Standard Deviation for 9/6 Jacks or Better
the square root of N X the standard deviation for one hand. This means that the standard deviation increases with the number of hands played. I would have thought that the more hands one plays, the closer one's result will be to the mean. Does this not imply that the standard deviation should decrease with the number of hands played?
Also, the Wizard of Odds website gives the standard deviation for 1-play, one credit Jacks or Better, for 1-play, 5 credit Jacks or Better and for 3-play, 5 credit Jacks or Better, but not for 3-play, one credit Jacks or Better. I would like to know this figure, as well as the standard deviation for 5-play and 10-play, one credit Jacks or Better.
Does anyone know what these are?
Look at it this way: Suppose you are playing an even money bet for $5 a shot. With one bet, the extreme range of your possible outcomes is +$5 to -$5. If you make a hundred of these bets, the possible range expands to +$500 to -$500. If the possible range is that much wider, wouldn't you expect the standard deviation of 100 $5 bets to be wider than the standard deviation of just one $5 bet?
What gets smaller is the standard deviation of your outcome as a fraction of the total amount bet. For the singe $5 bet, the standard deviation is $5 or 100% of your total amount bet. For 100 bets, the standard deviation is sqrt(100)*$5=$50, or just 10% of your total amount bet.
I don't play slots, so I didn't even read the second part of the question thoroughly.
About the standard deviation for multi-play one-coin video poker, may I ask why would anybody play one-coin video poker? I should remove reference to that on my site. Playing less than five coins reduces the return by 2%.
Quote: WizardAbout the standard deviation for multi-play one-coin video poker, may I ask why would anybody play one-coin video poker? I should remove reference to that on my site. Playing less than five coins reduces the return by 2%.
The answer is bankroll to bet size (and variance) vs. practical alternatives.
Suppose your bankroll can support $1/coin VP (JorB). That's a total full coin bet of $5. What is your better option? Playing an 8/5 $1 machine with 5 coins or a 9/6 $5 machine with one coin?
The Wiz can correct me if I am wrong, but I believe the 1 coin 9/6 is clearly better than the 5 coin 8/5 both from an edge and variance standpoint.
For all practical purposes, you can't find $1 9/6 machines on the strip. If you want to play $1 VP on the strip, and maximize your comps, I argue that a one coin 9/6 strategy is vastly superior to a 5 coin 8/5 strategy.
Sadly, it appears that the $5 coin 9/6 machines are becoming extinct as well. If you want a 9/6 VP game at the MGM, you now have to pony up to the pump at $25/coin.
Quote: scotty81Suppose your bankroll can support $1/coin VP (JorB). That's a total full coin bet of $5. What is your better option? Playing an 8/5 $1 machine with 5 coins or a 9/6 $5 machine with one coin?
The Wiz can correct me if I am wrong, but I believe the 1 coin 9/6 is clearly better than the 5 coin 8/5 both from an edge and variance standpoint.
That's correct. They are both ~98% games. Variance would actually be less on the one-coin because you are playing a more conservative strategy (i.e., not shooting for the royal).
Quote:For all practical purposes, you can't find $1 9/6 machines on the strip. If you want to play $1 VP on the strip, and maximize your comps, I argue that a one coin 9/6 strategy is vastly superior to a 5 coin 8/5 strategy.
Sadly, it appears that the $5 coin 9/6 machines are becoming extinct as well. If you want a 9/6 VP game at the MGM, you now have to pony up to the pump at $25/coin.
You can still play $1 9/6 at MGM in the high-limit room. The 50 and 100-play machines will let you play one line at a time. I hear these machines are often taken, though.
Personally, I don't see why anybody would play on the strip, when so much better is available so close. Two trips ago, I played the Palms 5-play $.25 9/6 Jacks for about 4 hours and put $13.3K through. My expected loss was $28 (with cashback), and I lost $300-400, but earned a $100 Visa gift card and a couple other $10-$25 gift certificates, plus triple cashback with an ACG coupon. Then this last trip I got three nights comped at Palms Place plus $125 in free play.
Quote: rdw4potusI think 9/6 jacks has a return of about 99.5%, and 8/6 jacks has a return of 98.5%. So if the full coins are worth 2%, then I think playing full coins at the lower denomination is the better choice.
9/6 at one coin sans the royal bonus is about 98%. This "Sophie's Choice" really only occurs on the LV Strip, which is a VP wasteland. Everywhere else, it is always preferable to play the lower denomination at full-coin rather than the higher denomination at one coin.
That said, I wouldn't ever do it because it doesn't really make a lot of sense.
