Answer Happy

1st problem: You have five decks of cards, each with 52 cards. On each deck, you are allowed to draw only 10 cards. Of each set of 10 drawn cards, you set aside the cards in the suit of hearts, then you assemble all of the collected hearts you have drawn from those 50 cards, eliminating any duplicates. You place them 2 through Ace in a horizontal layout. What is the probability of obtaining no hearts? Or 1, 2, etc, up to all 13 hearts? 2nd problem: What are the probabilities of being able to string together 4 or more sequential hearts in your layout? What about 5? 6, etc. - all the way up to 13. 3rd problem: So, now, with these sequential-based probabilities in mind, imagine that the player is betting $1 for this chance to string together sequential hearts from these 50 cards from five decks. Based on those odds, what would be the appropriate payout for achieving a string of 4 sequential hearts, 5, and so on, keeping in mind that there is also the potential to create more than one string of hearts in sequence of 4 or more within the range of 13 places. 3-6 and 9-K, for example. The goal in calculating these paybacks is for the game to pay back 98% of the player's bet over an indefinite amount of time.