K-man's pogo.com Informational Pages

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Roulette

Welcome to my informational pages for pogo.com's Roulette game. As with my other pogo.com pages, I will be concentrating on the odds of this game, and how to maximize the number of tokens you earn in the least amount of time.

Feel free to skip directly down to my roulette stats information if you want to.

Please note that when I talk about odds, win rate per hour or per day, etc., I'm talking about ON AVERAGE. In reality, you could have one really good hour where you win a good percentage of the time followed by another hour where you don't get a match at all! Also, when I use the phrases "coming up" or "hitting", what I am referring to is the "ball" on the roulette wheel landing in a space that matches a number or group of numbers on which you have placed a bet.

And, as a final introductory note, all the odds/math expressed in this article are assuming that pogo's roulette table is a fair table (that each number will come up an equal number of times in the long run). I have every confidence that the games at pogo are truly random. See below for more information on the true-ness of pogo's roulette wheel.

Roulette in a Casino

Here's how normal (casino-style) roulette works:

A roulette wheel contains 37 numbers, 1 through 36 (half of these numbers are "red" and half are "black") and 0 (green). Gamblers can place bets on any 1 number, several numbers, or any of numerous groupings of numbers such as red or black, odd or even, groups of 2, 3, 4, 12, etc. numbers. When the wheel is spun, if the ball lands on a number in one of the areas you have placed a bet, you will receive appropriate winnings based on the odds of that number or group of numbers coming up.

The casino makes money off of roulette in the long run, because the pay tables account for only 36 numbers, and don't include the "0". In the long run, for every $37 dollars bet at the roulette table, the casino will pocket $1 (this is how casinos make money, by offering odds that are slightly in their favor).

pogo.com's Roulette--how it compares to a casino

But, as usual, pogo.com wants its patrons to win tokens, and as such the pogo roulette wheel is skewed slightly in favor of the player. The way that pogo does this in roulette is they include 5 extra spaces on the roulette wheel. These spaces are known as "big shot" spaces and they are colored blue. When the ball lands on one of these spaces, players' winnings are multiplied by a random "big shot multiplier", like times 2, 3, 4, 5, or 10 or even more than 10 times if several big shot spaces are matched consecutively. Note that consecutive Big Shots are additive and not multiplicative (hence a 2x big shot followed by a 3x big shot makes a total of a 5x big shot, not a 6x big shot).

The important thing to understand here is this: the big shot winnings multiplier applies ONLY to your winnings on a spin (the amount that is returned to you MINUS your original bet). Therefore, for the most part, betting on anything other than single numbers is a losing strategy in the long run. For example, always betting on "red" is a losing strategy in the long run on any roulette table, and on pogo.com you will not win any of the big shot bonuses just by betting on "red". However, the existence of the big shot spaces does mean that in the long run, the game has a positive expectation (you will win tokens over time) if you make bets where the amount returned to you exceeds your original bet.

Players can bet anywhere from 1 token to 100 tokens. Because this is a positive expectation game, I highly recommend betting the maximum on each spin of the wheel, whether you put all your 100 tokens on one number or spread them out over many numbers. But remember--you should not place any bet on anything outside the main numbers grid to take fullest advantage of the big shot bonus multipliers. If, for example, you wanted to bet each of the lower-most 18 numbers, DO NOT place your bet on the area marked "19-36". Instead, you should place an individual bet on each number (or group the numbers inside the number grid)

How Big Shot Bonus Multipliers work

Disregarding the big shot bonuses, the payouts for each number (or grouping) are the same as in a casino: a single number has a payoff of 35 to 1. However, pogo's big shot bonus multipliers apply only to what you WIN on a particular spin, rather than what is returned to you. This is important. For example, if you bet your entire 100-token maximum bet on a single number and you hit that number, 3600 tokens are returned to you, but your actual winnings on that hand are only 3500 tokens (the 3600 that was returned to you, minus the 100 you originally bet). So, if you were betting 100 tokens on a single number and a 2x bigshot came up just before your number, your winnings on that spin would be 7000 tokens. Similarly, if you hit a 2x bonus, then hit a number on which you have only bet 10 tokens (and you have bet the other 90 tokens on various other numbers), you'll win 520 tokens (that is: you receive 360 tokens back, but only 260 of those tokens are considered "winnings", and therefore the bonus multiplier of 2x in this instance gives you total winnings of 520 tokens).

The reason this is important is because if you want to maximize your winnings in this game, you will want the big shot bonuses to apply to the maximum amount of tokens. So, for example, if you were betting a single number and the "moon shot" bonus of 10x came up just before your number, you would win 10 times your winnings, or 35,000 tokens. But if you instead were betting 50 tokens on two different numbers and that same 10x moon shot came up, you would win (((36 times 50) minus 100) times the 10x bonus multiplier) or 17,000 tokens. If you do this twice (you'll hit one of two numbers about twice as often as a single number), you'd win 34,000 tokens instead of the 35,000 you'd win hitting a moonshot with a single number.

