Gambling Systems Thread (Roulette). (1 Viewer)

[seanieg89]

A surprising number of people I have met seem to believe in the existence of profitable "betting systems" for casino games like Roulette. Casinos are very happy about this misconception.

Here is a thread for high school students to practice their combinatorics skills by suggesting and/or debunking such systems. If this gets a reasonable amount of activity, we can look at other games next.


The following assumptions will be made:

1. We are playing the version of Roulette with both a '0' and a '00'. The wheel is fair, spins are independent, and the payouts are as in: http://www.popupcasino.com/wp-content/uploads/2012/03/roulette-payouts.jpg.
2. You have a finite starting capital of M units, and each bet must be made in whole units.
3. The casino has infinite wealth.
4. You must use some kind of "stopping rule" to tell you when to terminate your betting. This can be something like: Stop when broke or when target of T units is reached, or it can be more complicated.
5. A betting system is a set of rules that determine what your n-th bet should be on and how much it should be, that can depend on things like M and what outcomes have happened so far in the game.

To get started, here are four basic strategies you can look at the expected profit/loss of:

A. Bet all M units on red straight away, and walk away regardless of outcome.

B. Bet all M units on the number 7 straight away, and walk away regardless of outcome.

C. Bet one unit at a time on red until you either go broke or reach 2M units.

D. Bet one unit on red to start. If you lose this bet, then bet two units on red. Keep doubling your next bet on each loss, and resetting your bet to one unit on each win. Walk away when you are either broke or reach 2M units.


Feel free to suggest your own strategies as well!

 

[braintic]

Years ago I had someone suggest to me his 'failsafe' system for winning at the races:

1. Back the favourite every time.
2. When you lose, just double your bet next time. When you eventually win, you must come out ahead.

Clearly he had no concept of finite funds.

 

[seanieg89]

Years ago I had someone suggest to me his 'failsafe' system for winning at the races:

1. Back the favourite every time.
2. When you lose, just double your bet next time. When you eventually win, you must come out ahead.

Clearly he had no concept of finite funds.

Haha yep, the martingale is a classic example of the fallacies some gamblers believe.

 

[brent012]

I actually recall there being a pretty popular runescape bot for capped players "box" staking (I.e. pretty much a 50/50 bet) that would follow a martingale-esque system. Despite there being plenty of logical people calling them out a lot of users seemed to maintain that it was unlikely to lose if you had enough to double at least 8 times (iirc). It apparently worked pretty well if you set your start bet very low, but there was still a good chance of getting cleaned out if you ran it for a long time. The big problem though was that after small success people would get greedy and start with a bet that just wasn't sustainable to maintain and thus be statistically far more likely to fail.

Moral of the story? Even if there were hypothetically a flawless system, its still gambling and people are going to get greedy and go against it.

 

[RealiseNothing]

Years ago I had someone suggest to me his 'failsafe' system for winning at the races:

1. Back the favourite every time.
2. When you lose, just double your bet next time. When you eventually win, you must come out ahead.

Clearly he had no concept of finite funds.

Or the concept of the favourite paying <$2

 

[Trebla]

sean I thought you hated financial maths?

 

[abbeyroad]

how about a nice game of chess?

 

[seanieg89]

sean I thought you hated financial maths?

Why did you think that? I haven't really done that much financial maths but this stuff is pretty easy.

I love mathematics to do with games, whether it is probability, random walks or game theory.

 

[braintic]

Or the concept of the favourite paying <$2

Yes, but if you've doubled your bet all the way up to $1024 then the winnings will be significant in comparison to your original bet.
The thing with this system is that, provided you always win before you run of funds then you must come out ahead. But its a huge IF.
And I guess there is nothing to say that you must back the favourite every time.
Taking 2^12 = $4096, it would be interesting to know how often the favourite misses out in 12 consecutive races.

 

[anomalousdecay]

tl;dr, but I just wanted to say something which might be useful for future games.

From my experience it is possible to build a circuit which would determine the best next step to do in a game by comparing the conditions given.

Just a little Boolean Algebra and a few gates and you will have a function that tells you the best next move.

If you added an artificial clock (by clock its moreso a sort of switch in this case that responds to the game), using a flip-flop in a combinational circuit instead, then it would play the moves indefinitely one after the other and you could play the game without doing a single thing (this is actually probably how AI computer chess works but with virtual combinational circuits).

 

[seanieg89]

tl;dr, but I just wanted to say something which might be useful for future games.

From my experience it is possible to build a circuit which would determine the best next step to do in a game by comparing the conditions given.

Just a little Boolean Algebra and a few gates and you will have a function that tells you the best next move.

If you added an artificial clock (by clock its moreso a sort of switch in this case that responds to the game), using a flip-flop in a combinational circuit instead, then it would play the moves indefinitely one after the other and you could play the game without doing a single thing (this is actually probably how AI computer chess works but with virtual combinational circuits).

