Jstark wrote: ↑Sun Mar 01, 2020 1:46 pm
So with approximately 240,000 hands, you'd have to figure out the probability to get dealt a high pair along with 3 to a royal at the same time. Example: K
K
Q
10
6
. Then it would be much easier to figure out.
True. If you're going to do this analysis, it's better to start with the RF3. The ones with three high cards (AKQ, AKJ, AQJ) have a higher probability of having a high pair in the hand than the ones with only two high cards (AKT, AQT, AJT, KQT, KJT, QJT).
For the ones with 3 high cards, (there are 12 of them, including suits), they each have 9 chances to pair up one of the existing high cards --- multiplied by the 38 possibilities for the fifth card. The fifth card cannot make two pair, trips, or a 4-card royal. So starting from (AKQ) of hearts and the A of spades, the fifth card may be any 2, 3, 4, 5, 6, 7, 8, or 9 (32 cards), plus any non heart ten or jack (6 more cards), leaving us with 38.
Multiplying that out, you get 12 * 9 * 38 = 4104 possibilities
You have to add in the possibility of getting the pair not in the royal cards --- such as (AKQ) of hearts and two black jacks. So there are the 12 starting hands multiplied by 3 ways to get a pair of jacks that doesn't include a heart. So we add 36 to the 4104 possibilities and get 4140 different ways to get a RF3 with three high cards and a high pair in the same hand.
Figuring out how many ways you can get an RF3 with two high cards and a high pair in the hand is an exercise that should be simple enough to figure out once you see the methodology above.
Once you find out the number of different ways to get a high pair and an RF3 in the same hand, remember there are 2,598,960 starting hands, it's easy to figure out how many of these combinations you should have had in 240,000 starting hands.
Without finishing the exercise, I STRONGLY suspect that the original poster hit one or more quads and either didn't notice at the time or has forgotten. Quads are "only" 125 coins in that game and unless you're paying $48 or more per hand, it won't come with a W2G.
If I'm made an arithmetic or analytic mistake in the above, I invite correction.