9/6 Double Double Bonus
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Re: 9/6 Double Double Bonus
alpax, not sure why anyone would give you flak for providing useful info, thanks for doing so.
I just don't see how you could interpret Dancers comments (I assume that is the "anyone") as flak.
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[QUOTE=notes1]
I just don't see how you could interpret Dancers comments (I assume that is the "anyone") as flak.
apparantly you missed his comments earlier in the year, where a poster mentioned his wife had won a good size amount. dancer proceeded to berate her for not playing properly. they did ask for assistance, he just felt compelled to point out her less than stellar play. and, he has done this numerous times, in a demeaning manner. i have stated many times that he is obviously well qualified to offer advice/assistance, but the manner in which he offers it has a lot to be desired. if you want to accept it, go ahead, not me.
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apparantly you missed his comments earlier in the year, where a poster mentioned his wife had won a good size amount.
I was not aware that your post was referring to something in the distant past. It appeared to me that your comment was in relation to Dancer's comments, immediately previous to yours, on the excellent analysis of the distribution of results in 9/6 DDB provided by Alpax.
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[QUOTE=notes1]
apparantly you missed his comments earlier in the year, where a poster mentioned his wife had won a good size amount.
I was not aware that your post was referring to something in the distant past. It appeared to me that your comment was in relation to Dancer's comments, immediately previous to yours, on the excellent analysis of the distribution of results in 9/6 DDB provided by Alpax.[/QUOTE]
my comments on this thread were nothing but positive toward alpax and i made no mention of dancer at all. you do not have to go too far in the past, to find a number of his demeaning comments.
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Interesting analysis, Alpax. The more you study these things, the more knowledgeable you'll get. And you'll understand it better when you write it up for others to look at. Keep it up!One thing is clear --- the "long run" is longer than 500,000 hands, at least for volatile games like DDB.
For certain I do know more today than I did yesterday about the game of DDB, which is the most popular game in most casinos (at least every one I have been to). I am aware 500,000 hands or roughly 12 royal flush cycles is a very low estimate compared to what the long run actually is. Every hand in video poker is an independent event, so confidence intervals (must be at least 25 royal cycles, but the more the better) and bell curves are used to get a range of estimates. The most alarming part is the potentially large bankroll that is required to withstand 500,000 hands of play. I am sure there are passionate members here that play well beyond the 500,000 hands in a shorter span. I do understand the reason you will not play 9/6 DDB unless if it is not accompanied by a gimmick like Ultimate X or Quick Quads. I will continue to study the game with 9/5 DDB, but I would expect the curve to shift more towards the negative, my assigned categories will be shifted, where the Best of the Best category gets eradicated and the Bankroll is Not Enough gets bigger.
alpax, not sure why anyone would give you flak for providing useful info, thanks for doing so. the difficulty for me, as a non math person, is to interpret all the data. my eyes get blurry just looking at it. i cannot remember the last time i played a quarter 9/6 DDB machine. would it be fair (asking for your opinion) to say that the higher the volatiity game and the lower the paytable, the more likely one is to lose money and lose it faster? another question, would it be a fair comparison to relate progressing from JOB to BP to DDB, the same as eating at home, eating at ponderosa to eating at ruth chris? one needs to account for the extra value/excitement one receives, when determining value.Â
The flak that I anticipate is potentially from the results that not many people will be willing to accept. I know DDB is a more favored game among our peers, but even at its greatest form available as "full pay" with one percent theoretical edge could result with a range of 4 percent loss to 2 percent win. Bottom like is some people can get unlucky and lose many thousands of dollars on a quarter game where the royal pays $1000 and aces with kicker pays $500.
<would it be fair (asking for your opinion) to say that the higher the volatiity game and the lower the paytable, the more likely one is to lose money and lose it faster?>
I would say so because you will play at a deficit nearly all the time until your bankroll is gone. The DDB lower than 9/6 is 9/5. You can eliminate the Best of the Best category. You will be very lucky to have minimal losses.
As far as the steak house analogy with DDB. I do not know of any Panderosa in the west coast, but I looked it up to be a budget restaurant. I do know that Outback steak house is available nationwide so I will use that as the middle ground. Ruth Chris is the higher end that is also available nation wide.
You can put it this way. You can go to a random Outback Steakhouse and by off chance you can get a lesser service/food for the price you paid, or you might get great service and food that tastes almost as good as Ruth Chris.