By "comparing the conditions given", do you mean evaluate the states that would be achieved by all possible moves and then choose the best one? Because if that's the case, that just shifts the bulk of the problem to finding this evaluation function. For games like chess whose complete computation is beyond the realm of current (and possibly future) technology, these evaluations are made by heuristics and parameters that are tweaked through machine-learning.

 

[anomalousdecay]

By "comparing the conditions given", do you mean evaluate the states that would be achieved by all possible moves and then choose the best one? Because if that's the case, that just shifts the bulk of the problem to finding this evaluation function. For games like chess whose complete computation is beyond the realm of current (and possibly future) technology, these evaluations are made by heuristics and parameters that are tweaked through machine-learning.

Not necessarily as that would be too complicated.

What I mean is that the output depends on various inputs. These inputs are determined by things which affect the play and consist of things like "if one of the following possible cards were shown, do this" (which for basic use you would use the OR Boolean operator) or "only allow this option to be on if all these inputs are in one specific combination" (which for basic use you would use the AND Boolean operator). This method would require a lot of calculations, but the calculations are simple.

You can do the choosing method, but that actually requires much more complex circuits, but can be done if you use already made IC's rather than gates easily (a few decoders and multiplexers would work), but would require rather tedious calculation methods.

Chess is done a bit differently as what you described actually uses memories. Not sure but maybe they use a Mealy finite state machine method using the property of hysteresis (it uses the previous states and current states to output the next state).

 

[anomalousdecay]

This current game you have is too difficult to design such a circuit, but if we ever get to one which seems like its quite easy to fulfil using a circuit during the mid-year break, I'll give it a crack and show you how you can design this type of stuff and take a different approach where all combinations of inputs show all the outputs possible for the conditions.

If you want I can give you a question of what I mean by this (but in private), which gave a rather delicate solution.

 

[brent012]

Pretty sure there are already extremely complex devices to cheat at roulette. But that's cheating - NOT a gambling system.

 

[anomalousdecay]

Pretty sure there are already extremely complex devices to cheat at roulette. But that's cheating - NOT a gambling system.

I actually was referring to all games in general. And with no doubt I agree with what you just said.

I actually derived an equation which would allow you to win a game of knots and crosses as long as the opponent makes one false move (it was a tutorial question lololol).

 

[RealiseNothing]

Yes, but if you've doubled your bet all the way up to $1024 then the winnings will be significant in comparison to your original bet.
The thing with this system is that, provided you always win before you run of funds then you must come out ahead. But its a huge IF.
And I guess there is nothing to say that you must back the favourite every time.
Taking 2^12 = $4096, it would be interesting to know how often the favourite misses out in 12 consecutive races.

You only ever make in profit an amount equal to your first bet. You bet all the way up to $1024, you will still only make $1 in profit (assuming you started at $1).

And the favourite will miss out in 12 consecutive races at least once every 4096 games which is equal to the profit you'll be making and you'll be back to square 1.

 

[braintic]

You only ever make in profit an amount equal to your first bet. You bet all the way up to $1024, you will still only make $1 in profit (assuming you started at $1).

And the favourite will miss out in 12 consecutive races at least once every 4096 games which is equal to the profit you'll be making and you'll be back to square 1.

I think you need to factor the odds into that calculation. Your $1 profit assumes that the odds in the final race are 1:1.
If the final horse is odds-on then you will lose. If it is odds-against (the more common scenario), then you win more than $1. I would think that the typical odds for the favourite are about 3:1 against, in which case you would be ahead by slightly more than double what you lost in the previous races.

Don't get me wrong, this 'system' is still BS.
But a proponent of this system might suggest that you don't bet on every race - only those races where the favourite is not odds-on or even money.

In the end, the main reason you will lose is the same for every system - the bookmakers don't pay high enough odds, in order to make their profit.

 

[seanieg89]

Horse races (and sports betting generally) aren't really the ideal setting for thinking about the fallacy of the Martingale system (because it is hard to quantify winrates and payout odds are determined by the public betting rather than these winrates).

Making profitable decisions in horse racing is then possible if you have an good eye for horses (and consequently a good internal gauge for winrates). Most bets won't be profitable because there is a house edge (the bookies earnings), but if you can spot good bets when they arise then you can profit (especially when the public perception is markedly different from the actual winrates).

You get the same phenomenon happening in poker. There may be a house edge (the rake) on average, but if you can exploit non-optimal play by opponents (whilst not being exploited too much yourself) then it will be them footing this bill.*


(*) Here "non-optimal" usually means things like "bluffs too much", or "always slowplays sets and better", with some respective exploitative adjustments being "call more, slowplay more good hands" and "play more drawing hands" for example.