Gambler's Fallacy again, looking for a succinct explanation of a variant of Martingale

[Big Bad Barney]

Surely a martingale would work if you roll it enough times?

https://en.wikipedia.org/wiki/Law_of_large_numbers

Could you argue that the closer you get to whatever that large number is...something different happens?
What about instances where the coin flip DOES have a memory? I.e. Non-determinism, freewill or quantum something or other
What if there is a bias towards brown horses amongst foolish punters with lots of money? A martingales would work in ones favour instead of the house in that instance?

[Tuco]

if you did implement this strategy, how are you going to decide which horse to bet on?

Out of a hat? Pin the donkey tail? Back the rank outsider? or are you going to 'place it on Lucky Dan' for the win?

[Crazyskier]

Martingale is for evens chances / 50:50 or as close to as possible, so European Roulette with La Partage rules where you receive half your evens bets returned on a zero.

CS

[silentdiver]

if you did implement this strategy, how are you going to decide which horse to bet on?

Out of a hat? Pin the donkey tail? Back the rank outsider? or are you going to 'place it on Lucky Dan' for the win?

The thread is purely about the staking plan and the fallacy as related to the flawed 'wait until X blacks/losses....' concept, not selection; so I'd prefer to keep it to that.

Since you ask though, in the absence of a sufficiently long pin, same as the others - whatever race is coming up next is included/excluded (and the stake, if included) determined according to a set of rules and on-the-fly plus pre-generated analysis - that's where I gather one might look for edges, I'm a relative beginner to all this, but that seems to be the best approach.

That's where I'm trying to lean my friend towards, rather than more convoluted versions of the same flawed concept of upping the stakes and relying on the win that's 'due soon'.

To be revised when materials technology allows a pin long enough that doesn't bend so badly

[silentdiver]

Martingale is for evens chances / 50:50 or as close to as possible, so European Roulette with La Partage rules where you receive half your evens bets returned on a zero.

CS

Thanks yes, from what I've read here and elsewhere the only non-sure-disaster-in-the-end application of Martingale is where the chances are it'll be a short series; either by reality insisting on it (not the case with horses or roulette of course, but with say, drawing from a deck of cards and not replacing, betting on a court card coming up having an absolute maximum of 40 losses in a row and a very small likelyhood of anywhere near that) and/or a hard limit that accepts the loss at a certain point and stops chasing it.

So for horses, aye, a win rate that isn't too small, with an absolute limit on total exposure; along with an acceptance that it will hit that limit a lot more than you'd probably think it should, or like it to !

[silentdiver]

What about instances where the coin flip DOES have a memory?

Sure, in another reply I suggested an example of drawing cards from a deck, not replacing and betting on a court card coming up. That'd be a case where you could calculate your increasing stake to suit your bankroll and know damn well that by card #41 you'd get the win and recoup all your losses (jokers and the bridge card aside, anyway !) - can't see anyone offering that deal though - or not without say, a limit on the number of cards you were allowed to draw before putting the discards back and shuffling the deck.

[jamesedwards]

What about instances where the coin flip DOES have a memory?

Sure, in another reply I suggested an example of drawing cards from a deck, not replacing and betting on a court card coming up. That'd be a case where you could calculate your increasing stake to suit your bankroll and know damn well that by card #41 you'd get the win and recoup all your losses (jokers and the bridge card aside, anyway !) - can't see anyone offering that deal though - or not without say, a limit on the number of cards you were allowed to draw before putting the discards back and shuffling the deck.

You wouldn't get any odds on the final pick because drawing a court card would be certain on card #41

[silentdiver]

You wouldn't get any odds on the final pick because drawing a court card would be certain on card #41

That's exactly what I meant by "unlikely to find anyone offering that deal"

I was giving a theoretical example of a series of bets where there's a fixed endpoint enforced by reality, where the win really is 'due soon' (unlike horse racing/roulette etc); so if a casino were mad enough to offer that game without limits you could calculate a 'perfect martingale' where you'd be guaranteed to win even in the eventuality that you reached pick #40 and turned over the last numbered card leaving all the court cards in the deck, your last stake on pick #41, assuming your stakes were correct, would win back your entire exposure so far plus whatever profit you calculated in just as your pockets became empty.

