** I don't mean to clutter up this board, but I was having problems posting before. So I'm just going to post this again. **
Among the many other counter-intuitive scenarios that show up in the game of Roulette is the observation that: the more you try to cover the table, the less money you actually win.
While this may be obvious to some, perhaps even more surprising is the fact that: the less you try to cover the table, the more you actually win. What I'm talking about here is probabilities, not statistics.
Let's look at the most common scenario, and take that as our base point.
On an Even Chance bet, you have 19/37 chances of losing, and 18/37 chances of winning. This amounts to 51.35% of the time you can expect to lose, and 48.65% of the time you can expect to win. Notice I said "expect to lose," and "expect to win." The Law of Large Numbers says that, over an (undefined) extended period of time, all numbers will approach their expected occurrences - this is what is known as "Regression to the Mean." In shorter trials however, there is often a large disparity between how many times a number should show up (in terms of it's probability), and how many times it actually does show up - in other words the number of wins and losses can vary greatly. So in, say, 100 trials of flat betting on red, you may actually end up winning a dollar or two - but that isn't to be expected. What's to be expected is that you lose about $51 and win about $49 - and overall lose about $2 or $3 dollars per 100 trials.
Okay, so practically speaking, if I'm going to flat bet $1 on red for 100 bets, then I should expect to lose (at best) -$2. So my expected loss for a bet that covers about 49% of the table is -$2.
Now what about if I want to cover more of the table? What should I expect when I cover, say 2 of the Dozens? Well, if I put $1 on each of the Dozens and use a flat bet, then I am covering 24 of 37 spaces, which means I can expect to win 64.86% of the time - or about 65%. So 65 times out of 100 I should see a profit of $1. That leaves 35% of the time I'll lose... which means in that same 100 spins I'll lose $2 35 times. So my expected loss for 100 spins is ($2 * 35) - $65 = -$5.
Hmmm. Even though I've covered more of the table, my expected loss has now increased by $3.
And when I decide to cover more of the board, things only get worse.
When I cover 5 of the 6 lines with $1 each, I've used $5 to cover 30 spaces, or 81% of the table. Now if I flat bet those $5 for 100 trials, I can expect 81 wins of $1 each, and 19 losses of -$5 each. This amounts to +$81 - (19 * 5) = -$14 as my expected loss.
And if I bet $1 each on 11 of the 12 streets, I cover 33 spaces on the table which is 89% of the table. So with my $11 I can expect a win $1 89 times out of 100 trials, and lose $11 for 11 times. This equates to +$89 - ($11 * 11) = 89 - 121, or -$32 as my expected loss.
So do things get any better when I cover less than half the table?
When I flat bet on a single dozen, I cover 12 numbers with my $1, or 32.4% of the table. So in 100 trials, I can expect to win $2 32 times = $64. In that same 100 trials, I can expect to lose on 25 of those numbers, which is 67.58% or 68%. So 68 times I will lose my $1. Now my expected loss is 64 - 68 = -$4. Lower, but still not as low as an Even Chance Bet.
Okay, now I'll flat bet on a single line covering 6 numbers. So my $1 covers 6 of 37 numbers, so I can expect it to hit 16 times in 100 trials (6/37 = 16.21%). When it hits, I profit by $5. So 16 * 5 = +$80. Since I will lose on 31 numbers, they will come out 84 times in that same 100 trials (31/37 = 83.78%). My losses are -$84, and my wins are +$80, giving me an expected loss of -$4. Still almost twice that of the House Edge.
I'll save you the rest of the math and simply point out that covering 3 numbers (a street) produces an expected loss of -$4, 2 numbers (a split) produces an expected loss of -$10, and a single number produces an expected loss of -$25.
None of this looks any good, and none of these flat bets do anything to cut into the house edge.
The only bet I left out was the corner bet.
