Are betting systems a wise choice if there is no or even negative House Edge?
Quote: GandlerNow I know everyone's argument against betting systems is that it cannot alter the HE. However lets go with martingale which is probably the simplest. Lets say you are playing a game with a negative HE (meaning the player has the edge, lets say .25 player edge). Since the player has an edge would an aggressive betting strategy like martingale be wise on a game like blackjack to quickly make up for loses as oppose to waiting for it to naturally balance?
No. Use the Kelly Criterion instead. That is the optimal way to grow your bankroll.
The more you bet the more you risk, relative to your bank roll.
The optimal betting strategy (call it "lifetime progression" if you like) is to bet a specific fraction of your bankroll, where the fraction is determined by the players edge.
Quote: GandlerNow I know everyone's argument against betting systems is that it cannot alter the HE. However lets go with martingale which is probably the simplest. Lets say you are playing a game with a negative HE (meaning the player has the edge, lets say .25 player edge). Since the player has an edge would an aggressive betting strategy like martingale be wise on a game like blackjack to quickly make up for loses as oppose to waiting for it to naturally balance?
What 'natural balance'? After a decision, the next result doesn't care about the previous result.
The Kelly or just flat betting is a far better way to maximize growth than the Martingale... in the Marty, you'll be increasing bets with only a thin edge, and increasing the risk of ruin. You -really- don't want to bust out when you have an advantage.
Quote: GandlerNow I know everyone's argument against betting systems is that it cannot alter the HE. However lets go with martingale which is probably the simplest. Lets say you are playing a game with a negative HE (meaning the player has the edge, lets say .25 player edge). Since the player has an edge would an aggressive betting strategy like martingale be wise on a game like blackjack to quickly make up for loses as oppose to waiting for it to naturally balance?
Bored with the board today, huh, Gandler? lol...on your head be it.
Quote: thecesspitWhat 'natural balance'? After a decision, the next result doesn't care about the previous result.
The Kelly or just flat betting is a far better way to maximize growth than the Martingale... in the Marty, you'll be increasing bets with only a thin edge, and increasing the risk of ruin. You -really- don't want to bust out when you have an advantage.
Sorry that was a bad word choice. What I mean to say is statistical expected return. Like if a coin was 1% heavier on one side you would expect heads to appear 51% of the time eventually after enough flips. So my thought was using a martingale type strategy on losses when you have an edge in BJ would make up losses quicker and profit faster?
Quote: GandlerSorry that was a bad word choice. What I mean to say is statistical expected return. Like if a coin was 1% heavier on one side you would expect heads to appear 51% of the time eventually after enough flips. So my thought was using a martingale type strategy on losses when you have an edge in BJ would make up losses quicker and profit faster?
I think that you misunderstand how reversion to mean works. The coin has no memory.
The main point here is that your bankroll is not infinite. Going broke is a disaster, because then you can't take advantage of your edge any more.
Anyway, again, this problem has been solved for years. The Kelly Criterion is the correct answer. For something more complex like blackjack (where you are not betting a fixed amount due to splits, doubles, etc), just maximize the expectation of the log of your bankroll after the hand.
Quote: GandlerSorry that was a bad word choice. What I mean to say is statistical expected return. Like if a coin was 1% heavier on one side you would expect heads to appear 51% of the time eventually after enough flips. So my thought was using a martingale type strategy on losses when you have an edge in BJ would make up losses quicker and profit faster?
In theory, you're right. But you should also be taking into consideration variance.
Quote: RSIn theory, you're right. But you should also be taking into consideration variance.
Theory and reality are the same. He's not right.
Quote: AxiomOfChoiceTheory and reality are the same. He's not right.
In theory you should bet more money when you have an advantage, but in reality you shouldn't because your bankroll can't support it.
Edit: Err, I was thinking he was just using the marty as an example but his point was to "bet more when you have an advantage", not the "always make +1 unit" strategy.
PS: Theory and reality are not the same. "Just because it works on paper doesn't mean it'll work in practice" comes to mind.
Quote: RSIn theory you should bet more money when you have an advantage, but in reality you shouldn't because your bankroll can't support it.