It is a matter of logic, therefore, that tells us that the way to maximize our winnings at this game is to simply always bet 100 tokens on a single number rather than spreading those 100 tokens over several numbers. But there are other factors you may wish to consider when making your bet!...

The Human Factor

However, there is a human factor at work here as well. I believe that it is human nature that we like to see a match on a number we have bet after a big shot bonus occurs. Since there are 5 big shot spaces on the wheel (out of a total of 42 spaces), one of these will hit approximately once out of every 8 spins. And if you are betting only a single number, which itself has only a 1 in 37 chance of coming up, you'll therefore combine your winning number with a big shot approximately only once every 300 spins (approximately once every 5 hours of playing time). And, the big shot that you've waited for for 5 hours might only be a 2x bonus, not 10x or more. Most of us are not patient enough to wait that long for that small of a chance at hitting such a bonus.

It's very important to keep in mind here that without the big shot bonuses, this would be a negative expectation game, just like it is in the casinos (that is, you'd lose tokens in the long run). You can play on average approximately 65 spins of the wheel per hour on pogo. If there were no bonus spaces (that is, if the wheel was the same as it is in a casino), and we were betting the maximum 100 tokens, we could expect to LOSE on average about 176 tokens per hour, or about 4200 tokens per day. So the only hope for us to gain an advantage and win tokens at this game is to wait for the bonus numbers to hit and hope that we have some tokens bet on the number that follows a bonus.

So if it's human nature that we like to match a number we have picked after a big shot bonus occurs, then what can we do to guarantee that we hit a lot of big shots? One way to ensure that you will always have the post-big-shot number chosen is simply to bet a single token or two tokens on all 37 numbers, right? (Note that it is not possible to bet three tokens on every number since we are restricted to a maximum bet of 100 tokens on each turn.) Unfortunately, we need to remember that big shot bonuses apply only to our winnings and not to the number of tokens returned. So if we bet 1 token on every number, we'll be betting 37 tokens. We are guaranteed to get 36 tokens returned to us on every spin of the wheel, but since the big shot bonus multiplier is applied only to our winnings (return minus original bet), we do not gain any tokens with big shot bonuses in this situation. In fact, betting 1 token on every number guarantees that we will lose exactly 1 token on every spin of the wheel. Luckily, pogo does the "right" thing when a big shot occurs--they do not penalize us more than the 1 token we lost!

What if I lose all my tokens?

There is another factor worth mentioning here which is the possibility that you will go bust (lose all your tokens). The chance that you will go bust before you win enough tokens to keep you afloat depends on the total number of tokens you start with (you share your roulette bankroll with other pogo games--more tokens means less chance of going bust) and how you bet (betting more numbers with lower token bets on each is less of a risk for busting than betting all 100 tokens on a single number which may not come up for a long time). However, on the pogo.com site, if you lose all your tokens, pogo will automatically give you 50 more tokens to start out again. The bust factor is therefore somewhat insignificant here.

There is one more related factor that could influence how you bet. Odds are odds, and they do dictate that in the long run, if you do choose to bet a single number, you will hit that number once every 37 games on average. However, it is actually possible that if you bet a single number, you could go for quite some time--maybe even an entire day--without ever seeing that number come up at all, let alone seeing it come up after a big shot bonus. You are more likely to have a long streak of no matches if you bet on a single number than if you bet multiple numbers. If this concerns you, you should definitely consider betting lesser tokens amounts on multiple numbers.

So, to try to maximize the chance that we will take advantage of a big shot bonus multiplier, while also maximizing the number of tokens applied to such a bonus, we might want to spread out our bets on several numbers rather than betting our entire 100-token maximum bet on a single number. Regardless whether you bet a single number all the time or whether you bet multiple numbers, you do always want to bet the full 100 tokens (since this is a positive expectation game!).

But how do we figure out what is the "right" number of numbers for us each as individuals to bet? This is where the human factor comes in. If you are the kind of person who is patient and likes taking risks in hopes of hitting a big single bonus payoff, you will probably want to bet all of your 100-token bet on a single number. If you prefer to win bonus tokens more frequently but with lower payoffs, you should spread your bet among several numbers. If you're interested in just seeing your total token count go up slowly but steadily, I might suggest that you make 5-token bets across 20 numbers. In doing so, you'll hit your numbers frequently and you'll take advantage of many bonus multipliers, but the overall payoff will be low.