Quote: JerryLoganThere is an advantage at times to playing one credit vs. max bet. When the 5-credit paytable plus goodies cannot be stretched out to = at least 100%, you'll lose less and theoretically will be better off playing just one coin.
That said, I wouldn't ever do it because it doesn't really make a lot of sense.
I think you're right if we're talking about playing one credit versus 5 credits at the same denomination. But I think the original question was about whether it is better to play $5 once w/9/6 pay-table or play $1*5 w/8/6 pay-table. In that scenario, it's better to play $1*5 because the royal bonus out-weights the effect of the lower payout on the full house.
Quote: scotty81
Suppose your bankroll can support $1/coin VP (JorB). That's a total full coin bet of $5. What is your better option? Playing an 8/5 $1 machine with 5 coins or a 9/6 $5 machine with one coin?
I think that scenario is rather unlikely. A casino generous enough to have $5 9-6 Jacks will probably have $1 9-5 or 8-6 Jacks, or $1 8-5 Bonus Poker. If the best $1 video poker you can find is 8-5 Jacks, you shouldn't be playing at all, if for no other reason than on principle.
Quote: scotty81
Sadly, it appears that the $5 coin 9/6 machines are becoming extinct as well. If you want a 9/6 VP game at the MGM, you now have to pony up to the pump at $25/coin.
In the high limit slots room they have two $1 50-play and one $1 100-play machines, both which have 9-6 Jacks. Just choose to play one hand. You'll look like a flea, but who cares. I've played those machines a LOT, and I often notice by the game state left by the last player than he/she was playing one hand only.
I would think that would be because they were down to their last dollar or two.Quote: Wizard...I often notice by the game state left by the last player than he/she was playing one hand only.
I play video poker to accumulate player points so that I get all the free food I want at the casino and free bus fare.
The cheapest and most efficient way to do this is to play 9/6 Jacks or Better. To accumulate the points, I must bet a total of $30,000 every six months. (Every June and December, my points are re-set to zero). Playing one hand, one credit, it will cost me about $400 to rack up the necessary points (approx. $500 less about $100 cash-back). At present, I am playing one hand at a time for 50 cents. I want to play as many hands as possible, to give myself the greatest chance of being close to the expected return of 98.37%. However, this means that I will have to play 60,000 hands over 6 months, which is boring and takes away from my time in the poker room.
The only machines at my casino that offer 9/6 Jacks or Better are 3-play, 5-play and 10-play. If I want to play max credits, I have to play at least 3 hands. The minimum cost per deal will be $3.75 (25 cents X 3 hands X 5 credits).
To earn the player points I need, I would be playing 24,000 hands in total, but only 8,000 unique hands. I am not comfortable with the large swings in cost that would result from doing this. I would rather know pretty much what my total cost is likely to be.
I would like to be able to figure out if it will cost me significantly more to play one credit for 3, 5 or 10 hands, beacuse if it doesn't increase the swings in cost by very much, playing that way would save a lot of time. To calculate my expected cost of playing multiple hands, however, I need to know the standard deviation.
Quote: teddyshttp://www.jazbo.com/videopoker/nplay.html
Thank-you for the reference. I have looked at this site. Unfortunately,it only gives the standard deviation for muli-play where 5 coins are bet per hand. It does not have the information I need.
Quote: HoldemJunkie52Thank-you for the explanation of standard deviation. The reason I want to only play one coin is as follows:
I play video poker to accumulate player points so that I get all the free food I want at the casino and free bus fare.
The cheapest and most efficient way to do this is to play 9/6 Jacks or Better. To accumulate the points, I must bet a total of $30,000 every six months. (Every June and December, my points are re-set to zero). Playing one hand, one credit, it will cost me about $400 to rack up the necessary points (approx. $500 less about $100 cash-back). At present, I am playing one hand at a time for 50 cents. I want to play as many hands as possible, to give myself the greatest chance of being close to the expected return of 98.37%. However, this means that I will have to play 60,000 hands over 6 months, which is boring and takes away from my time in the poker room.
The only machines at my casino that offer 9/6 Jacks or Better are 3-play, 5-play and 10-play. If I want to play max credits, I have to play at least 3 hands. The minimum cost per deal will be $3.75 (25 cents X 3 hands X 5 credits).
To earn the player points I need, I would be playing 24,000 hands in total, but only 8,000 unique hands. I am not comfortable with the large swings in cost that would result from doing this. I would rather know pretty much what my total cost is likely to be.
I would like to be able to figure out if it will cost me significantly more to play one credit for 3, 5 or 10 hands, beacuse if it doesn't increase the swings in cost by very much, playing that way would save a lot of time. To calculate my expected cost of playing multiple hands, however, I need to know the standard deviation.