[ruthlessimon]

Martingale + wasted time, what a lovely enhancement

[Big Bad Barney]

What about instances where the coin flip DOES have a memory?

Sure, in another reply I suggested an example of drawing cards from a deck, not replacing and betting on a court card coming up. That'd be a case where you could calculate your increasing stake to suit your bankroll and know damn well that by card #41 you'd get the win and recoup all your losses (jokers and the bridge card aside, anyway !) - can't see anyone offering that deal though - or not without say, a limit on the number of cards you were allowed to draw before putting the discards back and shuffling the deck.

Yeah, I guess it depends on if you're just talking about theory/maths, or looking for some kind of practical application for it... Maybe there are more obfuscated instances of the example above somewhere. I guess if so, flat staking would work anyway. Not like martingale would magically make it work better. I guess the thing is, even if the edge is in your favour, martingale doesn't give you any advantage. No progressive staking does.

...and lol, I just put it into an LLM, it reckons the only advantage of a progressive plan is psychological. It put it like this: Martingale is a variance-redistribution scheme, not an edge-generator. It trades frequent small wins for rare catastrophic losses.

[silentdiver]

Martingale is a variance-redistribution scheme, not an edge-generator. It trades frequent small wins for rare catastrophic losses.

I rather like that definition, important to distinguish between what Martingale (or any staking plan/system) does and an 'edge', from what I've gathered they're different things entirely.

They can be used together and perhaps in some specific situations it might even be beneficial in the long run to do that; but the key to success appears to be having an edge, not a system.

[wearthefoxhat]

Can bankroll management and Martingale staking be spoken about in the same sentence?....maybe.

Small wins v catastrophic losses, both will/could happen. So what's the plan? How much are you willing to make before it breaks?

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The biggest loss your martingale sequence can take, to equal a % of your overall bank

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Example:

So if you have £10,000 and you set a max sequence of 63 pts (last bet 32pts).
5% of bank = £500
1 pt = £500 / 63 = £7.94. (could round up to £8 or round down to £7).

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What to bet on? Lazy way is an "even money" chance with the lowest house edge.


Casino (House edge)

Roulette = (European) 2.7%
Baccaret = (Bank) 1.06%
Baccaret = (Player) 1.24%
Craps = (Pass/Don't Pass) 1.41%
Craps = (With odds bets added) 0.80% - ish.

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Hard way

Betfair Exchange (2% Commission)

Finding value bets/trades that make any bet/trade EV+, to equal an Even money coup.

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[silentdiver]

Can bankroll management and Martingale staking be spoken about in the same sentence?....maybe.

We still have some Martingale-ish workings, on selected markets/mean win rates, with limits on total exposure to cut off after losses exceed X. Initially when I was even greener than I am now, the idea (and similar 'staking plans') seemed to me like some sort of holy grail but I've learnt lessons since then, both from here and hard experience. Lately I'm trying to move us away from that approach where if we can just discover the magic multiplier, the profits will roll in.

Not given up the idea entirely I must confess, but it's no longer the focus of development.

The idea of this thread is to help me justify keeping moving away from using anything that increases stakes as a consequence of previous performance though.

I guess it needs to be similar to bankroll management playing poker, where you play on tables where the big blind (initial stake per hand) is no more than a specific tiny percentage of your bankroll. When you lose enough for your bankroll to not 'qualify for' that table any more, you move to a lower stakes table, where the play is less challenging, to lick your wounds and build back up; and can move up to a more expensive table with tougher opponents if, and only if you increase your bankroll enough to justify it.

In theory, as well as matching the risk to the depth of your pockets and stopping you going broke in a hurry; it auto-corrects the opponents you'll be up against to your current skill level.

That is, unless you have more money than sense and start as a complete beginner with a 10 grand bankroll anyway.