On a corner bet, I use my $1 to cover 4 of 37 numbers. So it covers 10.81% of the table, or about 11%. In 100 trials I can expect to win 11 times at $8 profit each, which is +$88. The other 89% of the time, I will lose my dollar. So my expected loss is +$88 - $89 = -$1.
-$1?
That's less than half the house edge of -2.7%.
It's still not a winning bet, unless my corner happens to win 11 times before it loses 89 times.
But what if I was only working with 36 numbers instead of 37? Honestly, the difference is only minimal, since 4/36 = 11.11%. So I should still expect my corner to hit 11 times with a profit of 8 dollars each to equal +$88, and I'll lose 89% of the time, so -$89 for an expected loss of -$1.
I realize that 10.81% is not 11%, but what else are we to do with that .81 but round it up? So yes, there is going to be some fluctuations. But still, it appears that this flat bet has cut the house edge by more than half.
I'm not sure what we can do with this information, but it is counter-intuitive to be sure - which is why I named this post as I did. I may just run a few hundred trials and see where it stands statistically, but as I see it, flat betting on a corner seems like a good way to not kill your bankroll. Maybe if we can siphon a few quick hits and move on...
Roulette cannot be beaten on the outside bets. It's about looking at the wheel, not the table.
OH yes and how do yo look at the wheel, its all the same , less you use a computer.
I have analyzed it and the mathematical point of view is certainly correct. Very Well nullified.
I would suggest an increase in the bet of 10% every 100 spins.
You bet in one corner for 100 spins if you are in deficit increases the stake of 10% from 1$ to 1,1$ for the next 100 spins and so on .... :yahoo:
Thank You
Pablo
This is incorrect.
I have just run 10 000 iterations of 100 spins and found the average loss per 100 spins, betting on a corner bet is -2.89 units.
The theoretical solution is simply 1*0.027*100 (Unit stake * house advantage * number of spins in trial) = 2.7 units
As you can see, the theoretical is close enough in this test. As you test more spins you will find the average result will get closer to the theoretical solution.
I also ran another 10 000 iterations of 100 spins on the even chance (High) and found that the average loss per 100 spins was -2.71 units
As you can see this is almost exactly what the theoretical value is (-2.7 units per 100 spins)
If the house edge is the same, then it does not matter if you bet one unit on an even chance, a dozen, or a corner. The expected result is the same, -2.7 units.
FIXED:
This is incorrect.
I have just run 10 000 iterations of 100 spins and found the average loss per 100 spins betting on a corner bet is -2.89 units.
The theoretical solution is simply 1*0.027*100 (Unit stake * house advantage * number of spins in trial) = -2.7 units
As you can see, the theoretical is close enough in this test. As you test more spins you will find the average result will get closer to the theoretical solution.
I also ran another 10 000 iterations of 100 spins on the even chance (High) and found that the average loss per 100 spins was -2.71 units
As you can see this is almost exactly what the theoretical value is (-2.7 units per 100 spins)
If the house edge is the same, then it does not matter if you bet one unit on an even chance, a dozen, or a corner for 100 spins. The expected result is the same: -2.7 units.
Luck of the Irish,
Excellent work on the testing. I have no doubt that they are correct. I probably could have saved you a lot of time and effort by pointing out that when I extend the session to 1,000 spins (instead of 100) the expected loss for this bet approaches and exceeds the house edge of 2.7%.
And no amount of testing is going to change that.
This is why I said I didn't know what to do with this information exactly.
If I play less than 100 trials, I still have to hope that I get 2 or 3 hits within about 10 spins to come out ahead, and then walk away.
As I approach 100 spins, I'm really relying on luck to hope that roulette "knows" enough about probabilities to figure out that it's supposed to give me 11hits in 100 trials.
Too bad roulette doesn't know probabilities.
The same is true with my "11% Solution", which I just posted about. If I play this "system" more than 100 trials, even though my expected wins ranges from +3 to +11, I still find myself crossing my fingers and hoping that roulette plays nice and gives me what I need.
So, it too is a hit and run.
But like I said earlier, it's a curious bet that does have potential...