Do ask continue to questions about this result if you are not certain about something. I broke the results into different categories that I thought was reasonable for recreational players to understand.
For certain I do know more today than I did yesterday about the game of DDB, which is the most popular game in most casinos (at least every one I have been to). I am aware 500,000 hands or roughly 12 royal flush cycles is a very low estimate compared to what the long run actually is. Every hand in video poker is an independent event, so confidence intervals (must be at least 25 royal cycles, but the more the better) and bell curves are used to get a range of estimates. The most alarming part is the potentially large bankroll that is required to withstand 500,000 hands of play. I am sure there are passionate members here that play well beyond the 500,000 hands in a shorter span. I do understand the reason you will not play 9/6 DDB unless if it is not accompanied by a gimmick like Ultimate X or Quick Quads. I will continue to study the game with 9/5 DDB, but I would expect the curve to shift more towards the negative, my assigned categories will be shifted, where the Best of the Best category gets eradicated and the Bankroll is Not Enough gets bigger.
alpax, not sure why anyone would give you flak for providing useful info, thanks for doing so. the difficulty for me, as a non math person, is to interpret all the data. my eyes get blurry just looking at it. i cannot remember the last time i played a quarter 9/6 DDB machine. would it be fair (asking for your opinion) to say that the higher the volatiity game and the lower the paytable, the more likely one is to lose money and lose it faster? another question, would it be a fair comparison to relate progressing from JOB to BP to DDB, the same as eating at home, eating at ponderosa to eating at ruth chris? one needs to account for the extra value/excitement one receives, when determining value.Â
The flak that I anticipate is potentially from the results that not many people will be willing to accept. I know DDB is a more favored game among our peers, but even at its greatest form available as "full pay" with one percent theoretical edge could result with a range of 4 percent loss to 2 percent win. Bottom like is some people can get unlucky and lose many thousands of dollars on a quarter game where the royal pays $1000 and aces with kicker pays $500.
<would it be fair (asking for your opinion) to say that the higher the volatiity game and the lower the paytable, the more likely one is to lose money and lose it faster?>
I would say so because you will play at a deficit nearly all the time until your bankroll is gone. The DDB lower than 9/6 is 9/5. You can eliminate the Best of the Best category. You will be very lucky to have minimal losses.
As far as the steak house analogy with DDB. I do not know of any Panderosa in the west coast, but I looked it up to be a budget restaurant. I do know that Outback steak house is available nationwide so I will use that as the middle ground. Ruth Chris is the higher end that is also available nation wide.
You can put it this way. You can go to a random Outback Steakhouse and by off chance you can get a lesser service/food for the price you paid, or you might get great service and food that tastes almost as good as Ruth Chris.
Do ask continue to questions about this result if you are not certain about something. I broke the results into different categories that I thought was reasonable for recreational players to understand.
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Way too much math for me ... But this is my game of choice - Once you get used to DDB - it's kind of boring to play plain old Jacks... I must admit - I have been in a drought for the past 6 weeks... very hard on the wallet...........
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alpax, i think Bobbi's comment says a lot and there are many players who feel the same. and, those who are caught up in the math or believe there may be a way to beat the machines have a difficult time understanding this line of reasoning. one does not have to be a math expert to understand that lower paytables, games that only pay even money for 2 pair and pay more for some quads, have greater risk. and greater risk, typically equates to larger potential losses, but they do not care. playing VP is their entertainment, they allocate a certain amount of money for this entetainment and when it is gone, they stop. now, some try doing different things like less than max coins to extend their play, but in the end, most are smart enough to understand you cannot win, in today's market. while i never post, i often read mendelson's site and know you post there. alan is obviously addicted to VP, so much so, he started his own forum. he does not hold himself out as a pro, but certainly knows the game and trys to play the best paytables. recently, he posted that over all the years he has played and with everything he knows, he has NEVER had a postive year playing VP. how honest and refreshing! i give him great credit for stating the truth, when so many will never do so. the research you presented shows how much greater the risks are playing DDB, but many just accept it and play the game they like, not the most practical game.
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Wait, there's a site or forum where the owner is a video poker addict and he admits to always losing? Where can I read up on this?
Being addicted to the game, and who isn't, doesn't mean you have to be a loser either. While most losers have a lot of financial problems, a humiliating divorce or two that's probably their own nasty fault, or they may be generally grouchy, winning addicts probably spend a good amount of time asking themselves what happened to their life that it got so out of control and valueless.
