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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

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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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