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Author: h | 2025-04-24

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In 1,186,106. 9/6 Jacks Royal Combinations Cards Held Combinations Probability 0 1,426,800 0.002891 1 16,805,604 0.034053 2 96,804,180 0.196154 3 195,055,740 0.395240 4 152,741,160 0.309498 5 30,678,780 0.062164 Total 493,512,264 1.000000 I was wondering if I could get your help on computing the probability distribution table for Jacks or Better. I know that 52 choose 5 = combin(52,5) = 2,598,960, yet in every table that I have looked at for video poker, there are 19,933,230,517,200 total combinations. I was wondering why there are so many more than 52 choose 5, and how to compute them. Mic There are combin(52,5)=2,598,960 possible combinations on the deal. The reason my video poker return tables have almost 20 trillion combinations is you also have to consider what could happen on the draw. Here are the number of combinations according to how many cards the player discards. Combinations on theDraw in Video Poker Discards Combinations 0 1 1 47 2 1,081 3 16,215 4 178,365 5 1,533,939 The least common multiple of all those combinations is 5×combin(47,5)= 7,669,695. Regardless of how many cards the player discards, the return combinations should be weighted so that the total comes to 7,669,695. For example, if the player discards 3, there are 16,215 possible combinations on the draw, and each one of them should be weighted by 7,669,695/16,215 = 473. So the total number of combinations in video poker is 2,598,960 × 7,669,695 = 19,933,230,517,200 . For more on how to program video poker returns yourself, please see my page on Methodology for Video Poker analysis. This question was raised and discussed in the forum of my companion site Wizard of Vegas.

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| 'ln' | 'log' | 'log2' | 'log10' | 'hypot' | 'sin' | 'asin' | 'sinh' | 'asinh' | 'sinc' | 'cos' | 'acos' | 'cosh' | 'acosh' | 'tan' | 'tanh' | 'atan' | 'atanh' | 'atan2' | 'sec' | 'asec' | 'sech' | 'asech' | 'csc' | 'acsc' | 'csch' | 'acsch' | 'cot' | 'acot' | 'coth' | 'acoth' | 'abs' | 'nabs' | 'sign' | 'min' | 'max' | 'avg' | 'gcd' | 'lcm' | 'combin' | 'permut' | 'hgd' | 'interp' ; argument-list: | expression | argument-list ',' expression ;primary-expression: | constant | '(' expression ')' ; constant: | named-constant | numeric-constant ; named-constant: | 'e' | 'π' | 'pi' | 'τ' | 'tau' ; numeric-constant: | integer-part [ fraction-part ] [ exponent-part ] | fraction-part [ exponent-part ] ; integer-part: | digit { digit } ; digit: | '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9' ; fraction-part: | '.' integer-part ; exponent-part: | exponent-char [ exponent-sign ] integer-part ; exponent-char: | 'E' | 'e' ; exponent-sign: | '+' | '-' ;uses AcknowledgementsWe would like to thank MathJS for inspiring this calculator and some of the source code.

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All five cards away there are combin(47,5)= 1533939 possible replacement hands. The total number of hands that must be analyzed to determine the best play of a specific hand is combin(47,5)+5*combin(47,4)+10*combin(47,3)+10*combin(47,2)+5*47+1, which coincidentally also equals 2598960. So if we took no short cuts at all we would have to analyze 25989602= 6,754,593,081,600 hands. Just reducing the initial hands to 191659 we still have 498,114,074,640 hands to analyze. Clearly more short cuts are in order. It would take a desktop computer several hours at least to work through this many hands. Personally I don’t actually score any hand but use carefully chosen formulas to determine the probability of improving a hand. For example with any pair and 3 singletons the probability of improving the hand to a two pair is always the same. Things get more complicated with straights and flushes but still manageable. My program can calculate the expected return for a game of jacks or better in about one minute. Considering it used to take me over a day I’m rather proud of it. I hope this answers your question. You give a standard deviation for a 9/6 Jacks or Better VP is 4.417542. I’m trying to figure out what that means. If I have played 100 hands, does that mean that 2/3 of the time my result would be within 441 Wagers? It seems counter to my experience playing the game. Ray from Maple Glen, Pennsylvania The standard deviation of 100 hands of 9/6 Jacks or Better is 1001/2*4.416 = 44.16. You can then use this information to determine what is the probability of winning or losing more than a specified number of units. For example the winning or losing within two standard deviations, or 88.31 units, is 4.55%. There is more to it than this. Please see my part on the standard deviation in my section on the house edge. Which of these ways to play jacks or better video poker has the greater risk of loss, assuming the payoff schedules are the same (9/6): 1000 plays of a dollar machine ($5 each play) or 1000 plays

