Probability of Drawing 3 of a Kind

[jetermacaw]

OK I'm still trying to get my head around the statement
VP RNGs in most jurisdictions just spit out random cards no matter what game is being played. So the odds of being dealt trips and the odds of converting trips to quads when you draw to them are the same among games. So the odds of getting dealt 3oak in JOB or TDB are the same, and holding said 3 oak should garner the same result no matter what the pay table is?

[Mr.Dawes]

Randomness is a required factor for payback percentage to be determined. It is in fact precisely because the game is random and replicates the odds of a live deck of cards that we can determine a particular paytables' payback percentage. If the software were designed in a manner that precluded randomness on the deal and draw then there would be no way for the player to determine payback.The second requirement to determine payback percentage is consistent play from the player. If the player chooses hold cards based on whim payback percentage cannot be determined. Lucky for us several people have done the math and written software for the player to learn correct play for each different dealt hand.If you aren't familiar with the process it goes like this.Say you are playing Jacks or Better and you are dealt 2H, 5H, 6H, 9H, 8D and choose to go for the flush. Since we have been dealt 5 of the 52 cards there are 47 cards left in the deck, 9 of which are hearts that will complete our flush. Since the draw is random each of those 47 cards are equally likely to occur, thus if we played this hand 47 times we can expect 9 flushes and 38 losing hands. You add up what you would win for the 9 flushes based on the paytable and divide that total by 47 to get the average amount won by holding the four hearts. Then you repeat this process for every combination of hold cards for this hand and play the hold combination that produces the highest average win. In short, without randomness and consistent method of play payback percentage can not be predicted.

[Mr.Dawes]

OK I'm still trying to get my head around the statement
VP RNGs in most jurisdictions just spit out random cards no matter what game is being played. So the odds of being dealt trips and the odds of converting trips to quads when you draw to them are the same among games. So the odds of getting dealt 3oak in JOB or TDB are the same, and holding said 3 oak should garner the same result no matter what the pay table is?Yes, the odds of getting trips on the deal and converting trips to quads is the same in both games. The odds of getting these results are independent of the paytable. The player uses the paytable to determine method of play. Since the payout for different winning hands varies from game to game so does the cards that the player should hold or discard. As Vman96 pointed out earlier in TDB there are times when you breakup a dealt full house to go for quads because it pays so much in TDB. You would not in JOB because quads are not that valuable.

[jetermacaw]

Thank you Mr.Dawes. And I was strictly talking dealt 3oak not full houses, so any dealt 3oak on any game every thing is equal.

[onemoretry]

Thank you Mr.Dawes. And I was strictly talking dealt 3oak not full houses, so any dealt 3oak on any game every thing is equal.
The outcomes, in terms of full houses, quads, etc., are equal.

But, the rewards are not. In plain vanilla JOB, all quads pay 125 for five coins bet. In TDB, some quads pay 250, some 400, some 800, and the really good ones 2000 or 4000. And, don't forget that, if you totally whiff on the draw, JOB pays 15, while TDB pays 10.

[mschaching]

Keeping in mind the probabilities listed, in "gimmick" games such as Deal Draw Frenzy where you need to draw 3OAKS, are the machines programmed to hit 3 OAKS more often or do you go follow the standard probability table?

[FAA]

What is the probability of being dealt four of a kind? Recently dealt four JOB fours at the end of a mano a mano with a machine. Unfortunately, by then I had reduced to two coin wagers! Just exasperating. I guessed wrong. 

[FAA]

You would not in JOB because quads are not that valuable.-------------------------------------------------------------------------------Everything is relative. $31 is $31.

[onemoretry]

What is the probability of being dealt four of a kind?

One in 4165.

[FAA]

Just my luck! The exasperation never ends with VP.