Bad Beats - Myths and Mathematical Regularities

One of the most discussed topics in the poker community is bad beats. Let's start with a...

 

... definition:

A "bad beat" (thus, a hand which you lost in a very unlucky way) – is when a player with a hand that is very likely to win (as a rule with a probability of winning significantly greater than 80%) still loses in the end.

  • Here's an example:

Player A has . Player B has . Both players go all-in before the flop. The probability of player A winning the hand is just under 93% before the flop. In other words, the pair of aces will win in 93 out of 100 cases.

Let's assume the flop is .

Now player A is even a 98% favourite to win with his aces. Player B needs the next two cards to be a ten and a queen (to make a straight), two kings for a full house, or the two remaining jacks for a split pot (which would then be quads with an ace kicker). If the next card is not a face card or a ten, player B can no longer win the hand.

The turn is the .

The aces remain a clear favourite to win, at 95.5%. But the probability has been reduced somewhat, as one of the two remaining kings would now complete player B's full house.

And indeed the river brings another . Ouch! So player B really has won the hand after all. Witchcraft? No, it's purely mathematical law. It is inevitable that even very improbable events will occur at some point of time, because if they did not, they would be impossible, not improbable. Thus, as long as there is still a chance that the player who is far behind can win, then this situation will in fact occur sooner or later. Once in 100 cases, three out of 100 cases or five out of 100 cases, depending on how high the probability is.

Of course we tend to call it "rotten luck" when this law of averages impacts us directly. But it has to happen to somebody. The truly unpredictable thing is that you never know when these unlikely events are going to occur. We only know the probability of their occurrence, and thus we know that they will materialize in the long run in x out of 100 cases. It may very well happen, however, that even extremely improbable events will occur multiple times in a row, but then not again for the next 1,000 times. People commonly refer to this distribution of random events as good luck and bad luck.

If a player loses a hand several times in a row despite being the favourite to win the anger is great, and people quickly start talking about the results being "impossible", or "a complete fraud".

How to deal with bad beats?

In general, bad beats should actually be met with composure. Because as a rule, a bad beat is nothing more than when my opponent puts his chips at risk despite his chances of winning being way too low to merit such action. If that's the case, my opponent will lose if he continues to play this way – it's a mathematical law that will come into effect as soon as a sufficient number of hands has been played. And that is exactely what we want. We want our opponent to make mistakes, and we want him to lose because of it in the long run. Because for every bad beat, we will win 20 times in a similar situation. That pays off in the long run! And that is precisely how the pros make their money.

Are there more bad beats online?

Generally speaking, bad beats occur at the same frequency whether you play online or in a casino. In other words, technology is not to blame for variance.
So why is it then that players often have the impression that there are more bad beats and "improbable constellations" online than in casinos or home games? Well, online you play much more hands per hour, since computers can shuffle and deal faster than human beings. The probability that players will experience more bad beats online than offline therefore increases as well. There are also two psychological aspects:

  • Many online players are beginners, and many of them are poorly trained. This means they make more mistakes than an average player and therefore are often still in the hand even though only a few outs could help them to win the hand. That's the only reason why such nasty bad beats often happen, while more seasoned players remain unscathed more often, because they generally fold as soon as they are offered unfavourable odds.
  • Online poker is generally anonymous, meaning unknown players are playing against other unknown players. The fact that no one knows them and no one can see them tempts some players into making really "wild" moves. There are no embarrassing looks from opponents in online poker, and there are fewer discussions about individual moves as well. Of course, completely crazy plays sometimes lead to heated debates in the chat. However, anonymity is always maintained, and that lowers inhibitions.

Does the computer shuffle at all?

This is another question that is frequently raised in this context. And if it does, what safeguards exist to make manipulations impossible?

First of all, online poker rooms have absolutely no interest in manipulating the cards. That's because the poker room doesn't play against the players, but they play against each other. The only thing the online poker room does is provide the platform to enable a fair game and to ensure that winnings are paid. The operators of a poker room don't care who wins or loses, because they get the same rake, a certain percentage of every pot played, whether player A wins or player B wins.

