Thread: Combining probabilities

Say I want to find out how lucky/good I am for example in poker at different sized table.

For example on a 10 player table I would expect to win 10% of the games but on a 2 player table I would expect to win 50%

Who would one go about combining the figure for various sized tables to get one over all figure?


I suppoe I coudl divide by the expected %age?

So on a 10 player table I would divid eby 10 to get 1
And on a 2 player table I would divide by 50 to also get 1.
etc on a 4 player table divide by 25 etc...

Seems reasonable I guess?

You need to know how many tables are there for each number of players.

Originally Posted by mathman

You need to know how many tables are there for each number of players.

Do you?, not sure it matters.

Originally Posted by esbo

Originally Posted by mathman

You need to know how many tables are there for each number of players.

Do you?, not sure it matters.

Yes. If almost all tables are 10 players, you have 1/10 survival prob. If almost all tables are 2 you have 1/2 survival.

Frankly I'm not sure what is a precise statement of the problem. It would help if you would describe the underlying situation.

you should expect to win about for n players at a table, in it's most simple form.

Multiply all of your percentages (in decimal form, which means you take your percentage and divide by 100 [or move the decimal point two places to the left]). So for example, if you have a 10% chance of winning at some table, and a 25% chance of winning at another table, your probability of winning about both is .1(.25)= .025, or 2.5%.

Not sure if I answered your question or not, but be sure to write back if I didn't.

Originally Posted by mathman

Originally Posted by esbo

Originally Posted by mathman

You need to know how many tables are there for each number of players.

Do you?, not sure it matters.

Yes. If almost all tables are 10 players, you have 1/10 survival prob. If almost all tables are 2 you have 1/2 survival.

Frankly I'm not sure what is a precise statement of the problem. It would help if you would describe the underlying situation.

Well what I was getting at basically what percentage of games a player wins.

OK start with the easy situtation, all the games are at 10 player tables, that is easy enough, you might see one player wins 12% of the games and one wins 7% and so on. You can deduce something from this perhaps, ie how lucky he is, or perhaps how aggresive he is (when he wins by making a big bet and nobody calls the bet).
The normal percentae here would be 10%

OK that is easy ennough, but say you have similar data for 6 player tables the normal percentage here would be about 16% (1/6).

What I would like to do is combine the data gathered from all table sizes into one figure.

The obvious way is to divide by the expected %age, so maybe 12% at 10 player table and 18% at a 6 player table would give.

(12/10 + 18/16)/2 = ( 1.2+1.125)/2 =1.1625

So that would tell you something (perhaps?).

since it's player dependant, the probability is variable.

Originally Posted by Arcane_Mathematician

since it's player dependant, the probability is variable.

???what?

Originally Posted by esbo

Say I want to find out how lucky/good I am for example in poker at different sized table.

For example on a 10 player table I would expect to win 10% of the games but on a 2 player table I would expect to win 50%

Who would one go about combining the figure for various sized tables to get one over all figure?


I suppoe I coudl divide by the expected %age?

So on a 10 player table I would divid eby 10 to get 1
And on a 2 player table I would divide by 50 to also get 1.
etc on a 4 player table divide by 25 etc...

Seems reasonable I guess?

The measure of success in poker is NOT the percentage of hands won, but the total gain or loss.

Poker is a zero-sum game. It doesn't matter how many players are in the game, on average a player will break even. If you make money you are above average. If you lose money you are below average. If you just break even you are average.

Originally Posted by esbo

Originally Posted by Arcane_Mathematician

since it's player dependant, the probability is variable.

???what?

see my first post in this thread. The probability of you winning is, approximately, in terms of percentages,% where n is the number of players at the table, since in a blind draw each of you has an equal probability of getting the winning hand.

And, Rocket makes a valid point on success, though I assume you simply wanted to know how often you would win, (i.e. suppose there were no money involved)

Originally Posted by Arcane_Mathematician

Originally Posted by esbo

Originally Posted by Arcane_Mathematician

since it's player dependant, the probability is variable.

???what?

see my first post in this thread. The probability of you winning is, approximately, in terms of percentages,% where n is the number of players at the table, since in a blind draw each of you has an equal probability of getting the winning hand.

And, Rocket makes a valid point on success, though I assume you simply wanted to know how often you would win, (i.e. suppose there were no money involved)

If there is no money involved you are playing some game other than poker. The whole point of poker is to balance probability, strategy and psychology. The skill in poker lies in the betting. Without betting and the player having some "skin" in the game, there little difference between poker and craps. Everybody at the table has an equal chance of getting a good hand. It is the skilled players who "know when to hold 'em and know when to fold 'em" and therein lies the essence of the game. Poker is not really a game of chance, except when players are relatively evenly matched or over a very short period of time.

Betting affects the probability of winning. That is part of the strategy of poker. If you leave that out of consideration you are analyzing some other game.

