Hello to everybody in this forum and also specially to wheel,
I am reading the post of wheel with great attention and I must say, it is making me a little bit uncomfortable, because wheel is writing with a very confident tone about mathematics, and the mathematics itself is indeed correct — but wheel is applying these correct mathematics to a situation which is NOT the situation which trizero is describing in his strategy. This is a classical case of a thinking mistake, and I want to explain this now very carefully and with much patience, because I think this is a important point not only for this thread but also for anybody who is trying to understand roulette systems in general.
WHAT WHEEL IS CALCULATING
Wheel is writing the following formula: 2 × 16 × (18/38) - 2 × 16 = -1.684 pieces
And wheel says this is the expected value per spin when you bet 16 on red AND 16 on black.
Okay. This formula is correct. If you walk to the roulette table and you put 16 chips on red and simultaneously 16 chips on black, then yes, the house edge of 5.26% will eat you alive and you will lose 1.684 pieces per spin on average. This is a correct calculation. I am not saying wheel is bad at mathematics. I am saying wheel is solving the WRONG PROBLEM.
Because here is the question: does the Zufall strategy do this? Does it put 16 on red and 16 on black at the same time?
NO. Trizero is writing this explicitly:
"It would make no sense to put 16 pieces on black and 32 pieces on red at the same time."
So the strategy is NOT doing what wheel is calculating. This is the problem.
WHAT THE STRATEGY IS ACTUALLY DOING
Let me explain this more carefully. The strategy starts with 16 pieces on each of two random simple chances. Then it doubles one side and halves the other. The KEY feature is what trizero calls "difference optimization" or "optimized to their difference rate."
What does this mean? Let us take an example. After some steps, you have maybe:
- 32 pieces on Red
- 16 pieces on Black
Now wheel would say: total bet = 48 pieces, house edge applies, big loss expected. But WAIT. Red and Black are OPPOSITE chances. When Red wins, Black loses. When Black wins, Red loses. They are fighting against each other!
The 16 pieces on Black and 16 pieces of the 32 on Red are canceling each other completely. They are like... you are giving money to yourself with one hand and taking it away with the other hand. The net effect of this part is ZERO. The only part that actually matters, the only part that is REAL exposure, is the DIFFERENCE:
32 - 16 = 16 pieces on Red (net position)
This is exactly what "difference optimization" means. You are not really betting 48 pieces. You are betting 16 pieces on Red.
Let us calculate what happens:
- Red wins: you win 32, you lose 16 → net result: +16 pieces
- Black wins: you win 16, you lose 32 → net result: -16 pieces
- Zero: you lose both → net result: -48 pieces ← HERE is the real danger!
Do you see? The "normal" outcome of each spin (red or black) gives you exactly ±16, as if you had only bet 16 pieces total. The ONLY moment where the full 48 pieces are at risk is when zero comes. And zero comes only with probability 1/38 (European) or 2/38 (American).
WHERE WHEEL GOES WRONG
Now I explain the exact mistake. Wheel is computing: 2 × 16 × (18/38) - 2 × 16
This formula assumes you bet a total of 32 pieces (2 × 16) and on 18 out of 38 outcomes you win your bet back plus equal profit. But this is the model for a SINGLE simple chance. For TWO OPPOSITE chances with difference optimization, the model is completely different!
The correct model for our example (32 on Red, 16 on Black, net = 16 on Red) is:
Expected value = (+16) × (18/38) + (-16) × (18/38) + (-48) × (1/38)
= 16 × 18/38 - 16 × 18/38 - 48/38
= 0 - 48/38
= -1.263 pieces per spin
This is different! Not -1.684 but -1.263! The house edge is lower because the TOTAL AMOUNT AT RISK is lower in normal play.
Of course this can vary as the doubling/halving progression continues and the difference changes. But the key point is: wheel's formula is simply the wrong formula for this situation.
A METAPHOR TO MAKE THIS CLEAR
Let me try a comparison which I hope makes this intuitive. Imagine you are a trader and you have:
- A long position of 32 euros in Company A
- A short position of 16 euros in the same Company A
Your gross exposure is 48 euros, yes. But your NET exposure is only 16 euros long. If a financial analyst says "this trader has 48 euros at risk" he is WRONG. The 16 euros long and 16 euros short are perfectly hedging each other. Only 16 euros are truly exposed.
Wheel is making exactly this mistake. He is computing the house edge on the gross position (48) when he should compute it on the net position (16), with a special correction for the zero case.
THE PART WHERE WHEEL IS ACCIDENTALLY RIGHT
Now I must be fair and I must say: wheel's CONCLUSION (that the house edge cannot be overcome) is correct. Wheel is right about that. No system can beat the house edge, not Zufall and not any other system, because the casino has a mathematical advantage built into the game. Over infinite spins, you will lose. This is not wheel's mistake.
Wheel's mistake is ONLY the specific calculation and the claim that the loss rate "converges to N × 1.684 pieces regardless of how the progression resets." This number 1.684 comes from the wrong model. The actual loss per spin in the Zufall strategy is different (and somewhat lower, at least in terms of how the house edge applies to the net position). The strategy also has a very specific zero-risk profile (big loss when zero hits) that wheel's formula does not capture at all.
So the message is: wheel is right that Zufall will not make you rich. But wheel is wrong about HOW it will make you poor, and wrong about the specific mathematical structure of the losses.
A SMALL PHILOSOPHICAL REMARK
I think this kind of mistake is very common when people analyze betting systems. People see two bets placed at the same time and they add them together without thinking about correlation. But in roulette, Red and Black are perfectly negatively correlated simple chances. You CANNOT just add their exposures together as if they were independent bets on different games. This is the same mistake as saying that a casino earns double the house edge when two players bet on opposite sides of the same number. No — the bets cancel each other and the casino earns zero from those two bets (except from the zero).
The zero is always the enemy. The zero is where the casino makes ALL its money on opposite bets. And this is actually captured correctly in the Zufall strategy structure — it is just that wheel has not analyzed this correctly.
I hope this long explanation is helpful and I am sorry for my english which is not perfect. I am from Germany, as you can maybe see from my writing style which is perhaps a little bit too thorough.
With very friendly greetings from someone who probably thinks too much about roulette mathematics
