck!
Last edited by: DJGenius on Nov 22, 2022
"The Quest stands upon the edge of a knife. Stray but a little, and it will fail, to the ruin of all." - Elf Queen Galadriel, teaching Frodo about the importance of blackjack basic strategy.

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