Probability of combinations in poker

by beautifulladybug938

I prоbably will not go into combinatorics much and describe the calculations in detail. Just tell you about the results.
In total, there are 7776 variants for dropped dice, each of which is equiprobable (unless of course you roll all five dice). Accordingly, the probability of falling out of each combination is as follows:
Poker 6/7776 = 0.077%
Kare 150/7776 = 1.93%
Full House 300/7776 = 3.86%
Straight 240/7776 = 3.086%
Troika 1200/7776 = 15.43%
Two pairs of 1800/7776 = 23.15%
The pair 3600/7776 = 46.3%
Nothing 480/7776 = 6.17%
As you can see, the probability of falling of pairs (one or two) or three is highest. In particular, the probability of getting “nothing” is much lower. Although it is much more interesting that the full house actually turns out a little more often than the straight, while it is valued higher.
However, all of the above is of little interest to the player – because if he had a certain combination, then the probability of this event is no longer important to him. Another thing is the probability of improving the available combination during the transfer.
Again, I will not consider all possible variants of transfer. And so it is intuitively clear that you need to transfer cubes not included in the available combination (unless there is no need to throw out poker or penalty). But here are some values ​​of the probability of the desired result worth thinking about.
Kare – the probability to improve this combination before poker – 1/6 = 16.7%.
Full house – if you try to transfer a couple of it, then the probability of losing poker will be 1/36, and penalty 10/36. 11/36 = 30.5% is more than one fourth. I do not know about you, but if I had a penalty and the opponent had a full house with a triple of greater importance, I would have thought more than once before raising the bet. But if he has a couple in a full house of greater importance than I have in the penalty, then the probability of throwing “more” penalty (moving the other three), he will only have 5/72 – that is, to transfer in any case you need a pair with the calculation for poker .
Straight is actually a pretty fucking deal, since the probability of improvement is extremely low. More precisely, it is the same as if you were throwing cubes anew. The only advice, if you still hope to improve the straight – move four dice, leaving one on which the maximum value. The probability of dropping the best cоmbination from this will not change, but if it falls out, it is with this value.