Edit: Err, I was thinking he was just using the marty as an example but his point was to "bet more when you have an advantage", not the "always make +1 unit" strategy.
PS: Theory and reality are not the same. "Just because it works on paper doesn't mean it'll work in practice" comes to mind.
Which means that the theory has just been disproven and should be discarded, or improved upon.
Quote: RSIn theory you should bet more money when you have an advantage, but in reality you shouldn't because your bankroll can't support it.
No, again, theory and reality are the same. In both theory and reality you should bet the optimal amount for your bankroll.
Quote:PS: Theory and reality are not the same. "Just because it works on paper doesn't mean it'll work in practice" comes to mind.
Yes, it does mean that it will work in practice. If the results differ then the theory was incorrect.
Quote: Lemieux66If you are playing a game where you have an edge every single hand/spin/whatever just flat bet the minimum. No broke and you'll get the money eventually.
What?? Why throw away so much money?
I set up a spreadsheet to test this theory that went up to 65K flips.
Every time you recalculate the spreadsheet, it re-flips all 65K times.
In one instance, as early as flip 32 the bet exceeded $1000 at $1024. I've seen it as high as 1,048,576 - after 20 consecutive tails.
But yes, in every instance the bottom line always grows.
Quote: AxiomOfChoiceWhat?? Why throw away so much money?
You don't want to risk going broke. It depends on what the minimum and what your bankroll is obviously, but say you had $500 and the min bet is $10. Flat bet the minimum there always obviously.
Quote: TerribleTomIf you're betting $1 on an true 50/50 bet that pays 1:1, sure. A Martingale will always come out ahead so long as you don't exceed your bankroll.
So, what you're saying is, it will work for everyone who has an infinite bankroll. In other words, nobody.
Quote: Lemieux66Also, as your bankroll grows a bit bigger and bigger, you should bet slightly more. But never proportionally. Lower your RoR and raise your bets at the same time. If you want to.
This is completely ridiculous. Again, this is math that has been done and proven decades ago. By moving your bets proportionally, your RoR is 0 (actually any system that has you never betting it all has an RoR of 0, since you can't lose what you can't bet, but Kelly betting maximizes growth, which is what you are concerned about)
Quote: AxiomOfChoiceThis is completely ridiculous. Again, this is math that has been done and proven decades ago. By moving your bets proportionally, your RoR is 0 (actually any system that has you never betting it all has an RoR of 0, since you can't lose what you can't bet, but Kelly betting maximizes growth, which is what you are concerned about)
So you can't have a long losing streak? Variance can't kick you in the face. Nonsense. You DO NOT want to go broke in a game where you are slightly ahead every single time. You will get the money. It just takes a long time.
Quote: Lemieux66So you can't have a long losing streak? Variance can't kick you in the face. Nonsense. You DO NOT want to go broke in a game where you are slightly ahead every single time. You will get the money. It just takes a long time.
Of course you can have a losing streak. That's why you bet proportionally. You lower your bets as your bankroll shrinks and raise them as it grows.
Again, this is math that was proven long ago and has been known for years. I don't understand why everyone is trying to re-invent the wheel here (and make it square while they are at it)
Quote: AxiomOfChoiceOf course you can have a losing streak. That's why you bet proportionally. You lower your bets as your bankroll shrinks and raise them as it grows.
Again, this is math that was proven long ago and has been known for years. I don't understand why everyone is trying to re-invent the wheel here (and make it square while they are at it)
I just said that.
As far as I know, the best way to bet [with an advantage] is to bet a fraction of Kelly. You don't just bet the table minimum or [somehow] increase your bets while decreasing ROR.
Quote: Lemieux66Also keep in mind that the OP said you are playing a game where the player edge is steadily .25%. It's never improving. So you want to bet something very small in relation to your bankroll so you'll be safe and steadily earn. That bet can go up a bit as your bankroll increases.
Are you even vaguely familiar with the Kelly Criterion? Did it occur to you to look it up and try to understand it before arguing against it?
Quote: RSPerhaps using the word "theory" wasn't correct. I meant something more like "intuitively" or "you would think" or "it appears".