What do you need to know the standard deviation for? Your expectation is always going to be edge*action. You shouldn't have to worry about standard deviation if you are sufficiently bankrolled. (As a poker player, I expect that you know something about bankroll).
Quote: WizardI think that scenario is rather unlikely. A casino generous enough to have $5 9-6 Jacks will probably have $1 9-5 or 8-6 Jacks, or $1 8-5 Bonus Poker. If the best $1 video poker you can find is 8-5 Jacks, you shouldn't be playing at all, if for no other reason than on principle.
For a multitude of reasons I don't want to get into here, it is important that I remain a high status at Harrah's properties. I haven't yet found a $1 VP machine at a Harrah's property that pays better than 8/5, but then again I haven't thoroughtly investigated the multi-play machines. If you know of any $1 VP machines at a Harrah's property that pay out > 98.3% I'd like to know where they are. I do know that MGM properties on the strip offer a better VP value (9/5 $1 machines on the floor), but their comp program does not reward their play nearly as much as the Harrah's program.
Quote: WizardIn the high limit slots room they have two $1 50-play and one $1 100-play machines, both which have 9-6 Jacks. Just choose to play one hand. You'll look like a flea, but who cares. I've played those machines a LOT, and I often notice by the game state left by the last player than he/she was playing one hand only.
Thanks for the info. I hadn't considered that the multi-play machines would have a higher pay scale than single play machines when you play a reduced number of hands. I'll check it out.
Harder and harder to find. Harrah's hates video poker players. I don't think there are any good plays in Vegas at any Harrah's now. Reno still has good plays, and some of the outliers like Laughlin, Ak-Chin or Rincon might still have decent games. Otherwise the pickings are slim. Atlantic City still has good plays. A lot of people will do the majority of their play on the good machines there and use their comps in Vegas. But that doesn't help if you are a West Coaster.Quote: scotty81If you know of any $1 VP machines at a Harrah's property that pay out > 98.3% I'd like to know where they are.
Quote: teddysHarder and harder to find. Harrah's hates video poker players. I don't think there are any good plays in Vegas at any Harrah's now. Reno still has good plays, and some of the outliers like Laughlin, Ak-Chin or Rincon might still have decent games. Otherwise the pickings are slim. Atlantic City still has good plays. A lot of people will do the majority of their play on the good machines there and use their comps in Vegas. But that doesn't help if you are a West Coaster.
Harrah's in Nevada has nothing that anyone who believes in playing only the best paytables would play. But I play there all the time and I do pretty darn well. I'm Diamond and their program is hard to beat for offers and invites. VPFREE has a lot of 7-Stars players ($1million minimum through per year) and most of the famous people we hear and read about are included. So they're either hypocrites, or Harrah's cranks up the paytables just for them when they appear.
Harrah's has decent paytables for high-denomination players (which would include most Seven Stars, natch). The Rio, for example, has $5 9/6 JOB. I know someone like Jean Scott plays a lot in Harrah's New Orleans, and Indiana and Laughlin where there are better paytables. But then again, she has so large of a bankroll a $5 game is like nothing to her.Quote: JerryLoganHarrah's in Nevada has nothing that anyone who believes in playing only the best paytables would play. But I play there all the time and I do pretty darn well. I'm Diamond and their program is hard to beat for offers and invites. VPFREE has a lot of 7-Stars players ($1million minimum through per year) and most of the famous people we hear and read about are included. So they're either hypocrites, or Harrah's cranks up the paytables just for them when they appear.
Quote: teddysHarrah's has decent paytables for high-denomination players (which would include most Seven Stars, natch). The Rio, for example, has $5 9/6 JOB. I know someone like Jean Scott plays a lot in Harrah's New Orleans, and Indiana and Laughlin where there are better paytables. But then again, she has so large of a bankroll a $5 game is like nothing to her.
I've heard there's little to be had in NO, and I know the Harrah's paytables are awful in Laughlin. Not sure about Indiana, where's that? Jean Scott lives in LV so there's no doubt she plays most of her 7-Stars play there. Remember she's a very senior citizen with an ill partner, so she's not jet-setting to casinos much any longer.
It's part of that large area in between Lake Mead and the Hudson River :)Quote: JerryLoganNot sure about Indiana, where's that?
Seriouly: Horseshoe Hammond. It's near where she's from, and she blogs about going there. They have great paytables for mid-to-high rolling VP.
