I it seems to be ~ to be seeing another player, or myself, having 4 the a kind as soon as every 100 - 150 hands.

You are watching: Odds of 4 of a kind

This has happened in the an ar of 20+ times over the food of 2 weeks. I supplied to watch 4 of a kind when every 1000 - 2000 hands.

I"m recognize it fairly odd, I"ve had it around 6 time myself in the past 2 weeks. In the period of seeing all of these 4 that a kinds, I"ve played around 2000 - 2500 hand at most.

How frequently statistically, should any kind of player in ~ a 9 seat table be obtaining 4 that a kind? even if lock fold and I don"t view it, what"s the basic odds of 1 in 9 football player making 4 of a kind?

As a bonus question, if ns may, what are the odds of losing with 4 the a type to a better 4 of a kind?


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edited may 24 "16 in ~ 5:56
Dom
asked might 23 "16 at 20:19
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1) according to http://wizardofodds.com/games/sdrta.net/, the probability that you deserve to see quads at a 9-player table (assuming no one ever folds) is:0.013183% or ~ once every 7586 hands

2) For her bonus question, i am not fairly sure if that"s what you are looking for, however have a look in here: http://forumserver.twoplustwo.com/25/probability/quads-over-quads-odds-866086/(assuming the 2 players start with 2 pocket pairs,and they"re walking to check out all 5 ar cards) that is calculated: ~ 1 in 38,916 hands

++ quick tip by the way: ns would"t worry too lot if I ever won/lost a huge pot with/to quads. Due to the fact that it happens that rarely, the doesn"t make lot of a difference in her gameplay, winrate etc. I would focus much more on "everyday" stuff, like cbet frequency, opening range, calling down frequencies etc and minimize my leaks in those sections.


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edited may 24 "16 in ~ 9:20
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How regularly statistically, should any player in ~ a 9 seat table be gaining 4 of a kind? also if castle fold and also I don"t check out it, what"s the general odds that 1 in 9 football player making 4 the a kind?

The cardinality (whole possible hole + commie cards) is 52 taking 7: 133784560The wanted scenarios for you involve freezing 4 cards being same (13 scenarios) and also 3 the end of the continuing to be 48 cards: 13 * 17296 = 224848.

The odds are like 0.0017 through dividing desired / cardinality, however this will include instances of 4oak being ar cards.

If you desire to to exclude, the in-table 4-of-a-kind (you desire it just for you), then you will need to calculate prefer this:

cardinality: 674274182400 (52 acquisition 7 in details order).scenarios: 13 * 17296 * 5040 (13 sdrta.nets, 48 acquisition 3 totally free cards, 5040 means 7! i m sorry contemplates arbitrarily sort) - 48 * 47 * 13 * 46 * 120 (scenarios where you don"t have one the those cards in her hand, yet anyway the is 4oak, while the last 120 is 5! i m sorry contemplates arbitrary kind in the commie cards; arbitrary type is already contemplated in the hole cards as soon as multiplying 48 * 47).

The an outcome is 0.0014 here.

In this 0.0014, however, one more player (only one!) could also have 4oak, if the happens, scenarios are favor this:

XX vs YY through XXYY? : 13 * 6 * 12 * 6 * 44 * 120 (which stand for: 44 as the ?, 120 as 5! because that arbitrary flop order, 6 in both cases for suit mix in hands) = 29652480.?X vs YY with XXXYY : 13 * 4 * 44 * 12 * 6 * 120 (which stands for: 44 together the ?, 120 as 5! because that arbitrary flop order, 4 and 6 because that suit mix in hands) = 19768320.XX vs ?Y v XXYYY : 19768320 very same situation yet reciprocal.

The inquiry marks change bricks. Therefore you desire to discard those scenarios when another one has actually a different 4oak:

cardinality: 674274182400 (52 acquisition 7 in particular order; this one did not change).scenarios: 13 * 17296 * 5040 - 29652480 - 19768320 - 19768320 = 902154240.

Your odds of acquiring exclusive 4oak and also nobody rather getting one more 4oak is: 0.0013. In the various other 0.0001 case the various other one will get one more 4oak, therefore by having actually an exclusive 4oak there"s a 1/14 possibility the other one has one more exclusive 4oak as well.

Please I need a cross-review in this point! I"d like to inspect if 0.0013 is a an excellent result or ns screwed v the calc application. I recognize it looks quite weird come me this 1/14 difference

As a bonus question, if ns may, what room the odds of shedding with 4 that a sort to a much better 4 the a kind?

Now concentrating on the conditional analysis on the game table. If your hand/commie currently look prefer this:

XX through XXYYY: One arbitrary opponent has a possibility of having actually 4oak in 44 / 45 * 22 = 0.04444?X v XXXYY: One arbitrary adversary has a possibility of having 4oak in 1 / 45 * 22 = 0.00101XX through XXYY?: One arbitrary adversary has a opportunity of having actually 4oak in 1 / 45 * 22 = 0.00101

By having actually those script configurations, you need to map the value of X like this:

2 is precious 0, 10 is worth 8.J Q K A is worth 9 10 11 12.Lets speak to MAP(X) this mapping the converts the values choose I told.12 will be the maximum worth here.

Given those three scenarios which can risk of having one more 4oak from only one arbitrarily opponent, girlfriend require secondary condition: and also the other player beats me through an Y-valued sdrta.net, therefore the worths are:

0.04444 * (12 - MAP(X)) / 12 for scenario XX XXYYY.0.00101 * (12 - MAP(X)) / 12 because that scenario XX XXYY?.0.00101 * (12 - MAP(X)) / 12 because that scenario ?X XXXYY.

See more: The Standard For Comparison In An Experiment, Scientific Method Review

Disclaimer: These outcomes are probabilistic fractions, i m sorry are constantly in close up door interval <0..1>. Since none of these worths is zero, you have the right to calculate H = 1 / value and later on say "the possibilities are 1 in H hands".