I don't play a lot of vp, but when I do I enjoy it. I can't imagine going to and sitting at machines day in and day out. What a waste of life.
Being addicted to the game, and who isn't, doesn't mean you have to be a loser either. While most losers have a lot of financial problems, a humiliating divorce or two that's probably their own nasty fault, or they may be generally grouchy, winning addicts probably spend a good amount of time asking themselves what happened to their life that it got so out of control and valueless.
I don't play a lot of vp, but when I do I enjoy it. I can't imagine going to and sitting at machines day in and day out. What a waste of life.
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Way too much math for me ... But this is my game of choice - Once you get used to DDB - it's kind of boring to play plain old Jacks... I must admit - I have been in a drought for the past 6 weeks... very hard on the wallet...........
alpax, i think Bobbi's comment says a lot and there are many players who feel the same. and, those who are caught up in the math or believe there may be a way to beat the machines have a difficult time understanding this line of reasoning.
I understand people play out of recreation and accept the cost to play the game so I've stopped talking about how bad 9-5 DDB is on the Video Poker Stories section. I know most people are aware 1 for 1 on 2 pairs is likely a loser, but, I think there is a chance some people have learned from looking at the report that it is possible to come out a winner without worrying about the casino benefits that players can get. High variance games should not just be looked at by its number 41.9, it is also a long term outlook that reflects the game is truly a gamble!
I go with Jack or Better for most of my entertainment so that my entertainment costs are lower on average per trip. It is not a thrilling game to play to say the least, but I do still enjoy the game enough to keep playing it. I am used to Three Card Poker and Crazy 4 Poker table games which are slow and have higher odds.
I completed the analysis for 9/5 DDB based on the same premises earlier.
500,000 Rounds
Bankroll of 25 Royal Flushes
All hands played computer perfect
A. Bankroll Ruined (<96%) - 2.42% 1 in about 43 Players
B. Below Theoretical Edge
96-97% ($0.01-$240) - 13.59% - 1 in about 7 Players
97-98% ($240.01-$480) - 36.67% - 1 in about 3 Players
C. Above Theorectical Edge
98-99% ($480.01-$760) - 36.99% - 1 in about 3 Players
99-99.5% ($760.01-$880) - 6.44% - 1 in about 16 Players
D. Semi-Pro (with good comps, mailers, and cashback)
99.5-100% ($880.01-$1000) - 2.69% - 1 in about 37 Players
E. Outright Winners
100%-101% ($1000.01-$1240) - 1.16% - 1 in about 86 players
101% ($1240-$1280+) 0.05% - 1 in about 2000 players
There is still a slight chance to be a winner on 9-5 DDB, but for 8-5 DDB, it simply is not winnable. If I had the choice of 9-5 DDB for quarters or 9-6 DDB for dollars, it will be the 9-6 DDB, but it would mean a short session each visit.
alpax, i think Bobbi's comment says a lot and there are many players who feel the same. and, those who are caught up in the math or believe there may be a way to beat the machines have a difficult time understanding this line of reasoning.
I understand people play out of recreation and accept the cost to play the game so I've stopped talking about how bad 9-5 DDB is on the Video Poker Stories section. I know most people are aware 1 for 1 on 2 pairs is likely a loser, but, I think there is a chance some people have learned from looking at the report that it is possible to come out a winner without worrying about the casino benefits that players can get. High variance games should not just be looked at by its number 41.9, it is also a long term outlook that reflects the game is truly a gamble!
I go with Jack or Better for most of my entertainment so that my entertainment costs are lower on average per trip. It is not a thrilling game to play to say the least, but I do still enjoy the game enough to keep playing it. I am used to Three Card Poker and Crazy 4 Poker table games which are slow and have higher odds.
I completed the analysis for 9/5 DDB based on the same premises earlier.
500,000 Rounds
Bankroll of 25 Royal Flushes
All hands played computer perfect
A. Bankroll Ruined (<96%) - 2.42% 1 in about 43 Players
B. Below Theoretical Edge
96-97% ($0.01-$240) - 13.59% - 1 in about 7 Players
97-98% ($240.01-$480) - 36.67% - 1 in about 3 Players
C. Above Theorectical Edge
98-99% ($480.01-$760) - 36.99% - 1 in about 3 Players
99-99.5% ($760.01-$880) - 6.44% - 1 in about 16 Players
D. Semi-Pro (with good comps, mailers, and cashback)
99.5-100% ($880.01-$1000) - 2.69% - 1 in about 37 Players
E. Outright Winners
100%-101% ($1000.01-$1240) - 1.16% - 1 in about 86 players
101% ($1240-$1280+) 0.05% - 1 in about 2000 players
There is still a slight chance to be a winner on 9-5 DDB, but for 8-5 DDB, it simply is not winnable. If I had the choice of 9-5 DDB for quarters or 9-6 DDB for dollars, it will be the 9-6 DDB, but it would mean a short session each visit.