Numbers and Graphs and Stuff

It's worthwhile to take a bit of a closer look at some of the numbers associated with these different betting strategies Here's a table showing outcomes of different betting strategies (information about this table is under the table):
Tokens/Bet #'s covered win amt. Hit % BSM's/day TW/hour TW/day
5 20 80 54.1% 100.4 828 19,872
10 10 260 27.0% 50.2 1,456 34,944
20 5 620 13.5% 25.1 1,769 42,456
25 4 800 10.8% 20.1 1,832 43,968
50 2 1700 5.4% 10.0 1,958 46,992
100 1 3500 2.7% 5.0 2,020 48,480

Interpreting the table: originally I had included win amounts for various big shot bonuses (2x, 3x, etc.) but the table got pretty wide so I have excluded these--but calculating them is straightforward. Also note that I've included only 6 possible betting strategies. Note that these are not exhaustive--there are many more ways that you can spread your 100-token maximum bet across various roulette numbers, but I think the table above represents the most common bets.

The data in the table assumes the following: we assume an average of about 65 spins of the wheel per hour (in reality, this number is somewhere between about 60 and 70 or so. The reason it varies is because it takes longer to play a game in which one or more Big Shots come up than it does a game where no Big Shot comes up). Betting the max at 65 games per hour represents risking 6500 tokens each hour, (or 156,000 tokens per day!). The frequency of a big shot occurring is 5 out of 42 spins (5 big shot spaces on the wheel out of 42 spaces total), or 11.9%. I assume an average big shot win is a 4x. (some data I've obtained recently leads me to believe that 4x is a reasonable number to use as an average big shot multiplier. The last 2 columns above are based on this 4x average big shot win. And finally, I assume in the tables above that if we were playing in a casino with no big shots in sight, we'd lose on average about 176 tokens per hour or around 4200 per day. (Again, this is ON AVERAGE, according to the odds of the game).

The table's 7 columns (all of the following represent a total bet of 100 tokens):

  1. Column 1 represents the number of tokens per bet (that is, the number of tokens you have placed on each of your selected numbers)
  2. Column 2 represents how many numbers you've covered. Column 1 times column 2 should always equal 100 tokens
  3. Column 3 represent the win amount if the wheel matches any one of the numbers you have covered. Note that this amount is the amount you received back minus the amount of your original bet, and is only for full 100-token bets
  4. Column 4 represents your hit percentage--that is, the percent of the time that you will hit one of the numbers you have covered.
  5. Column 5 represents the average number of times per day that your bet will coincide with a Big Shot multiplier. So if you like seeing lots of Big Shot multipliers (with only fairly small wins), you should play 20 numbers of 5 tokens each, and on average you will hit a number with a Big Shot about once every 15 minutes or so.
  6. Column 6 represents the average number of tokens you can expect to win per hour, assuming the average Big Shot multiplier is a 4x.
  7. Column 7 represents the average number of tokens you can expect to win per day, assuming the average Big Shot multiplier is a 4x.

Finally, I present you with the following graph:

image of roulette game

The graph above is a simple representation of column 6 of the table above. (If you're still awake at this point and you're paying attention, you'll note that I have interpolated some of the data to get a smoother curve--however, interpolating the data required the addition of some nonsensical real-life data, such as betting 15 tokens each on 6 and two-thirds numbers, which is impossible in real life of course).

The X axis represents the number of tokens bet per number covered (multiply by 5) and the Y axis represents the average number of tokens won per hour, assuming of course a 4x big shot is hit. We end up with a logarithmic graph, one that clearly shows that the fewer numbers you bet the greater your overall winnings.

But another way to think about the graph is from a "human factors" standpoint. We see that as the number of covered numbers decreases, we do indeed have a higher hourly win rate. However, the win rate only increases logarithmically. So while betting all of our 100 tokens on a single number gives us an hourly win rate almost two and a half times better than if we bet 20 numbers with 5 tokens each, the hourly win rate is only about 15% better than if we were to bet 5 numbers with 20 tokens each. And since we'll see 5 times as many "big shot" wins by betting 5 numbers instead of 1, you might be more inclined as an individual to do so.

Closing notes--how fair is pogo's roulette table?

(Note: for more information on the random-ness of all the games at pogo, you can check out my fairness web page.

Many gamblers, and many roulette players in particular, often base their betting or choice of numbers on instinct. That is, they may feel that certain numbers or groups of numbers (like red or black) are "hot" and are therefore more likely to "hit".

However, as I discuss in other areas of my pogo pages, I have every reason to believe that all of pogo's games are truly random, and are not "fixed" in any way. In other words, as this relates to roulette, I have every reason to believe that whenever the pogo roulette wheel is spun, the results of the spin will be truly random--each of the 42 spaces will come up once on average every 42 spins.

As a recent exercise, I did keep track of the numbers that came up for a couple straight hours. This accounted for about 250 data points that I kept track of. In this data, I did note a couple things that seemed not random (and therefore unexpected) to me:

Take this information with a grain of salt. My sample size was ridiculously small, and from personal observation, pogo seems to make all their games perfectly random.