The house edge at roulette (with single zero) is familiar to most players,
it is 1/37th or in other words 2.70%.
For easy chances (like red) it depends on the zero-payout scheme, but mostly it is half, e.g. 1.35%.
Some online or slot machine players do not know the "second tax"
of European roulette, called the tronc.
Depending on the country, casino, or even the table, the rules for tronc are different.
Generally it can be said:
The tronc costs 1 piece of the profit on a single number.
Traditionally, after a win at the casino it sounds like: "One piece for the employees!"
Thus, the house edge is already 2/37th or 5.40%.
The tronc traditionally applies only to wins on Singles, so for other chances: no piece for the employees.
This post is less about the tronc itself —
the precise rules of a specific casino can be found in brochures or on their websites —
but rather about how it could be avoided.
Betting only one number, the tronc simply cannot be avoided.
But as soon as more than one Single is bet, the Single-tax can sometimes be bypassed.
If two of the Singles placed are next to each other on the tableau (the betting table),
they can also be bet as a Split.
Avoiding Tronc at Roulette – Optimizing Single Bets
The more Single numbers that are played, the better the chances of avoiding the tronc.
Ideally, as many Singles as possible should be combined into lower chances,
as this can free the former Singles from the tronc.
For example, the numbers from 1 to 12 would become the 1st Dozen, or all red Singles the easy chance Red.
This not only saves the tronc, but also means fewer chips to place — the game becomes clearer.
This chart shows to what extent Single bets can be replaced with lower chances:
The horizontal axis shows the number of Singles originally to be bet.
On the vertical axis, the number of chances that could replace these Singles is shown.
For the chart, 20,000 random number combinations between 1 and 36 single numbers were used.
The color represents the frequency of such combinations according to the scale.
Since the numbers of ECs Odd/Even and Red/Black are distributed unfavorably on the tableau
for a summary of chances, an "island" forms at the right edge of the chart.
That is the consequence of this irregularity.
For example, replacing 20 Singles would yield on average about 10 chances containing these Singles.
An example for the conversion of 27 Singles. In the chart above, this constellation would be found at 27 right and 10 high.
27 Singles: 0 3 5 6 7 8 9 10 11 12 14 16 17 20 21 22 24 26 27 29 30 31 32 33 34 35 36
replaced with:
1 TVS 7 /12 7 8 9 10 11 12
2 TVS 31/36 31 32 33 34 35 36
3 Corner 26/30 26 27 29 30
4 Split 0 / 3 0 3
5 Split 5 / 6 5 6
6 Split 14/17 14 17
7 Split 20/21 20 21
8 N 16 16
9 N 22 22
10 N 24 24
If one wants to implement this approach in a real game, it quickly becomes clear:
This is not so trivial.
Therefore, the roulette strategy simulator does this automatically when optimize chances is used.
The advantage for one's own strategy can be determined with a few mouse clicks:
Simply run a test with and without this function over the same permanence.
This function can also be used practically via Live Mode.