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I have continued the analysis of 9/6 DDB for 1 million and 2.5 million rounds. I am trying to conclude by providing a 5 million round analysis. I was not looking to do a 2.5 million round analysis, but after 800,000 rounds, the simulator starts slowing down probably due to the exponential calculations it must be doing. So I did a pause to do an analysis for the 2.5 million one, now I hope it will continue and finish reaching 5 million. This is for recreational players, I would predict most will not play 1 million, but playing 2.5 or even 5 million would be very noteworthy amounts.
A few different things have been adjusted from the 500k simulation provided earlier. The more you play the more bankroll it will require. The round number, the last digit to the right most is cut off, but it is 1 million and 2.5 million respectively.
I expanded the range of bankrolls to eliminate the RUINED situation to get a better understanding of the range of values.
60 Royal Flush Bankroll ($2400) for 1 million rounds. It will be $50,000 coin in so the bars representing $500 off of the vertical black line will represent 1% of the total return.
100 Royal Flush Bankroll ($4000) for 2.5 or possibly 5 million rounds. When the coin in is $125,000 for penny hands. $1250 will represent 1 percent return off the vertical mark.
Analysis #1 - 1 Million Rounds
Losses beyond double theoretical edge (96.4%)
0.15% About 1 in 700 players
Red Bar 1 $720.01-$800 0.02%
Red Bar 2 $800.01-$880 0.04%
Red Bar 3 $880.01-$960 0.09%
Below expected return with double theoretical edge (97-98)%
7.91% About 1 in 13 Players
Red Bar 4 $960.01-$1040 0.2%
Red Bar 5 $1040.01-$1120 0.4%
Red Bar 6 $1120.01-$1200 0.74%
Red Bar 7 $1200.01-$1280 1.29%
Red Bar 8 $1280.01-$1360 2.1%
Red Bar 9 $1360.01-$1440 3.18%
Below expected return 98-99%
46.02% Nearly half of the players
Red Bar 10 $1440.01-$1520 4.51%
Red Bar 11 $1520.01-$1600 5.99%
Red Bar 12 $1600.01-$1680 7.45%
Red Bar 13 $1680.01-$1760 8.7%
Red Bar 14 $1760.01-$1840 9.54%
Red Bar 15 $1840.01-$1920 9.83%
Above Expected Return 99%
25.76% About 1 in 4 Players
Red Bar 16 $1920.01-$2000 9.54%
Red Bar 17 $2000.01-$2080 8.71%
Red Bar 18 $2080.01-$2160 7.51%
Semi Pro 99.5%
14.19% About 1 in 7 Players
Red Bar 19 $2160.01-$2240 6.1%
Red Bar 20 $2240.01-$2320 4.69%
Green Bar 1 $2320.01-$2400 3.4%
Winners Circle
Outright Winner (100%+)
5.82% About 1 in 17 Players
Green Bar 2 $2400.01-$2480 2.34%
Green Bar 3 $2480.01-$2560 1.52%
Green Bar 4 $2560.01-$2640 0.94%
Green Bar 5 $2640.01-$2720 0.55%
Green Bar 6 $2720.01-$2800 0.31%
Green Bar 7 $2800.01-$2880 0.16%
Significant Winner (101%)
0.14%, About 1 in 700 players
Green Bar 8 $2880.01-$2960 0.08%
Green Bar 9 $2960.01-$3040 0.04%
Green Bar 10 $3040.01-$3120+ 0.02%
Analysis #2 - 2.5 Million Rounds
Still Unlucky (97.5% - 98%)
