# Dart Roulette: Probability, Odds, House Edge, Payouts, Strategy, Systems

Written by Ion Saliu on October 15, 2001; later updates.

I receive quite often messages on various games. People ask me for systems, free if possible. It is all right for anybody to ask me for a freebie first. Of course, if I reply NO, then insisting has no effect.

After my newsgroup postings on the bureaucratic odds I received more messages on my software and systems. The “trigger” was my usage of the Fundamental Formula of Gambling (FFG) and how random numbers repeat. FFG undeniably shows that in 50% of the cases, the numbers repeat after a number of tries (draws, spins, hands, tosses, etc.) LESS THAN or EQUAL TO the probability median. The probability median is calculated as the number of trials N for a degree of certainty DC = 50%.

Furthermore, FFG shows that only a limited number of favorable outcomes show up within total number of possible outcomes. I used two examples in my posting: roulette (straight-up bet) and pick-3 (straight combination). Math-savvy readers realize that the repeat bias calculated by FFG can be of sizable advantage to the player. Accordingly, some ask me for a sure-fire winning system. I received an interesting message on…dart! I never played that game. It seems that dart can be used as makeshift roulette! Here is the message that presents an amazingly ingenious game:

"Every night at our local bar there is a great gambling game that I think that you might beat, and it has something to do with wine (well, almost). Every night someone volunteers from the crowd to get "drunk" (he has to sign that he is doing it at own risk and that there will be someone to drive him home safely). After he had a couple of drinks, he has to blow into one of those alcohol testers that the police use. So when he is finally credited as being drunk enough the gambling starts. The Drunk has to throw a dart onto the dartboard and whichever number he throws is the winning number (regardless the 'double' and 'triple' feature on the dartboard).

The payouts are fair, meaning 1 to 19 (there is only 20 numbers) and the only house advantage that the bar has is when the drunk throws an outer or inner bull, then all the bets lose. But I mean the surface area of the bull in relation with the rest of the board is so small that I think it really doesn't matter.

One disadvantage is that you may bet no more than 10 bucks on one number. (There are no chips you just bet anything from 1 buck-10 bucks on a number) You may bet on more than one number if you want to but the maximum still stays 10 bucks per number {in other words if you bet on 5 numbers you may not pay more than 50 bucks}. Do you think it can be beaten? What's the mathematics towards this? Can you say that most of the time the numbers below the bull will come up because when your drunk you lack power in your throw.

By the way the session usually lasts for only 40 minutes (until the poor man becomes soberized) and there are usually 2 throws a minute.

And ALL the best of luck to all."

I analyzed more thoroughly both real life roulette spins and real pick-3 draws. The results are even more favorable to the player then I had thought. Initially I thought that around 692 unique (distinct) pick-3 combinations will show up within the previous 1000 lottery draws. (There are 1000 total possible or probable outcomes in the pick-3 lottery.) Unquestionably, all pick-3 combinations have the same probability p=1/1000. FFG takes into account this very important factor, p.

Nevertheless, FFG demonstrates that the pick-3 combinations repeat irregularly, despite their equal probabilities. I have a large database of pick-3 draws (over 3000 in Pennsylvania lottery). I used the LotWon report generator (SUPER3) and the combination generator (POWER-3). The pick-3 straight-up bet is designated as TOT or Total in LotWon. If I set MAXIMUM_TOTAL_1 to 1001 in POWER-3, the program will generate only combinations that came out in the last 1000 draws.

Traditionally, users expect a number of 1000 distinct combinations, since the combinations have an equal probability, 1/1000. On the other hand, I thought previously that only 692 unique combinations would be generated. The results are even better from a player's perspective. Consistently, only around 630 combinations are generated! It makes sense! Some combinations will repeat more than once! Thus, FFG can be used one step further. Among the 692 combinations more likely to repeat (the 1st step of FFG), some will repeat again, and probably again (the 2nd step in FFG). The difference 692 – 630 = 62 is represented by multiple-repeat combinations.

I put together all my roulette software, systems and strategies in a comprehensive package named BrightR. The winning roulette systems, strategies and software are free at this website with a (nominal) paid membership fee to download them all.

## Roulette: Software, Systems, Super Roulette Strategy

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