As far as I know, the best way to bet [with an advantage] is to bet a fraction of Kelly. You don't just bet the table minimum or [somehow] increase your bets while decreasing ROR.
This is safe, but it's simply not practical in a casino. Can't bet coins. So you round up or down. It's best to round down for safety.
Quote: RSPerhaps using the word "theory" wasn't correct. I meant something more like "intuitively" or "you would think" or "it appears".
As far as I know, the best way to bet [with an advantage] is to bet a fraction of Kelly. You don't just bet the table minimum or [somehow] increase your bets while decreasing ROR.
That fraction is 1.
Actually, the existence of a minimum bet amount throws a wrench into the plans, a bit. You would have to modify things (and recalculate everything).
But with a reasonable bankroll the effect is negligible. Your goal is really just to get ramped up to betting table max as quickly as possible and then flat-bet table max until the casino says "no more". Not sit there betting table minimum trying to grind out a dollar or two per hour.
Quote: Lemieux66Yes I do. I am saying the same thing as you just in a different way. I just am saying be slightly more cautious.
No, you are not. You are saying bet table minimum, and, if you do increase your bets, don't do it proportionally. You are not saying anything even remotely close to the correct answer.
Quote: AxiomOfChoiceQuote: RSPerhaps using the word "theory" wasn't correct. I meant something more like "intuitively" or "you would think" or "it appears".
As far as I know, the best way to bet [with an advantage] is to bet a fraction of Kelly. You don't just bet the table minimum or [somehow] increase your bets while decreasing ROR.
That fraction is 1.
Actually, the existence of a minimum bet amount throws a wrench into the plans, a bit. You would have to modify things (and recalculate everything).
But with a reasonable bankroll the effect is negligible. Your goal is really just to get ramped up to betting table max as quickly as possible and then flat-bet table max until the casino says "no more". Not sit there betting table minimum trying to grind out a dollar or two per hour.
It depends on bankroll though. Obviously you can bet bigger if you have a huge BR. It also slows down the game and gets you heat if you are constantly recalculating your bets on every previous win or loss.
Quote: AxiomOfChoiceNo, you are not. You are saying bet table minimum, and, if you do increase your bets, don't do it proportionally. You are not saying anything even remotely close to the correct answer.
Ok. So what you advise is completely worthless and impractical in a casino setting.
Quote: Lemieux66It depends on bankroll though. Obviously you can bet bigger if you have a huge BR. It also slows down the game and gets you heat if you are constantly recalculating your bets on every previous win or loss.
The Kelly Criterion takes the size of your bankroll into account. It gives you a percentage of your bankroll to bet.
Recalculating your bets each time is really, really easy and should not slow down the game at all.
Quote: AxiomOfChoiceSo, what you're saying is, it will work for everyone who has an infinite bankroll. In other words, nobody.
Exactly. I encourage the OP to proceed with his plan, what could possibly go wrong?
Quote: AxiomOfChoiceQuote: RSPerhaps using the word "theory" wasn't correct. I meant something more like "intuitively" or "you would think" or "it appears".
As far as I know, the best way to bet [with an advantage] is to bet a fraction of Kelly. You don't just bet the table minimum or [somehow] increase your bets while decreasing ROR.
That fraction is 1.
Actually, the existence of a minimum bet amount throws a wrench into the plans, a bit. You would have to modify things (and recalculate everything).
But with a reasonable bankroll the effect is negligible. Your goal is really just to get ramped up to betting table max as quickly as possible and then flat-bet table max until the casino says "no more". Not sit there betting table minimum trying to grind out a dollar or two per hour.
The fraction is 1 if you want optimal growth and are able to resize your bets downward and are OK with a high ROR. Most players don't play at full kelly for a reason. I didn't say anything (positive) about playing the table minimum.
Quote: AxiomOfChoiceThe Kelly Criterion takes the size of your bankroll into account. It gives you a percentage of your bankroll to bet.
Recalculating your bets each time is really, really easy and should not slow down the game at all.
Are there ever situations in which betting something involving coins is the correct play if you want to be perfect? If so, it's not allowed. Obviously.
