# What are the odds?

I get a lot of emails. I obviously respond to everyone, even if the time in which I am extremely bad. So I thought to write this article to answer a question I am often asked in different forms. The question goes something like this: "I had such and such a hand that was very good, but my opponent beat me as those with a better hand than me. What are the odds of that happening?

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An interesting analysis of a more interesting hand

I get a lot of emails. I obviously respond to everyone, even if the time in which I am extremely bad. So I thought to write this article to answer a question I am often asked in different forms. The question goes something like this: "I had such and such a hand that was very good, but my opponent beat me as those with a better hand than me. What are the odds of that happening?

From here, you're probably wondering how I'm going to answer the question, "What are the odds" for several situations in this article. Well, I will not answer exactly. In fact, answer the question is not an issue for most useful discussions of poker and actually "what are the odds that" it is often a question unanswered. Let me give you an example.

A friend of mine recently questioned me on a hand in which a player had a flush to the ace was beaten by K Q for a straight flush. Our hero had A 8 , While the board J was 10 9 an unpaired board therefore K Q was literally the only hand that could beat the flush to the ace.

"What were the odds that this guy is the King and Queen of Diamonds" asked my friend?

I told him with a step back, "Well, what do you mean? "He replied:

"Well you know, what are the chances that this particular player will be distributed the King and Queen of Diamonds"?

"Ok, I said after thinking a bit" is 1 chance in 1225 to receive two cards you're talking about me, "and then I tried to explain that even if the chances that the opponent has K Q were 1 in 1225 that any player at the table would have played this hand, the odds change significantly. I told him also mentioned that the board cards had to be considered.

Unfortunately, I later returned to what I said when I heard the details of the hand because I would have advised caller supposedly flush with the ace because I would (supposedly) said the chances that the opponent has K Q were 1 in 1,225. Indeed, even without knowing the action in this hand, I knew that the chances that the enemy has K Q were much better than 1 in 1225. To demonstrate this, try to estimate the current probabilities.

First, do some calculations without considering the action of the hand. It was a hand with 5 opponents (table 6 players) and therefore, the chances of a 5 opponents is dealt K Q were about 1 in 250 or 0.4%. (The odds of a particular player is done to distribute the hand are 5 times less large).

Let this hand travel to the river without K or Q on the board. We can therefore say that there are 45 unknown cards making the likelihood of a specific player has K Q only 1 out of 990 and the likelihood that someone is dealt K Q about 1 in 200. So the probability of 1 in 1225 is clearly not right.

But all these mathematical completely miss the importance of this hand. A mathematician poker (and I feel more comfortable to appoint me as a "real mathematician") should consider the action early. So what have been the actions? I later learned that the enemy in question had wedged a raise of \$ 2 before the flop, checked the flop (our hero also checked), checked the brick on the turn (our hero still here also checked) bet \$ 5 on the river and raise all in (\$ 75) due to raise our hero to \$ 15.

It may not be very elegant to analyze the hand this way, but are starting on the river. Which hand a player would build this river then reraiser all in? Certainly K Q is one of those hands. A flush with aces or 8 7 would also be possible, but not in this case because our hero A 8 . Several players have also made a reraise flush with the king. Other players still could have made this game with a smaller flush or a straight, but at this moment, I would say that my friend described to me the opponent as "tight" what makes us exclude these possibilities. Now back to the action of the beginning of the hand. If that player was tight, there is not much he could have connectors with a king. The K J , K 10 , And K 9 are impossible because of the board. K 8 is impossible because our hero 8 and K 7 or worse, is not a typical hand that a tight player Raises the call preflop. Thus, the only hand I really think the player could have reraiser value for K is actually Q .

The next question is whether this player bluff tight times? Well, without more information (all the information I have on all poker players are treated as "no more information", ie, as partial information) I would say that this player bluff occasionally because bluff almost every player, whether or not often. They are not poker players if they never bluffing. But the most logical hand with which he could bluff is if he had the A and, again, this is impossible because our hero that hand. What is the percentage now that this player has attempted a big bluff with something like 7-7 or 5-5 or possibly with only the Q or K ? This question is more important than knowing what the probability that our opponent is seen distributing K are Q before any action has taken place. It is the key to whether a call is profitable because our flush the ace beats no reraise for value here (ie it only beats a bluff).

What's funny is that in making my first analysis, I told my friend with A 8 Because it was the second nuts, the call was good. After watching and studying the hand closer (and obviously known actions of the hand), I estimated the chances that the opponent in a low limit has exactly K Q approximately 80%, which clearly requires our hero folder with its flush to the ace. But, believe it or not, learn to fold this big is not what will transform the average player into a good player or a good player into a great player. Instead, the hero should ask why he tried slowplaying the second nut until the river is that this way of doing will bring him much in the long run?