Constant Proportion Roulette Strategy
The Constant Proportion strategy consists of wagering a certain percentage of your current bankroll in each roulette spin. This means that the bet sizes will change, but the size of these bets in relation to your current bankroll will be constant. Hence the name I’ve chosen for this strategy.
I will show you how this strategy works for different bet types and bet sizes through my rigorously tested simulations, so that you can understand how these factors could influence your chances of winning at roulette.
Keep reading this article and find out:
- What are the best types of bets to place?
- What bet sizes should you use to maximize your chances of winning?
- What are the chances of winning big by wagering the same percentage of your current bankroll over and over again?
- How the Constant Proportion strategy works
- Simulations of the Constant Proportion strategy
- Conclusion and recommendations
How the Constant Proportion strategy works
The Constant Proportion strategy is very similar to the Constant Bet strategy, but with an additional element. When using the Constant Bet strategy, the bet sizes remain the same whether the player is doing well or doing horribly. On the other hand, the Constant Proportion strategy utilizes variable bet sizes that fluctuate depending on previous results.
So, if a player is doing well and winning, their bet sizes will keep rising and enable them to win even more. On the other hand, If they are losing money their bet sizes will slowly decrease and their potential losses will not accumulate as quickly as they would through the Constant Bet strategy. This self-regulating mechanism is what makes the Constant Proportion strategy a bit more advanced than the Constant Bet strategy.
EXAMPLE
So that everything is completely clear, here is an example of the Constant Proportion strategy in action. Let’s say the player wants to wager 10% of his bankroll on a Color bet. They start with $100 and place a bet of $10 on red. If they win they will then have $110, followed by placing a $11 in the next round. If they lose, they will drop to $90 and will only place a bet of $9 in the next round. The player will keep on doing this until they run out of money or decide to stop playing.
Just as in the Constant Bet strategy, the Constant Proportion strategy is also about finding a balance between:
- High volatility – big possible wins but also with a big chance of losing everything quickly
- Low volatility – smaller possible wins but also with a smaller (or non-existent) chance of losing everything quickly
High volatility is caused by more volatile bet types and bigger bets. Low volatility is caused by less volatile bet types and smaller bets. You could bet your entire bankroll on a specific Straight Up number and most likely lose everything in just one spin, or you could bet 1% of your bankroll on red or black, causing fluctuation to occur around your initial bankroll, but with a higher chance of ending up with less than your initial bankroll.
Logically, the best possible scenario will be somewhere in between and I will use my simulations to pinpoint exactly why.
Bet size rounding and minimum bet limits
There are two potential issues that need to be addressed. When betting a fixed proportion of your current bankroll, the amount you will need to bet will not always be "nice" or rounded. If you can’t place the exact amount according to your calculations, round your bet size up or down to the nearest number.
If you are unlucky and your calculated bet size is lower than the minimum bet of the roulette table will allow, just place the minimum bet size instead. I used this approach in my simulations.
Simulations of the Constant Proportion strategy
Rigorous simulations are the best way to view how the strategy works, and how little changes in your playstyle can cause big differences in the expected results. I’ve used a number of simulations to test multiple Constant Proportion strategy bet types, and find outthe optimum percentage of your bankroll you should wager in each of them.
Methodology and utilized variables
All simulations were run using my own carefully designed simulation software, including rules, probabilities and payouts for single zero roulette with no special rules (such as En Prison or La Partage). If you play classic European roulette your results should be in line with the results from my simulations.
Players had a starting bankroll of $100 and proceeded as follows:
- They placed the same type of bets (Color, Corner or Straight Up) over and over again, but with a variable bet size.
- The bet size was calculated as a fixed proportion of their current bankroll, rounded up to the nearest $1.
- The minimum bet size was set to $1. If the calculated bet size was lower than $1, they placed a bet of $1 instead.
- The players continued betting until they lost their entire bankroll or until they played through a total of 100 Roulette spins.