I have a friend who makes money pretty regularly playing poker. His secret ? He only bets when the likely return justifies the bet. He wins because he knows the odds and because he gets into games with people who don't know what they are doing. He just loves playing with idiots.

That is why good poker players can make money, while those who gamble on most other games eventually lose. In poker you do not play against the house, you only play against other players. The house only gets a small fee for each pot. After that the players play against each other, and that is a zero-sum game. Good players can consistently come out on top, because there is strategy involved. Bad players consistently lose. This is despite the fact that there should be no long-term statistical difference in the hands that they are dealt. If it were not for strategy, then in the long run everybody would come out even (less the fee paid to the house). But the sheep get sheared regularly, and the good players are not gambling.

Esbo, want a game ?

Originally Posted by DrRocket

Originally Posted by esbo

Say I want to find out how lucky/good I am for example in poker at different sized table.

For example on a 10 player table I would expect to win 10% of the games but on a 2 player table I would expect to win 50%

Who would one go about combining the figure for various sized tables to get one over all figure?


I suppoe I coudl divide by the expected %age?

So on a 10 player table I would divid eby 10 to get 1
And on a 2 player table I would divide by 50 to also get 1.
etc on a 4 player table divide by 25 etc...

Seems reasonable I guess?

The measure of success in poker is NOT the percentage of hands won, but the total gain or loss.

Poker is a zero-sum game. It doesn't matter how many players are in the game, on average a player will break even. If you make money you are above average. If you lose money you are below average. If you just break even you are average.

Poker is not a zero sum game, not when played online anyway as there is a commisiion 'rake' which goes to the poker site, usually 5% of each 'pot' won.
So you have to make 5% just to beak even.

I never said it was a measure of success, it is a measure of many things combined such as playing style and indeed luck.
The statistics are not much good unless you have a lot of data anyway (usually).

It is more helpful when you combine it with other statistics, such as how the hand was won, which would also need to be combined for table sizes.

Originally Posted by DrRocket

Originally Posted by Arcane_Mathematician

Originally Posted by esbo

Originally Posted by Arcane_Mathematician

since it's player dependant, the probability is variable.

???what?

see my first post in this thread. The probability of you winning is, approximately, in terms of percentages,% where n is the number of players at the table, since in a blind draw each of you has an equal probability of getting the winning hand.

And, Rocket makes a valid point on success, though I assume you simply wanted to know how often you would win, (i.e. suppose there were no money involved)

If there is no money involved you are playing some game other than poker. The whole point of poker is to balance probability, strategy and psychology. The skill in poker lies in the betting. Without betting and the player having some "skin" in the game, there little difference between poker and craps. Everybody at the table has an equal chance of getting a good hand. It is the skilled players who "know when to hold 'em and know when to fold 'em" and therein lies the essence of the game. Poker is not really a game of chance, except when players are relatively evenly matched or over a very short period of time.

Betting affects the probability of winning. That is part of the strategy of poker. If you leave that out of consideration you are analyzing some other game.

I have a friend who makes money pretty regularly playing poker. His secret ? He only bets when the likely return justifies the bet. He wins because he knows the odds and because he gets into games with people who don't know what they are doing. He just loves playing with idiots.

That is why good poker players can make money, while those who gamble on most other games eventually lose. In poker you do not play against the house, you only play against other players. The house only gets a small fee for each pot. After that the players play against each other, and that is a zero-sum game. Good players can consistently come out on top, because there is strategy involved. Bad players consistently lose. This is despite the fact that there should be no long-term statistical difference in the hands that they are dealt. If it were not for strategy, then in the long run everybody would come out even (less the fee paid to the house). But the sheep get sheared regularly, and the good players are not gambling.

Esbo, want a game ?

I agree the best way to play is against people who do not know what they are doing, unfortunately there do not seem to many of them about these days!!
It probably does not take bad players to realise they are on a hiding to nothing and they may as well play roulette where they will have the same chance as eeryone else. What usually happens is all the player have a high skill level so it is only the house which wins!!
Being 5% better than even a moderate player is pretty tough, occasionally you will get a really bad player at the table who is chucking their money away although sometimes this may actually be a good player who has had such a bad run of luck that all rational play has gone out the window (known as 'tripping'), however you can still lose your shirt to such a player if he gets lucky!!

When you get 10 good players around a table it basically is gambling and it is a good time to leave, so I will probably turn down our invitation!!
I don't play much for money these days, playing well can be very very boring and there is a fair chance you are playing against a computer, whose boredom threshold will be considerably higher than mine!!
You also have the possibility of various forms of cheating, including the site itself cheating!!
There may also be problems with tandom nnumber generators they use.
Hene I will turn down your invation I don't like playing 1 on 1 much anyway.
Besides I don't like to take money off you :wink:

There is a great deal of maths in the game though, and psychology, it's a very easy game to play when you get good luck, imposible when you don't!
I think it is one of the few games where humans can still beat computers!

