Constant Proportion Roulette Strategy

The Constant proportion strategy consists in wagering a certain percentage of your current bankroll in each roulette spin you play. That means the bet sizes will change, but their proportion 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 using my thorough simulations, so that you understand how these factors influence the chance to win in roulette.

• What is the best types of bets to place?
• What bet sizes should you use to maximize your chances to win?
• What are your chances to win big by wagering the percentage of your current bankroll bet over and over again?

Note: This article is focused solely on the Constant proportion strategy. In the main article on roulette strategies, I talk about other strategies that might be better for you. The main article also contains important information needed to understand this one completely, so it’s definitely a good idea to read it before getting to the specifics of the Constant proportion strategy.

How the Constant proportion strategy works

The Constant proportion strategy is very similar to the Constant bet strategy, but it has one more element to it. When using the Constant bet strategy, the bet sizes remain the same whether the player is doing well or horribly. On the other hand, the Constant proportion strategy has variable bet sizes that chance depending on the previous results.

So, if the player is doing well and winning, his bet sizes will keep rising, allowing him to win even more. If he is losing money, his bet sizes will slowly decrease, which means he will not as quickly as he would should he be using 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

Just so that everything is clear, I will include 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. He starts with \$100 and places a bet of \$10 on red. If he wins, he will have \$110 and he will place \$11 in the following game round. If he loses, he will only have \$90 and will place a bet of \$9 in the following round. He will keep doing this until he runs out of money or decides to stop playing.

Just as the Constant bet strategy, the Constant proportion strategy is also about finding a balance between:

• High volatility – big possible wins but also a big chance to lose everything quickly
• Low volatility – smaller possible wins but also a smaller (or non-existent) chance to lose 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 number Straight up and most likely lose everything in just one spin, or you could bet 1% of your bankroll on red or black, causing you to just fluctuate around your initial bankroll, with a higher chance to end up with less than your initial bankroll.

Logically, the best possible scenario will be somewhere in between and I will use my simulations to find it.

Bet size rounding and minimum bet limits

There are two potential issues that need to be addressed. Obviously, when betting a fixed proportion of the current bankroll, the numbers will not always stay "nice". If you can’t place exactly as much as you should place according to the calculations, just round your bet size up or down to the nearest amount you can place.

If you are unlucky and your calculated bet size is lower than the minimum bet of the roulette table you are playing at, just place the minimum bet instead. I used this approach in my simulations as well.

Simulations of the Constant proportion strategy

Thorough simulations are the best way to really see how the strategy works and how little changes in your playstyle can cause big differences in the expected results. I’ve used simulations to test multiple bet types used in the Constant proportion strategy and discover the optimum bankroll proportion to wager in all of them.

Methodology and used variables

All simulations were made using my own carefully designed simulation software with rules, probabilities and payouts of single zero roulette without any special rules (like En Prison or La Partage) in use. If you play classic European roulette, your results should be in line with those from my simulations.

The players have a starting bankroll of \$100 and behave like this:

• They place the same type of bets (Color, Corner or Straight up) over and over again, but with a variable bet size.
• The bet size is calculated as a fixed proportion of their current bankroll rounded up to the nearest \$1.
• The minimum bet was set to \$1. If the calculated bet size is lower than \$1, they place a bet of \$1 instead.
• The players play until they’ve lost their entire bankroll or until they’ve played 100 through 100 Roulette spins.

Regarding the types of bets, I considered all of the alternatives and decided to use these in 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)

For each of the bet types mentioned above, I tested various bankroll proportions to wager in each game round, ranging from 1% to 50%.

As I already mentioned, the starting bankroll is \$100, but other starting values should bring similar but not identical results. This is because of the minimum bet limit of \$1 I use in my simulations. Higher bankrolls will be affected by this less, while smaller bankrolls will be affected more. If the minimum bet rule wasn’t in place, any starting bankroll should yield statistically identical results.

I’ve tested a million player sample in all of the simulations. This sample size should make sure the results are statistically reliable results, but some statistical deviations might still be in place. That being said, they really shouldn’t significantly influence the results.

Bet size analysis and simulations #1: Color (red or black)

I’ll start the analysis of the simulation results by taking a look at players wagering their money on the Color bet (red or black). This is the least volatile option, which should be noticeable when compared 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%

Right from the start, you can clearly see that betting 50% of the 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, which makes this bet size has a very bad value for the player. Only 0.137% of players end up with more money than they started with.