As to the types of bets used, I took all alternatives into consideration and decided to use the following for my simulations:
- Color – Red or Black (chance to win: 18/37, payout: 2x)
- Corner – Four numbers that share one corner (chance to win: 4/37, payout: 9x)
- Straight Up – One specific number (chance to win: 1/37, payout: 36x)
I tested various bankroll proportions ranging from 1% to 50% wagered in each round, for each of the bet types mentioned above.
I tested a sample of one million players in all of the simulations. This sample size should ensure that the results are statistically reliable, but with a number of statistical deviations that could still occur. This really shouldn’t significantly influence the results, however.
Bet size analysis and simulations #1: Color (red or black)
Let’s start this analysis of the simulation results by taking a look at players who wagered their money on the Color bet (red or black). This is the least volatile option, which should be evident in comparison to the other types of bets. Let’s take a look.
| Bet size | % of total winners | Winners leaving with $100-$200 | Winners leaving with $200-$500 | Winners leaving with $500-$1k | Winners leaving with $1k-$5k | Winners leaving with >$5k | Average cost |
|---|---|---|---|---|---|---|---|
| 1% | 35.5% | 35.5% | 0% | 0% | 0% | 0% | $2.7 |
| 2% | 35.4% | 35.4% | 0.0054% | 0% | 0% | 0% | $5.3 |
| 3% | 33.8% | 33.5% | 0.3% | 0% | 0% | 0% | $7.7 |
| 4% | 31.9% | 30.4% | 1.4% | 0% | 0% | 0% | $10.2 |
| 5% | 29.5% | 26.7% | 2.8% | 0.0074% | 0% | 0% | $12.6 |
| 10% | 22% | 14.1% | 7% | 0.75% | 0.13% | 0.0002% | $23.8 |
| 20% | 9.75% | 3.9% | 3.9% | 1% | 0.8% | 0.07% | $42 |
| 50% | 0.137% | 0.017% | 0.058% | 0.028% | 0.018% | 0.016% | $90 |
| Bet size | Players losing everything before finishing 30 spins | Players losing everything before finishing 50 spins | Players losing everything before finishing 75 spins | Players losing everything before finishing 100 spins |
|---|---|---|---|---|
| 1% | 0% | 0% | 0% | 0% |
| 2% | 0% | 0% | 0% | 0% |
| 3% | 0% | 0% | 0% | 0% |
| 4% | 0% | 0% | 0% | 0% |
| 5% | 0% | 0% | 0% | 0% |
| 10% | 0% | 0% | 0.08% | 0.6% |
| 20% | 0.11% | 2.8% | 12.5% | 25.6% |
| 50% | 57.2% | 85% | 96% | 99% |
You can immediately see that betting 50% of your current bankroll in each round is just too risky, as almost none of the players make it through the entire 100 spins. They lose $90 of their $100 on average, making this bet size very bad value for the player. Only 0.137% of players ended up with more money than they started with.
The players wagering 20% in each game round had a much higher probability of making it to the 100-spin mark. Almost 75% of them actually got to play 100 spins. The chance of winning big is quite high, but due to the average cost being $42, this is a bit too much.
On the other side of the spectrum, players betting 1% to 4% of their current bankrolls have a 100% chance to play the full 100 spins, but with the possibility of winning big being just too low. This strategy is a bit better with a 5% proportional bet, but it’s still a bit boring because of the very small chance of winning big.
Best bet size to use
The strategy of betting 10% of your current bankroll in each round is the most interesting for this specific strategy. Players lost $23.8 of their $100 bankrolls on average but had quite a high chance of winning amounts of up to $500, and even a small chance of winning over $1,000, or even $5,000.
They have a good chance of winning big, and are still pretty much guaranteed to play the full 100 spins, as only 0.6% of players lose everything before the 100-spin mark. All in all, 22% of players end up with more money than they started with, while more than 77% of players are left with less than their initial bankroll (but with more than $0) after playing 100 game rounds.