Quote: teddysAk-Chin
As of last weekend, no. To be fair, I haven't looked at the $1+ machines in a while, but the quarter machines feature 6-5 Jacks. I highly doubt the $1 machines are much better than 7-5. (Alternatively, you can get 7-5 Jacks at the nickel Spin Poker machines.)
Update 8/1/2010:
So we were there yesterday, and I went down in the morning to check things out, so here goes:
Your bog standard video poker machines are 25¢-50¢-$1 with a dozen games with really shitty house edge. The main games are:
6-5 Jacks (95.00%)
6-5 Bonus (96.87%)
9-6-4 Double Bonus (96.37%)
7-5 Double Double Bonus (95.71)
25-15-10-4-3-2-2 Deuces (94.82%)
They also have a ten coin max (although you still get the bonus at five coins). If you go to multiline, the situation gets slightly better, with 7-5 Jacks, although the rest are basically the same.
Over in the high limit room, the situation gets better, with $1-$2-$5 machines that have:
8-5 Jacks (97.29%)
6-5 Bonus (96.87%)
9-7-5 Double Bonus (99.10%)
8-5 Double Double Bonus (96.78%)
20-12-10-4-4-3-2 Deuces (97.58%)
at $1 and $2, and
9-6 Jacks (99.54%)
7-5 Bonus (98.01%)
9-7-5 Double Bonus (99.10%)
9-5 Double Double Bonus (97.87%)
Ugly Ducks Deuces (98.91%)
at $5. So it's available, but you have to look for it. I only saw a couple VP players in the HL room, while the main floor machines were at about 30-40% capacity (10 am Saturday, although some of them were playing keno). I didn't check what people were playing, but I wouldn't be surprised to find people playing $1 not knowing how badly they're getting screwed.
HOWEVER.
I encountered one 25¢-50¢-$1 machine that featured 90-9-6 Jacks. All the rest of the games were the same shitty mix, so I figure it's gotta be a mistake. You better believe I played that machine, and I felt like a naughty schoolboy getting away with his pranks every time I hit a full house or flush. I'll play it again next time we go if it's still there. It's over by the main entrance to the poker room... there's a bank of eight video slots, a bank of four Super Times Pay, and then the bank with this machine. It's facing the poker room, on the right as you're looking at it (your back to the poker room).
Quote: teddysWhat do you need to know the standard deviation for? Your expectation is always going to be edge*action. You shouldn't have to worry about standard deviation if you are sufficiently bankrolled. (As a poker player, I expect that you know something about bankroll).
Because I want to know what the probability is that the cost of my player's card for each six month period will be within a few dollars of 1.67% X $30,000 ($501). This probability depends on the standard deviation, which increases from one play to 3-play, 5-play and 10-play. If it doesn't increase by very much, then I can reduce the number of hands I have to play, by playing multi-play, without having my cost vary significantly from one 6-month period to the next.
Edit: That might be a bit high. Let me bring down that estimate to $.75 on the three play, increasing perhaps to $1.25 on the five play for increased risk. The ten play is much too high a variance.
Quote: teddysAh, okay. I understand where you're coming from now. It sounds like variance is as important if not more important than the house edge to you. Therefore, I think you should play multi-play JOB with one coin per hand, five or ten play. That's $1.25-$2.50 a spin, but will give you less variance than a single play $.25/$.50 machine. I think you will come very close to the expected result on those machines if you play the short-coin (no royal) strategy correctly.
Thank-you for your thoughts. I have studied the information available on the Wizard of Odds website. The second question under the tab "ask the Wizard" has to do with standard deviation for multi-play and the answer references a larger section about the subject. What seems to happen is this: If one plays 5,000 hands of 3-play (5,000 unique hands, 15,000 hands total), the standard deviation will be greater than if one played 15,000 unique hands and less than if one played 5,000 unique hands.
If one wants to come very close to the mean of 98.37%, then the more unique hands one plays, the better. That's just common sense: the more trials one runs, the closer one will be to the average return.
Since there doesn't seem to be anywhere I can find the figures I'm looking for, extrapolating form the situation where one is playing 5-coins, the variance does not increase very much from one-play to 3-play. The increase from one to 5 also isn't very big, but the number of unique hands I would be playing would be reduced significantly.
It looks like I'm just going to have to try different strategies & see which one I like the best. I was going to play one hand at a time for 50 cents a hand - but this takes too long. I've switched to one hand at a time for $1 per hand, which is working out ok, but is a lot more volitile. I'm thinking a reasonable compromise might be 25 cents per hand at 3-play, which will give me 40,000 unique hands - so I'll have to play fewer hands than I would at one for 50 cents, but I'll see more hands than I would playing one at a time for $1.
