Undermining the House Edge

[nullified]

Undermining the House Edge

In some of my previous research I tackled the problem of trying to nullify the House Edge, and then trying to create a roulette system based on my findings.

My earlier work on "The 11% Solution," and "The Curious Case of the Lone Corner Bet" [nolinks://nolinks.vlsroulette.com/index.php?topic=19776] were the results of my findings.

It continued to bother me however that the longer I played (i.e. more than 500 spins), the more the house edge crept back to its statistical advantage.  And although my previous work was exciting and had a lot of potential, it remains underdeveloped.

Getting back to basics is often the best place to go when one has to go back to the drawing board.  In my case, I went back to the basics of probability theory.

And my motivation was simple. I still had in mind to improve upon my Magnus Opus - Parrondo's Paradise [nolinks://nolinks.vlsroulette.com/index.php?topic=19805], specifically, the main part of the bet that emulates a 75% chance of doubling your money. I had left my solution to this problem incomplete (or maybe it was just unsatisfactory), since I figured that any bet that incorporated more than one spin AND covered a large portion of the table was going to be good enough.  And perhaps my solution was, in fact, good enough.

But the problem with being a perfectionist is... things are never good enough.

Anyway, the main problem with many of our roulette systems and methods is that in order to maintain their effectiveness, they often require multiple spins and an increase in cash.  Needless to say, this works in favour of the house edge.

For example: the odds of me winning an even chance bet on one spin of the wheel is 18/37 = 49%; and the odds of me winning twice in 2 spins 18/37 x 18/37 = 24%. So, even though the odds per spin remain the same, the more I play, the worse things get.

But hold on.  What about when I'm NOT trying to win two bets in a row?  What if all I want to do is win ONE of two?

In probability theory, this is easy to calculate: we just take the inverse of what we don't want to see.  In other words, what we don't want to see is two losses in a row.  Well, what are the odds of getting two losses in a row? That would be 19/37 x 19/37 = 26%.  And the inverse of that is 1 - P, which is 1 - 0.26 = 0.74, or about 74%.

So what is this 74%?  It is the inverse, or opposite of losing two even chance bets in a row. If I don't lose two bets in a row, it is because I won at least one of those two bets.  So that means that I actually have a 74% chance of winning at least one out of two even chance bets.

And it gets better the longer we go.  What are the chances of me winning a least once in four spins? That would be the inverse of losing four in a row.  And losing four spins in a row is 19/37 x 19/37 x 19/37 x 19/37 = 6.7%. The inverse of that is 1 - P, or 1 - 0.067 = 93.3%. Therefore I have a 93.3% chance of winning at least 1 of my four spins.

So how does this idea help us to undermine the House Edge?

Simple.

If I flat bet $1 on Dozen 2 for 100 spins, 68 times I lose my $1 and 32 times I win $3 (net $2). 32 x $2 = $64 in wins - $68 in losses = -$4 per 100 spins.

But what happens when all I want is to win 1 out of every 2 spins?

Let's figure it out. The chances of me losing 2 bets in a row is 25/37 x 25/37 = 0.46, or 46%.  The inverse of that is 1 - P, or 1 - 0.46 = 0.54, or 54%.  So the chances of me winning at least one time in two spins is 54%.

Okay, so now I know that all I need to do is play my sessions as games of two spins each, and I will have 54 winning sessions compared to 46 losing sessions for every 100 spins.

To make this method capable of undermining the House Edge, it becomes necessary to increase the second bet of the session to $4.  What this means is that whether I win on the first or second bet, I come away profiting in both cases.

Alright, let me put this all together.  I choose a Dozen to work on.  I play in sessions of 2 spins each. Each session will go either one of three ways.  Either 1) I lose both spins and I am down $5; or 2) I win on the second spin, and I profit $7; or 3) I win on the first spin, I profit $2 and then let the second spin go without betting on it (to ensure I'm not messing up the probabilities).