Players' trust is therefore of vital interest for any online poker room. An enormous amount of effort is invested into making online poker rooms highly secure. Not only do operators deploy every available tool to ensure that the cards are shuffled at random; they also make sure players don't "team up" and thereby gain an advantage over their opponents. Fraud protection is one of the most important issues when it comes to the organisation and technical implementation of online poker rooms.

Let's return to how the cards are shuffled: PokerStars deploys an own hardware that guarantees the cards are truly shuffled at random by collecting random frequency combinations in "atmospheric noise". These "chaotic" data are then distributed randomly once again by mixing the positions of the mouse pointers of thousands of users at a random point of time. The cards are then shuffled based on these completely randomly determined number sequences – individually for each table. That means that somewhere, there is a designated, protected, shuffled deck of cards on a secure server for each and every open table accessible via the PokerStars client software. The shuffled decks for each table are thus fixed for the duration of the game, and are not changed after the flop, turn or river. The cards are shuffled again not until the hand at that table is finished.

 

Myths

In most cases, what people call a "bad beat" not really is tremendous bad luck or luck. Most of the time it's simply due to ignorance about how the odds of individual hands are distributed.

  • Let's look at another example:

We are in the late stage of a tournament. Player A is in the big blind holding , player B is on the button, and decides to go all-in with with his few remaining chips after everyone else has folded in front of him. Since player A has a very good hand, he calls. But in the end the board is and player B wins the hand with a pair of sevens. Did player B really get lucky? Was it a bad beat for player A?

Let's take a look at the probabilities. is a favourite against before the flop, but "only" 60% to 40%. Thus, loses in four out of ten cases, based purely on mathematical law. Amazing, isn't it?

So why is doing so good? Well, and is nothing more than two overcards. It is not a pair or better and are two undercards, not dominated, they do not play against a pair, and it is therefore sufficient, if one of the two cards forms a pair with the board. In addition you may even make a straight or a flush, two pair, etc. Of course has to improve to win, since is a favourite before the flop (due to high card ace). But there are nevertheless a lot of possibilities, and in 40% of cases not only improves on the one hand, but does not catch up on the other hand. Thus, this is NOT a bad beat.

  • Here's another example:
Player A is in late position with . Player B is in the big blind holding . Everyone folds to player A. He raises to three times the big blind. The small blind folds and player B decides to make a fairly loose call.

The flop is . Player B checks in the big blind, player A bets, player B raises, so that both players are now all-in.
The turn is the , the river the . Thus, player B wins with a flush. Was it a bad beat for player A?

Of course, player A was way ahead before the flop (his chance of winning against was 83%). But both players were not all-in at that point. And a speculative call with is thoroughly justifiable.

After the flop, however, the situation looked completely different. Here each player had almost a 50/50 chance to win the hand. Neither of the players has therefore played badly, since each of them would win 50% of the time and since there were already some chips in the pot. In other words, it was virtually a "coin flip" and therefore not a bad beat by any stretch.

  • And here's another, final example from live poker:

The following hand came up at the WSOP 2006:

Jennifer Harman and Cory Zeidman were both sitting at the TV table of the world's biggest poker tournament. Jennifer was holding , Cory . Pre-flop, Jennifer was almost an 80% favourite to win. The flop was . Cory flopped the straight, Jennifer top set. Now Cory Zeidman's hand had a better chance of winning with 64%. Both players bet again. On the turn came the and the favourite changed again. Now Jennifer had a full house and was a clear favourite with just under 98%. There was only one card left in the deck that could help Cory, and that was the . After both players had bet again, the river came and it was in fact the only card that could beat Jennifer. Just after this Jennifer lost an all-in with and thus dropped out of this prestigious, big-money tournament on the first day. All in all the hand was defined by changing favourite roles and so it is not possible to reproach either player.
During the whole discussion involving missed opportunities and unfortunate losses, we should first of all recognise that it helps to know the odds of single hands. To do this, tools are available that compare hands and calculate which hand is the favourite by how many percent and which hand is the "underdog". We at IntelliPoker have developed an odds calculator and made it available at www.IntelliPoker.com.

So the next time you hear a bad beat story, it is wothwile to ask first exactly when the chips went into the middle and then check which hand really was the big favourite at that point of time.

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