1.13% About 1 in 90 Players
Red Bar 1 $832.01-$936 0.01%
Red Bar 2 $936.01-$1040 0.02%
Red Bar 3 $1040.01-$1144 0.05%
Red Bar 4 $1144.01-$1248 0.09%
Red Bar 5 $1248.01-$1352 0.17%
Red Bar 6 $1352.01-$1456 0.3%
Red Bar 7 $1456.01-$1560 0.49%
Below Expected Return 98-99%
56.25%, About a little more than half the players
Red Bar 8 $1560.01-$1664 0.79%
Red Bar 9 $1664.01-$1768 1.21%
Red Bar 10 $1768.01-$1872 1.78%
Red Bar 11 $1872.01-$1976 2.49%
Red Bar 12 $1976.01-$2080 3.34%
Red Bar 13 $2080.01-$2184 4.3%
Red Bar 14 $2184.01-$2288 5.29%
Red Bar 15 $2288.01-$2392 6.25%
Red Bar 16 $2392.01-$2496 7.08%
Red Bar 17 $2496.01-$2600 7.69%
Red Bar 18 $2600.01-$2704 8.01%
Red Bar 19 $2704.01-$2808 8.02%
Above Expected Return 99%
34.34%, About a little more than third the players
Red Bar 20 $2808.01-$2912 7.7%
Red Bar 21 $2912.01-$3016 7.1%
Red Bar 22 $3016.01-$3120 6.3%
Red Bar 23 $3120.01-$3224 5.37%
Red Bar 24 $3224.01-$3328 4.4%
Red Bar 25 $3328.01-$3432 3.47%
Semi Pro (99.5%)
7.77% About 1 in 14 Players
Red Bar 26 $3432.01-$3536 2.63%
Red Bar 27 $3536.01-$3640 1.92%
Red Bar 28 $3640.01-$3744 1.35%
Red Bar 29 $3744.01-$3848 0.91%
Red Bar 30 $3848.01-$3952+ 0.59%
Green Bar 1 $3952.01-$4056 0.37%
Outright Winner (100%-100.5%)
0.69% About 1 in 145 Players
Green Bar 2 $4056.01-$4160 0.23%
Green Bar 3 $4160.01-$4264 0.13%
Green Bar 4 $4264.01-$4368+ 0.07%
Green Bar 5 $4368.01-$4472 0.04%
Green Bar 6 $4472.01-$4576 0.02%
Green Bar 7 $4576.01-$4680+ 0.01%
Conclusion
The 1 million rounds does not normalize too much off of the 500k simulation. The results are 2.2% within theoretical return. 96.8 - 101.2. A handful of people can still win outright.
The 2.5 million round simulation really normalizes things but still falls short of reflecting what the "long run" is. Results are within 1.5% of the theoretical return. The people who win outright are VERY FEW, a fraction of a percent.
For both curves, it reflects the vast majority ~85% being within 1% below the theoretical return of 98.9808%. It would take an anomaly to be more than 1 percent off.
I will have concluding remarks if I am able to reach 5 million rounds.
A few different things have been adjusted from the 500k simulation provided earlier. The more you play the more bankroll it will require. The round number, the last digit to the right most is cut off, but it is 1 million and 2.5 million respectively.
I expanded the range of bankrolls to eliminate the RUINED situation to get a better understanding of the range of values.
60 Royal Flush Bankroll ($2400) for 1 million rounds. It will be $50,000 coin in so the bars representing $500 off of the vertical black line will represent 1% of the total return.
100 Royal Flush Bankroll ($4000) for 2.5 or possibly 5 million rounds. When the coin in is $125,000 for penny hands. $1250 will represent 1 percent return off the vertical mark.
