"You're making it sound like betting $799 to win $1 is a really good bet. Will all your probabilities help you pay off a $5000 bet at 799 to 1 odds?"
This sentence makes it clear that you don't intend to use logic, you're just here to argue with everything I say. I obviously would never take a 5000 dollar bet. The lottery can, because there pockets are deep enough to take losses if a huge bet has to be paid off. And some lotteries still restrict sales on individual numbers to prevent these giant swings, but they still have a giant edge. Personally I don't think that the caps need to be anywhere near as low as they are in some states, but that's their decision.
"My first post on LP questioned why an Online lottery site would pay $900 to 1 when any player is getting 3 to 2 odds by betting $1 on 600 numbers. It's exactly the same as Free Odds bets on the 5 and 9 on any Crap table. The casinos pays even money on Pass Line bets that favor the house by 3 to 2 while the Online sites were paying 50% more on virtually the same type of bet."
It's not the same bet as free odds. I did the math for 5/9 on the the Pass Line's odds/payouts and the example you gave, (If you meant the don't pass, the math would be reversed, but have the same answer.) and as you can see below, the pick 3 bet has a house edge while the odds on craps don't. And the math behind the pass line is more complex than that, and casinos do allow odds bets. It appears you don't know how to play Craps.
Odds on 5/9 in Craps, you have a 60% chance to lose 2 units, and a 40% chance of winning 3. (note that you have 3 AND your original 2) The math is expressed as (-2*.6)+(3*.4)=0. The expectation is that you'll break even in the long run. (Short term luck is what makes these games entertaining, but that's the math) If you placed this bet with your described 600 dollars, then winning will pay you 900 AND you keep your 600.
On the Pick 3 bet, you will have a 60% chance to gain .5 unit, and a 40% to lose 1. The math is ((.5*.6)+(-1*.4))=-.10, giving the house a 10% edge.
"By betting $1 on five different numbers, a pick-3 player is getting a 0.5% chance of winning $500. By betting $5 on one number another player is getting a 0.1% chance of winning $2500. The implications are simple, by taking a slightly less chance and 0.004 is a slightly less chance, the second player can win $2000 more."
This is an interesting comment, in that what you're stating is obvious, but not thought of by too many gamblers. If you're hope is to win big, and you're playing against a negative expectation game, the best chance you have is take whatever budget you have and play for a single shot to score big rather than many shots to score relatively small. This isn't an investment strategy I would recommend, and personally, I don't find the Pick 3 any more entertaining than I'd imagine picking a random stock would be.
"It's easy enough to figure the probabilities of any three digit number being drawn in the next 1000 drawings, but the results of the last 1000 drawings show many of the three digit numbers weren't drawn and several were drawn multiple times. Why is it your probabilities never match the facts?"
I have tried to explain standard deviation (variance) to you in the past, but I will leave it at that. Variance.
As for your criticism of Jimmy's simulation, you have to realize that it's intention is to show that if you play for many years, you are very unlikely to be ahead. If the game had 0 house edge, you'd be just as likely to be ahead by 1000 as down by 1000. But because there is an edge, and because it is so huge, there is a giant disparity in the number of winners and losers, and the amount they won or lost.
There are many other simulations you can do based on betting strategies and the like. Having studied the effects of variance a decent amount in my free time (mostly in pursuit of understanding how to manage risk) I can tell you how individual strategies are likely to look on a similar chart, but I can also tell you now that introducing elements like rising bets, or bigger bets is going to create a few more winners, and way more - bigger losers. It makes you more likely to win, sure. It also makes you way more likely to lose more quicker. Mathemetically, all your bets only have the SAME edge, but in reality you are betting it quicker and with more variance. I'm not gonna say that's wrong, since I actually think if you have X bankroll and you have to play a game like Pick 3 until you lose it or win Y amount, the best way to achieve it is probably to bet big, assuming Y is large compared to X. But since that's a pretty unrealistic and strange hypothetical, I'd recommend to people that the Pick 3 is really a waste of time unless you find it really fun, and worth the cost of a ticket.
"Betting the Field in Craps is a bad bet and betting the "2" and/or "12" are the worse bets on the table, but I saw a guy starting with $100 while I was rolling the dice, parlayed enough in winnings by making those bets to make a $500 bet on the "12" and win $15,000. We all know the probabilities and the odds and so did the Pit Boss, but he still had to explain that huge loss to his bosses."
Just because you saw something once doesn't matter. Obviously people wouldn't gamble if variance didn't allow them to get lucky sometimes and win. I'm sure the Pit Boss wasn't blaimed for anything, as long as there was no cheating involved they're fine. Casinos know there are possibilities of big losses, but they are more likely to win than lose so they don't care. And most gamblers keep on gambling against that edge after winning big, often moving up in stakes. So they actually like many people who win big, because so many of them are "free" advertizement in that they give it all back.
"it's possible with a betting strategy to profit much more from the unexpected."
No, it's not, because the probabilities of any betting strategy can be quantified down to it's probabilities in any number of draws. It's all mathemetically solid. I don't know quite how to put this - if something is unlikely doesn't mean it's impossible. It means that it's only going to happen to X amount of people. In the Pick 3, which was the example I originally used because it's easier to demonstrate the point, you can calculate (because that's insanely taxing, most people use simulations instead) the probabilities of anything happening with any betting strategy. And no strategy has ever outperformed the mathemetical edge. Perdiod. Some have made it more likely to win any amount at the risk of losing larger, and vice versa. NONE have ever changed the edge.