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Monthly Instagram users count has recently reached one billion. No wonder that the platform is a proper place for all kinds of influencers, businesses, and entrepreneurs. Aside from all the promotion opportunities, only content is capable of attracting a new audience and, more importantly, make it stay with you on your Instagram page. But sometimes it’s challenging to plan your content manually. Scheduling posts and stories in bulk is easier with a free Instagram planner – Combin Scheduler. What is Combin Scheduler? Combin Scheduler is a desktop app for automated publishing Instagram posts and stories. With the app, users are able to create a beautiful Instagram feed and schedule their content in advance in the meantime enjoying the easy-to-use interface and the distinct of its features. Regular users who take pictures on their phones can easily upload posts via the native app, especially if they do it rarely. But businesses or bloggers simply need solutions for automated publishing. And since Instagram desktop does not allow uploading posts and stories, photographers or other bloggers who take photos with professional cams want to effortlessly share their art without saving the pictures back and forth through devices. Combin Scheduler allows sharing posts from your PC and planning them for days, weeks, and even months ahead. If you want to share something with your audience immediately, you can easily do it as well. Just upload a photo or video, write a caption if you wish to, and select a publishing date. Then you’re free to do something more important and be sure that your post will be automatically published without a reminder. In a caption, you can tag any other Instagram account and add hashtags to promote your publication. The app offers a bunch of templates of captions with thematic hashtags. The caption allows you to write 2,200 characters in accordance with Instagram rules, which is very convenient for those brands and users who love writing long stories on Instagram. This is not that easy to do from the smartphone. Adding a location tag will help you grab the attention of those living in the area. If your photo appears not to fit the Instagram standard ratios, use the crop and zoom features to adjust the multimedia. Right within the app, you can alter the size to square, vertical, portrait, and landscape. Instagram is a visual social network, so the decision whether or not to follow you often depends on how your account looks like. Typically, famous Instagram accounts have some concept or theme. Within the in-app calendar in Combin Scheduler, you can control and style the grid of your content. In-bulk stories publishing is another time-saving feature of the app. You probably already

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The player and banker draw a card, only 8 cards will remain in the shoe for the last hand. If you are tracking the cards, and know the last 8 cards are all 0-value cards, a table max bet on tie would net you a huge profit. My question is, what are the odds that the last 8, 9, or 10 cards in an 8 deck shoe are all 10 value? Also if you knew exactly what the last 8 cards were, could you use a formula or program to figure the odds that the next hand will be banker, player, or tie? Mike S. from Michigan City To answer your first question, the probability that the last 8 cards in an 8-deck shoe are all 0-valued cards is combin(128,8)/combin(416,8) = 0.0000687746. So, it isn't something to wait around for. I know of no easy formula for what to bet in other situations. If you could find a casino that would allow you to use a computer, the advantages would sometimes be huge towards the end of the shoe, especially on the tie. Why do casinos burn cards in blackjack and baccarat? Matt from Fort Myers, FL A minor reason is to foil card counters. However, instead of burning x cards, the dealer could move the cut card x cards forward, and achieve the same purpose. The major reason is game protection. For one, the player might catch a glimpse of the top card, and alter his bet and strategy,. Growth Fenton 2025; Electronic Growth Chart; Growth WHO 0 - 24m; Growth CDC 0 - 36m; Growth CDC 2 - 20y; GA Calc; Growth Olsen 2025; BMI Olsen 2025; Down Syndrome 0 -

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Etc.Price: Vista Social has a free version. Our paid version, the “Standard” package, costs $39 per month. You can add 8 social media profiles in our Standard package.2. PlanableImage Source: Planable.ioStreamline the content development and publishing processes with Planable.It features a beginner-friendly social media calendar complemented with a scheduler, an approval system, and team collaboration tools for agencies. Feature highlights:Accurate post previews for the schedulerOne-click post approvals Mobile approval app for clientsPrice: Starts at $13 per month for one workspace per user3. Combin SchedulerImage Source: Combin.comThe Combin Scheduler is a desktop app that features a lightweight, intuitive interface for post scheduling, image editing, hashtag management, and so on. It works like an interactive calendar that lets you schedule and publish Instagram posts on one page. Feature highlights: Supports bulk Instagram Stories uploading Discover trending hashtags Customizable image sizes and post aspect ratiosPrice: Beyond the free, limited version, pay for Combin for as little as $15 per month4. PreviewImage Source: ThePreviewApp.comThe Preview app is a certified partner to Instagram that will help you plan your posts weeks or even months ahead of time. Rearrange the order of your scheduled posts to manage what your profile feed will look like. Feature highlights:Complete image editing tools with filtersHashtag group management and analyticsCollaborate with your team on Instagram campaignsPrice: Starts at $6.67 per month for the complete suite of features5. Hopper HQImage Source: HopperHQ.comHopper HQ is designed to help you breeze through your Instagram content creation and scheduling tasks. Get hashtag suggestions, edit your