The players wagering 20% in each game round have a much higher probability of making it to the 100-spin mark. Almost 75% of them actually gets to play 100 spins. The chance for a big win is quite nice, however, the average cost is \$42, which is a bit too much.

On the other side of the spectrum, the players betting 1% to 4% of their current bankrolls have a 100% chance to play the full 100 spins, however, their chance to win big is just too low. It’s a bit better with a 5% bet proportion, but I think it’s still a bit too boring because of a very small chance of winning big.

Best bet size to use

I find the strategy of betting 10% of the current bankroll in each game round the most interesting for this specific strategy. The players lost \$23.8 of their \$100 bankrolls on average, but they have quite a nice chance to win amounts around \$500 and even a small chance to win big, over \$1,000 or even over \$5,000.

They have a nice chance to win big, and they 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 and 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 between the least volatile and the most volatile roulette bet, which makes it more balanced. That should also be noticeable from the results of my simulations, so let’s take a look at them.

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 betting 50% of their bankrolls lost everything before reaching 100 spins. It’s a bit better for players wagering 20%, but still too risky.

What’s interesting is the fact that the average cost for players wagering 20% of their bankrolls was lower that when betting on Color (the previous simulation), while the percentage of winners is also lower. That means that less players end up in a profit, but those who do simply win much more money. Nevertheless, it’s still too risky.

The bet size of 10% 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) and the average cost is \$25.5, which is higher than the average cost for the same bet size proportion of players placing their chips on red or black.

On the other hand, the bets of 1%, 2% and 3% of the current bankroll offer only a very low chance to win big. You are pretty much sure to make it to the 100-spin mark, but at a cost of sacrificing the chance to walk away with more than \$500 or \$1,000 (although a small chance still exists).

Best bet size to use

This strategy yields the best overall results, in my opinion, when wagering 4% or 5% of the current bankroll in each game round. The results for these two proportions are quite similar, but there are still important differences worth pointing out.

The average cost is a bit higher for the 5% bets, which is kind of obvious, as the players wager more money overall. The percentage of winners is also lower, at 20.2% for the 5% bets, compared to 25.7% for the 4% bets. However, players wagering 5% of their bankroll in each game round have, of course, a higher chance to win big.

So, what it comes down to, is your preference. If you want to have a strategy with better RTP and a reasonable chance of a substantial win, choose the 4% bets. However, if you want to increase your chances of a big win (over \$1,000 or even over \$5,000), the 5% bets will be better for you.

Bet size analysis and simulations #3: Straight up (one numbers)

Now, let’s take a look at the most volatile Roulette bet and its use 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%

Again, it’s obvious that the 50% and 20% bets are too volatile, but for this specific strategy, I would add 10% bets into 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 to end up with more money than they started with (48.8% and 25.9% respectively), but their chance to win big is very low, which is why I’d prefer the slightly higher stakes in this scenario.

Best bet size to use

The sweet-spot of this specific strategy lays somewhere between the 3% and 5% bets. However, after taking a closer look at the results of players wagering 4% and 5% of their current bankrolls in each game round, it’s clear that the 5% bets are simply inferior to the 4% ones.

The players wagering 5% have a worse chance to win almost in all categories mentioned in the table above, apart from the chance to leave with \$200 to \$500, 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, between which the comparison is not 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 have a lower chance to walk 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 nicely demonstrate the fact that higher volatility is better in the long term, just as I mentioned in the main roulette strategies article. When betting on Color, the bet sizes have to be high to have a realistic chance to win big, which means the players wager more money in total, which also means they lose more on average.

That’s why I wouldn’t choose the Color bet. If you really like betting on red or black, the best bet size to use is 10% of your current bankroll in my opinion, however, I think you will be much better of wagering your money on Corner or Straight up bets.

For players starting with \$100 and seeking to play 100 game rounds max, these are the best options in my opinion:

• Corner bet – 4% or 5% of your current bankroll
• Straight up – 3% or 4% of your current bankroll

However, the Constant proportion strategy is just one of the strategies I present in my article on roulette strategies. There are other good strategies to use, some of 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.

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