Quote: Lemieux66Are there ever situations in which betting something involving coins is the correct play if you want to be perfect? If so, it's not allowed. Obviously.
You can round down. Instead of betting $416.38, maybe you'll bet $415 or $400.
Quote: RSThe fraction is 1 if you want optimal growth and are able to resize your bets downward and are OK with a high ROR. Most players don't play at full kelly for a reason. I didn't say anything (positive) about playing the table minimum.
There is no high ROR. ROR is 0 with proper Kelly betting (you can't go broke if you never bet everything, and you never do)
As I said, the existence of a minimum bet throws a wrench into this, since you can no longer do "proper Kelly betting". But with any sort of reasonable bankroll this effect is negligible. I think that the Wizard ran some simulations with a 1% edge, a $100 bankroll, and a minimum bet of $1. The risk of ruin really was negligible.
The only time that risk of ruin becomes a big deal is if you start with a bankroll so small that your optimum bet is lower than the table minimum. But then your high risk of ruin is not because of the Kelly Criterion; it is because you are forced to overbet Kelly.
Quote: AxiomOfChoiceThere is no high ROR. ROR is 0 with proper Kelly betting (you can't go broke if you never bet everything, and you never do)
As I said, the existence of a minimum bet throws a wrench into this, since you can no longer do "proper Kelly betting". But with any sort of reasonable bankroll this effect is negligible. I think that the Wizard ran some simulations with a 1% edge, a $100 bankroll, and a minimum bet of $1. The risk of ruin really was negligible.
The only time that risk of ruin becomes a big deal is if you start with a bankroll so small that your optimum bet is lower than the table minimum. But then your high risk of ruin is not because of the Kelly Criterion; it is because you are forced to overbet Kelly.
So you support (pros) and teams betting full kelly? Is that what you're saying?
Quote: RSYou can round down. Instead of betting $416.38, maybe you'll bet $415 or $400.
I advised this. When I said a couple pages back about min betting 10 with a 500 dollar BR, 10 is still far too much. But hey, that's the min in most games.
An optimal idea is to get a job and save a real roll.
Quote: Lemieux66I'm also go to apply real world scenarios into a hypothetical game. Betting small(say 100 dollar bets instead of 400 dollar bets, even if your BR can support full Kelly) can deflect heat and keep this game going without casinos realizing what a destructive game they are running.
Betting less because of heat (or potential heat) hasn't a thing to do with optimal betting. Heat is an outside factor.
Quote: RSSo you support (pros) and teams betting full kelly? Is that what you're saying?
With teams betting simultaneously (different tables) it's a little difficult because you have no way of knowing if your teammates at the other tables are suffering heavy losses (causing your bankroll to be smaller than it is, causing you to overbet). So, in this case I would probably underbet a little bit to be prepared for this possibility. If it's a 2-person team you can mitigate this (somewhat) by agreeing to a single-session stop-loss (until you have communicated your loss to the other player, so you can both re-size accordingly). With many players playing from a shared bankroll (possibly in many casinos) this communication would be a lot harder. Kelly betting requires you to be able to accurately determine your bankroll -- if you can't do this you risk overbetting, which is obviously very dangerous.
For a "lone wolf" I absolutely advocate full Kelly betting. This requires that you have accurately determined your edge, of course (over-estimating your edge means that you're overbetting -- again, obviously very dangerous). If you're in a game with a variable edge like blackjack, this can be a problem. If you're in a game with a fixed edge off the top (eg, a 100% hole-card game) then you should be fine (note that you need to correctly take variance into account when performing the Kelly Criterion calculation -- simply multiplying edge by bankroll is NOT the Kelly Criterion!)
I could see betting differently for cover purposes, maybe? Certainly, absent heat (and absent the threat of future heat), I'd bet optimally. Why wouldn't I?
Quote: RSBetting less because of heat (or potential heat) hasn't a thing to do with optimal betting. Heat is an outside factor.
Nobody ever reads what I write.
I know what you mean. You're right. But to keep this hypothetical game going you have to bet numbers that won't draw attention. It's best to have a game going that you can beat forever rather beating it for more one night and never seeing it again.