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Having a strong follower count on Instagram is important for all content creators. However, over time, your account can be bloated with follows from unengaged or fake accounts.If it’s just a few, you can simply remove them manually. However, if the accounts number in the hundreds or even thousands, then you’ll need a dedicated tool to help you clean and organize your account. This is where Unfollow apps come into the picture. They help you easily unfollow users from your Instagram account.Some of the top Instagram Unfollow apps include Followers & Unfollowers, FollowMeter, Unfollow Users and several others. Though the best Unfollow app for Instagram is Massi. It helps you Unfollow several accounts at once, thus saving you a lot of time.Let’s dig into these apps to find out more. What's In This Guide? Best Unfollow Apps For Instagram 1. Unfollow Users 2. Massi – Best Unfollow App for Instagram 3. Followers & Unfollowers 4. FollowMeter for Instagram 5. Followers+ Track for IG 6. Unfollow Pro – Unfollowers 7. UnFollowers for Instagram+ 8. Follow Cop 9. Followers – Unfollowers 10. nFollowers 11. Unfollow for Followers 12. Followers Pro + for Instagram 13. Unfollowers/Lost Followers 14. Followers Assistant 15. Combin 16. AiGrow 17. Reports: Followers Tracker 18. Analyzer Plus-Followers Report 19. Followers Pro+ 20. Followers – Tracker Insight 21. Reports+ Unfollowers Followers Best Unfollow Apps For Instagram – onclusion Enjoyed the post? Share on Pinterest Best Unfollow Apps For Instagram1. Unfollow UsersUnfollow Users is one of the best unfollow apps for. Growth Fenton 2025; Electronic Growth Chart; Growth WHO 0 - 24m; Growth CDC 0 - 36m; Growth CDC 2 - 20y; GA Calc; Growth Olsen 2025; BMI Olsen 2025; Down Syndrome 0 -

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Andrews, G.E., Berndt, B.C.: Ramanujan’s Lost Notebook, Part II. Springer, New York (2009) Google Scholar Andrews, G.E., Eriksson, K.: Integer Partitions. Cambridge University Press, Cambridge (2004)Book Google Scholar Andrews, G.E., Newman, D.: Partitions and the minimal excludant. Ann. Comb. 23, 249–254 (2019)Article MathSciNet Google Scholar Andrews, G.E., Newman, D.: The minimal excludant in integer partitions. J. Integer Seq. 23, 2–20 (2020)Berndt, B.C.: Number Theory in the Spirit of Ramanujan. American Mathematical Society, Providence (2006)Book Google Scholar Berndt, B.C., Kim, B., Yee, A.J.: Ramanujan’s lost notebook: combinatorial proofs of identities associated with Heine’s transformation or partial theta functions. J. Combin. Theory Ser. A 117, 957–973 (2010)Article MathSciNet Google Scholar Berndt, B.C., Yee, A.J.: Combinatorial proofs of identities in Ramanujan’s lost notebook associated with the Rogers-Fine identity and false theta functions. Ann. Comb. 7, 409–423 (2003)Article MathSciNet Google Scholar Blecksmith, R., Brillhart, J., Gerst, I.: Parity results for certain partition functions and identities similar to theta function identities. Math. Comp. 48, 29–38 (1987)Article MathSciNet Google Scholar Blecksmith, R., Brillhart, J., Gerst, I.: Some infinite product identities. Math. Comp. 51, 301–314 (1988)Article MathSciNet Google Scholar Cooper, S., Hirschhorn, M.: On some infinite product identities. Rocky Mt. J. Math. 31, 131–139 (2001)Article MathSciNet Google Scholar Corteel, S., Lovejoy, J.: Overpartitions. Trans. Am. Math. Soc. 356, 1623–1635 (2004)Article MathSciNet Google Scholar Dabbagh, M.Z.: \(2\)-colored Rogers–Ramanujan partition identities. A., Mukhopadhyay, A., Sarma, R.: New relations of the mex with other partition statistics. N.J.: Basic Hypergeometric Series and Applications. American Mathematical Society, Providence (1988)Book Google Scholar Gasper,