What this all amounts to is this: 46 of my sessions will be losing sessions, whereby I lose both my $1 and $4 bets totalling $5 x 46 = -$230.  But 54 of my sessions will be winning sessions.  Since we don't know which of those sessions will win on the first spin (netting us $2) or the second spin (netting us $7) we must assume that either case is equally as likely.  In other words, 1/2 of my 54 winning sessions will net me $2, and the other 1/2 will net me $7.

My winning sessions then will look like this: 27 x $2 = $54 (profits from winning on the first spin). 27 x $7 = $189.  Total profits = $54 + $189 = $243 - $230 in losses = +$13.

That might not seem like a lot, and you'd be right.  But consider a couple of things first.  1) Our expected outcome is now +$13 after 100 spins, compared to a -$1 or -$2 that represents the ever-present House Edge. 2) Even more incredibly, the greater the 'spread' in our bets, the more profits we come away with.  In other words, the 'spread' of our sessions is 3: $1 for the first bet and $4 for the second bet.  If we increase that 'spread' to 4 or 5 or more, we still undermine the House Edge AND come away with more profits! 3)We're not betting every single spin. When we win on the very first spin of our 2-Spin session (the $1 bet), we DON'T bet on the second spin. This ensures that we're not giving back any of our profits with greed.

Let me summarize this.

1. Choose a Dozen to bet on, and stick with it.
2. Play in 2-Spin Sessions only.
3. The bet sequence is: Spin #1 - $1; Spin #2 - $0, or $4.
4. Never deviate from the bet sequence.
5. Never bet after winning the first bet. If you do, you're giving back your winnings AND messing up the probabilities.
6. Don't let oddities dishearten you.  Oddities like 12 spins in a row without a win, and that kind of thing.  Those types of things happen.  In most other methods, you'd lose your shirt when that happens.  With this method, you might lose $60 or so.  Keep playing.  We've just seriously undermined the House Edge, so time is on your side.

[superman]

Hi nullified

Seems plausible, but what's the gap between sessions?

[LuckoftheIrish]

I have just tested this system on 100 000 single zero spins (50 000 sessions of 2 spins).

End result: -4349 units

Most up: +17 units

Placed bets at 1 unit: 50 000
Placed bets at 4 units: 33 591
Virtual bets: 16 409

[rouletteKEY]

nullified, if I may ask, what is your bet selection process?

[nullified]

@Superman>>>>>>
There is no gap between the sessions.

@LuckOftheIrish>>>>
Would you mind sending me a copy of your tests? I would love to analyze what's happening.  Also, if it's not too hard, could you try testing a)without the gaps, and/or b) a progressive bet selection where the bet is increased to 2 - 5, 3 - 6, 4 - 7, 5 - 8, etc (I don't have a copy of Roulette Xtreme to try myself).

@ rouletteKey>>>>>
I'm not sure what you mean by my "bet selection process." Can you clarify please?

[nullified]

When I was playing this method, here is the way I played:

Sessions are still in two spin cycles, always betting on the same Dozen or Column.

Level 1 - $1 & $4
Level 2 - $2 & $5
Level 3 - $3 & $6
Level 4 - $4 & $7
... On consecutive Levels, move up by $1 for both of the spins

As I played, I moved "up" a Level when I lost both spins.  I only moved "down" one level after I had won on the second spin of that session.

So a typical round might look like this:

Spin 1 & 2 - bet $1 and $4; loss: -$5.
Spin 3 & 4 - bet $2 and $5; loss: -$12.
Spin 5 - bet $3; win; Spin 6 - bet $6; loss: -$11 (although I won the first spin on this session, I did not move back "down" to the previous Level, since I didn't win on the second spin).
Spin 7 & 8 - bet $4 and $7; wins: +$4.

If I had not won spin 7, I would in fact have been sitting at -$8 after winning spin 8, in which case I would then "step down" to the previous level and bet $3 and $6 for the next session.

Notes:
1) I would always move up or down the Levels as I won or lost (sort of like the Guetting progression, or Oscar's Grind)
2) I would only move back "down" to a previous level when I had won the second bet of that session.
3) I would always keep track of where my money was at before I began to play any of the Levels, so that I would know whether I was in profit or not.
4) I would stop after being in profit, and start over at Level 1.

[nullified]

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