Analysis #1 - 1 Million Rounds
Losses beyond double theoretical edge (96.4%)
0.15% About 1 in 700 players
Red Bar 1 $720.01-$800 0.02%
Red Bar 2 $800.01-$880 0.04%
Red Bar 3 $880.01-$960 0.09%
Below expected return with double theoretical edge (97-98)%
7.91% About 1 in 13 Players
Red Bar 4 $960.01-$1040 0.2%
Red Bar 5 $1040.01-$1120 0.4%
Red Bar 6 $1120.01-$1200 0.74%
Red Bar 7 $1200.01-$1280 1.29%
Red Bar 8 $1280.01-$1360 2.1%
Red Bar 9 $1360.01-$1440 3.18%
Below expected return 98-99%
46.02% Nearly half of the players
Red Bar 10 $1440.01-$1520 4.51%
Red Bar 11 $1520.01-$1600 5.99%
Red Bar 12 $1600.01-$1680 7.45%
Red Bar 13 $1680.01-$1760 8.7%
Red Bar 14 $1760.01-$1840 9.54%
Red Bar 15 $1840.01-$1920 9.83%
Above Expected Return 99%
25.76% About 1 in 4 Players
Red Bar 16 $1920.01-$2000 9.54%
Red Bar 17 $2000.01-$2080 8.71%
Red Bar 18 $2080.01-$2160 7.51%
Semi Pro 99.5%
14.19% About 1 in 7 Players
Red Bar 19 $2160.01-$2240 6.1%
Red Bar 20 $2240.01-$2320 4.69%
Green Bar 1 $2320.01-$2400 3.4%
Winners Circle
Outright Winner (100%+)
5.82% About 1 in 17 Players
Green Bar 2 $2400.01-$2480 2.34%
Green Bar 3 $2480.01-$2560 1.52%
Green Bar 4 $2560.01-$2640 0.94%
Green Bar 5 $2640.01-$2720 0.55%
Green Bar 6 $2720.01-$2800 0.31%
Green Bar 7 $2800.01-$2880 0.16%
Significant Winner (101%)
0.14%, About 1 in 700 players
Green Bar 8 $2880.01-$2960 0.08%
Green Bar 9 $2960.01-$3040 0.04%
Green Bar 10 $3040.01-$3120+ 0.02%
Analysis #2 - 2.5 Million Rounds
Still Unlucky (97.5% - 98%)
1.13% About 1 in 90 Players
Red Bar 1 $832.01-$936 0.01%
Red Bar 2 $936.01-$1040 0.02%
Red Bar 3 $1040.01-$1144 0.05%
Red Bar 4 $1144.01-$1248 0.09%
Red Bar 5 $1248.01-$1352 0.17%
Red Bar 6 $1352.01-$1456 0.3%
Red Bar 7 $1456.01-$1560 0.49%
Below Expected Return 98-99%
56.25%, About a little more than half the players
Red Bar 8 $1560.01-$1664 0.79%
Red Bar 9 $1664.01-$1768 1.21%
Red Bar 10 $1768.01-$1872 1.78%
Red Bar 11 $1872.01-$1976 2.49%
Red Bar 12 $1976.01-$2080 3.34%
Red Bar 13 $2080.01-$2184 4.3%
Red Bar 14 $2184.01-$2288 5.29%
Red Bar 15 $2288.01-$2392 6.25%
Red Bar 16 $2392.01-$2496 7.08%
Red Bar 17 $2496.01-$2600 7.69%
Red Bar 18 $2600.01-$2704 8.01%
Red Bar 19 $2704.01-$2808 8.02%
Above Expected Return 99%
34.34%, About a little more than third the players
Red Bar 20 $2808.01-$2912 7.7%
Red Bar 21 $2912.01-$3016 7.1%
Red Bar 22 $3016.01-$3120 6.3%
Red Bar 23 $3120.01-$3224 5.37%
Red Bar 24 $3224.01-$3328 4.4%
Red Bar 25 $3328.01-$3432 3.47%
Semi Pro (99.5%)
7.77% About 1 in 14 Players
Red Bar 26 $3432.01-$3536 2.63%
Red Bar 27 $3536.01-$3640 1.92%
Red Bar 28 $3640.01-$3744 1.35%
Red Bar 29 $3744.01-$3848 0.91%
Red Bar 30 $3848.01-$3952+ 0.59%
Green Bar 1 $3952.01-$4056 0.37%
Outright Winner (100%-100.5%)
0.69% About 1 in 145 Players
Green Bar 2 $4056.01-$4160 0.23%
Green Bar 3 $4160.01-$4264 0.13%
Green Bar 4 $4264.01-$4368+ 0.07%
Green Bar 5 $4368.01-$4472 0.04%
Green Bar 6 $4472.01-$4576 0.02%
Green Bar 7 $4576.01-$4680+ 0.01%
Conclusion
The 1 million rounds does not normalize too much off of the 500k simulation. The results are 2.2% within theoretical return. 96.8 - 101.2. A handful of people can still win outright.
The 2.5 million round simulation really normalizes things but still falls short of reflecting what the "long run" is. Results are within 1.5% of the theoretical return. The people who win outright are VERY FEW, a fraction of a percent.
For both curves, it reflects the vast majority ~85% being within 1% below the theoretical return of 98.9808%. It would take an anomaly to be more than 1 percent off.
I will have concluding remarks if I am able to reach 5 million rounds.