Bet size analysis and simulations #2: Corner Bet (four numbers)
The Corner Bet is somewhere in-between the least volatile and the most volatile type of roulette bet, which makes it more balanced. This should also be noticeable by looking at the results from my simulations, as shown below.
| Bet size | % of total winners | Winners leaving with $100-$200 | Winners leaving with $200-$500 | Winners leaving with $500-$1k | Winners leaving with $1k-$5k | Winners leaving with >$5k | Average cost |
|---|---|---|---|---|---|---|---|
| 1% | 39.7% | 39.4% | 0.35% | 0% | 0% | 0% | $2.7 |
| 2% | 34.6% | 29.3% | 5.15% | 0.09% | 0.002% | 0% | $5.2 |
| 3% | 28.8% | 20.8% | 7.2% | 0.74% | 0.09% | 0.002% | $7.6 |
| 4% | 25.7% | 16.1% | 7.7% | 1.5% | 0.31% | 0% | $10.5 |
| 5% | 20.2% | 10.9% | 7.3% | 1.58% | 0.54% | 0% | $12.4 |
| 10% | 7.8% | 3.5% | 2.2% | 1% | 0.8% | 0.0002% | $25.5 |
| 20% | 0.86% | 0.38% | 0.25% | 0.03% | 0.16% | 0.07% | $32.5 |
| 50% | 0% | 0% | 0% | 0% | 0% | 0.016% | $100 |
| Bet size | Players losing everything before finishing 30 spins | Players losing everything before finishing 50 spins | Players losing everything before finishing 75 spins | Players losing everything before finishing 100 spins |
|---|---|---|---|---|
| 1% | 0% | 0% | 0% | 0% |
| 2% | 0% | 0% | 0% | 0.23% |
| 3% | 0% | 0% | 0.03% | 0.63% |
| 4% | 0% | 0% | 0.45% | 2.9% |
| 5% | 0% | 0% | 2.3% | 8% |
| 10% | 0% | 12.6% | 34.6% | 52% |
| 20% | 34% | 67% | 87% | 95% |
| 50% | 98.5% | 99.9% | 100% | 100% |
The bets of 20% and 50% of the current bankroll are just too volatile in my opinion. Every single player who bet 50% of their bankrolls lost everything before reaching 100 spins. It’s a bit better for players who wager 20%, but it’s still too risky.
What’s interesting is the fact that the average cost for players wagering 20% of their bankrolls was lower than when betting on Color (the previous simulation), while the percentage of winners is also lower. This means that less players end up with a profit, but those who do win finish with much more money. Nevertheless, it’s still too risky.
The 10% bet size of the current bankroll seems interesting, but I think it’s still a bit too risky. Only 48% of players make it to the end (100 spins) at an average cost of $25.5, which is higher than the average cost for the same bet size proportion for players who placed their chips on red or black.
On the other hand, bets of 1%, 2% and 3% of the current bankroll have a very low chance of winning big. You are pretty much sure of making it to the 100-spin mark, but at the cost of sacrificing your chance or walking away with more than $500 or $1,000 (although a small chance still exists).
Best bet size to use
In my opinion, this strategy yields the best overall results when wagering 4% or 5% of the current bankroll in each game round. The results for these two proportional bet sizes are quite similar, but there are still important differences worth pointing out.
The average cost is a bit higher for the 5% bet, which is quite obvious considering that the players wager more money overall. The percentage of winners is also lower, at 20.2% for the 5% bet in comparison to 25.7% for the 4% bet. Of course, players wagering 5% of their bankroll in each game round have a higher chance of winning big.
What it comes down to is preference. If you wish to have a strategy with better RTP and a reasonable chance of earning a substantial win, choose the 4% proportional bet. However, if you would like to increase your chances of winning big (over $1,000, or even over $5,000), the 5% bet size will be better for you.
