probabilities and odds

Got a question: how does the inventor/casino calculate out the house advantage, the rtp, and the probability of a certain hand? And to get the correct payout to pay the player. Such as 40 to 1 in 3 card poker, I know that the probability / by the rtp = the payout(40 to 1), but how are they figuring the probability factors. I know its based on the over 22, 000 hands available and I know that there's only 48 straight flushes available, but I'm kind at a loss as to how there coming up with that/those payouts. I mean its like if for ex. you have 54 cards and there's 2 jokers in that deck, what are the odds that both jokers will be the first two cards, or even say you discard 4 cards and then the next 2 cards would be the 2 jokers., or even lets just say whats the probability of 1 joker showing up after the 4 discards, or whats the probability of turning over the red joker vs. the black joker in either of the two cards dealt. I'm no math genius by any stretch of the imagination, but I would seriously like someone to explain this process, please like someone to enlighten me on this subject. Thanks for your time very much. Would very much appreciate the feedback. Thanks

I would suggest you go to WizardofOdds.com and look up 3 card poker to start. The Wizard publishes a probability chart for each commonly known paytable, and there are several for 3CP as it's offered.

Each probability chart shows the number of hands that can possibly be made from the deck (3CP is a single-deck game), both in how many hands (as you say, 48) and in the percentage of total hands you can make a SF (48/22100). This is done for each type of hand, including those that pay nothing or lose.

When playing the odds of getting a hand, like the Pairs Plus bonus bet on 3CP, the probabilities are multiplied by how much they pay, which can be manipulated to give the game a house edge acceptable to the casino.

When the player's cards must beat the dealer's to win, an additional comparison is made for the percentage of hands the dealer can make from the remaining cards to win, vs. those that will lose. This is done for each player hand. Because in most games, if they did not have a house mechanism that would be 50/50, another element is added and the effect evaluated. In 3CP, that house effect is the dealer must have Q high or better, or they only pay the play and push the ante, no matter how good your hand is. But they take all the money on your folded hands (the ante), before you know whether they qualified or not. It's a built-in way for the house to make money.

Anyway, that's a start on your questions. As you add jokers, or more cards to consider, it's the same type of process but more complicated to calculate. That's what the guys here are paid to figure out/verify, so I'm not sure you'll get much more specific info, but a lot of it can be gathered from the analyses at WizardofOdds, as he has deconstructed nearly every table game in the same way, and the info is yours for free! (I still find that amazing.)

I replied in your blog

Quote: billygoat

Got a question: how does the inventor/casino calculate out the house advantage, the rtp, and the probability of a certain hand? And to get the correct payout to pay the player. Such as 40 to 1 in 3 card poker,

I've written a bit about that. Here is a start.

http://advancedadvantageplay.com/wp-content/uploads/2015/03/Introduction_to_Gaming_Mathematics.pdf

It sounds like you're looking for a course in probability theory. There are many good ones online; that's a better bet than reading answers to specific questions here. Once you better understand the topic, you'll be able to make more sense of the game design process.