Bet size analysis and simulations #3: Straight Up (one numbers)
Let’s take a look at the most volatile type of Roulette bet, and how it combines with the Constant Proportion strategy.
| Bet size | % of total winners | Winners leaving with $100-$200 | Winners leaving with $200-$500 | Winners leaving with $500-$1k | Winners leaving with $1k-$5k | Winners leaving with >$5k | Average cost |
|---|---|---|---|---|---|---|---|
| 1% | 48.8% | 43.3% | 5.39% | 0.16% | 0.008% | 0% | $2.9 |
| 2% | 25.9% | 15.3% | 8.8% | 1.3% | 0.48% | 0.008% | $5.5 |
| 3% | 20% | 10.5% | 7.5% | 1.4% | 0.71% | 0.04% | $8.1 |
| 4% | 14.4% | 8% | 4.2% | 0.7% | 1.25% | 0.16% | $9.8 |
| 5% | 12.3% | 7% | 3.6% | 0.71% | 1.14% | 0.16% | $14 |
| 10% | 1.8% | 0.43% | 0.8% | 0.12% | 0.32% | 0.12% | $18.8 |
| 20% | 0.025% | 0.006% | 0.01% | 0.001% | 0.006% | 0.002% | $95 |
| 50% | 0% | 0% | 0% | 0% | 0% | 0% | $100 |
| Bet size | Players losing everything before finishing 30 spins | Players losing everything before finishing 50 spins | Players losing everything before finishing 75 spins | Players losing everything before finishing 100 spins |
|---|---|---|---|---|
| 1% | 0% | 0% | 0% | 0% |
| 2% | 0% | 0% | 0% | 9.2% |
| 3% | 0% | 0% | 14% | 22% |
| 4% | 0% | 0% | 19% | 36% |
| 5% | 0% | 0% | 36% | 52% |
| 10% | 0% | 61% | 79% | 91% |
| 20% | 76% | 93% | 99% | 99.8% |
| 50% | 99.9% | 99.99% | 100% | 100% |
Once again it’s pretty evident that the 50% and 20% bets are too volatile so, for this specific strategy, I would also add 10% bets to this category. Only 9% of players wagering 10% of their current bankroll in each game round get to play the full 100 Roulette spins, which is too low.
The players betting 1% or 2% of their current bankroll have a great chance of ending up with more money than they started with (48.8% and 25.9% respectively), but their chance of winning big is very low, which is why I prefer the slightly higher stakes in this scenario.
Best bet size to use
The sweet-spot for this specific strategy lays somewhere between the 3% and 5% bets. However, after taking a closer look at the results for players wagering 4% and 5% of their current bankrolls in each game round, it’s clear that the 5% bets are inferior to the 4% ones.
The players wagering 5% have a lower chance of winning in almost all of the categories mentioned in the above table, apart from the chance of leaving with $500 to $1,000, which is only 0.01% higher for the 5% bets. The 4% bets are superior in all other categories.
For this specific strategy, I would choose either the 3% or the 4% bets, with the comparison between each of them not being so one-sided. The players wagering 3% of their bankrolls lose less on average and have a greater chance of getting through the full 100 spins, but they also have a lower chance of walking away with more than $1,000.
So, if you want to have a bigger chance of getting into four figures, choose 4%. If you don’t "need" to win that much and you want to spend more time playing Roulette (on average), feel free to choose the 3% bets.
Conclusion and recommendations
The results of these simulations help to demonstrate the concept that higher volatility is better over the long-term, just as I mentioned in the main roulette strategies article. When betting on Color, bet sizes need to be high in order to have a realistic chance of winning big, but with players wagering more money in total and therefore losing more money on average.
This is why I wouldn’t choose the Color Bet. In my opinion, if you really like betting on red or black, the best bet size is 10% of your current bankroll, but I think you would be much better off wagering your money on Corner or Straight Up bets.
For players starting with $100 and seeking to play 100 game rounds max, the following options are the best in my opinion:
- Corner Bet – 4% or 5% of your current bankroll
- Straight Up – 3% or 4% of your current bankroll
The Constant Proportion strategy is just one of the many strategies I present in my main article on roulette strategies. There are also other good strategies you can use which might be more suitable for you and your preferences. Be sure to check them out before making a decision on how to play Roulette, and whether to play it at all.