One odd thing about the game is that there are some hands which are very hard to play, you just can't figure out i your have your opponent beaten or not, and then it comes to the showdown, and you find out why - you both have exacly the same!!
I mean you can tell the difference between an opponent holding AJ and AQ.

I lilke the more complicated games now though such as Omaha hi/low and also 'razz' which is not poker but a game where the worst hand wins!!
I play a lot of freerolls now - more fun, no stress, nothing to lose but a chance of a small prize which means people play seriously.

Actually I find that the more hands you win the more money you lose, for eample on a ten player table I find, the optimum win rates is about 8% less than the 10% average.

Anyone winning more then 10% is either very lucky or playing too many hands.

You can win more hands by bluffing, however you don't win much and eventually you run into some one with a very good hand, and all your previous winning and more will not be enough to make him put it down as often they will have the best hand possibleor if not they will have a good idea you bluffed you way to earlier pots.

Anyway bluffing is basically betting against the odds, not a good long term strategy!!

Some of my worst loses, an Ace flush against a straight flush (very rare) and 4444 v 9999, the last one was against a player I knew was incredibly good, the board was 4499A so I am thinking he either has AA or 99.
He could have just had a 9 but his earlier betting ruled that out and indicated a pocket pair. I had to call his all-in just to see the showdown, of course he had 99!!
Lost about £13 IIRC

I will leave it to you to work out the odd of that!!!

Originally Posted by esbo

Actually I find that the more hands you win the more money you lose, for eample on a ten player table I find, the optimum win rates is about 8% less than the 10% average.

Anyone winning more then 10% is either very lucky or playing too many hands.

You can win more hands by bluffing, however you don't win much and eventually you run into some one with a very good hand, and all your previous winning and more will not be enough to make him put it down as often they will have the best hand possibleor if not they will have a good idea you bluffed you way to earlier pots.

Anyway bluffing is basically betting against the odds, not a good long term strategy!!

Some of my worst loses, an Ace flush against a straight flush (very rare) and 4444 v 9999, the last one was against a player I knew was incredibly good, the board was 4499A so I am thinking he either has AA or 99.
He could have just had a 9 but his earlier betting ruled that out and indicated a pocket pair. I had to call his all-in just to see the showdown, of course he had 99!!
Lost about £13 IIRC

I will leave it to you to work out the odd of that!!!

Ouch, what a bad beat.

Originally Posted by salsaonline

Ouch, what a bad beat.

Yes an I didn't even get a 'bad beat jackpot', it needed to be JJJJ or higher.

I actually lost more on the other hand about £40 IIRC I had the ace of something else of hearts and the river gave me an ace flush as there were two other hearts on the board, it never crossed my mind that a straight flush was possible I just though I had the nuts I could not beleive I had lost!!
Just my luck I get an ace flush when a straight flush is on, or is it rigged? However I guess I only have myself to blame for not checking properly but I think a lot of players would have missed it too. Perhaps
I didn't play at that site again for a while.

I know lot of sites allow players to change thier idenity which is unfair as they know my game but I don't know theirs, I basically think it is all rigged these days so I don't play much for my own money anymore.

casinos are much better, less computer generated randomness, more REAL randomness. No rigging realistically possible in a casino Hold 'um game, nor advantageous to the house, so its less likely that the house would even WANT to rig a Hold 'um game.

Originally Posted by Arcane_Mathematician

casinos are much better, less computer generated randomness, more REAL randomness. No rigging realistically possible in a casino Hold 'um game, nor advantageous to the house, so its less likely that the house would even WANT to rig a Hold 'um game.

The rake is higher in a casino, there are also many ways of cheating there.

but those 'ways of cheating' don't benefit the house, and it's in the best interest of the house to prevent cheating everywhere possible. Physical card games are necessarily random, a computer program is not necessarily random, and that is the big difference to me.

Originally Posted by Arcane_Mathematician

but those 'ways of cheating' don't benefit the house, and it's in the best interest of the house to prevent cheating everywhere possible. Physical card games are necessarily random, a computer program is not necessarily random, and that is the big difference to me.

The house can cheat. I was at one casino playing a form of poker, a special casion type where there was little skill involved, the cards were dealt from a 'shoe' (a ig stack of cards in a box), I notied the dealer was wining, I suspected the cards were stacked, so I worked out the best place to sit assuming the cards were stacked for the sealer (eectively the 'house'). I started winning then, eventually a new dealer ame along, with a new 'shoe' of cards (why couldn't he use the old shoe?).
Anyway I started losing then aand the dealer started winning, when I had lost all my winnings I quit playing.

There are numerous ways to cheat, what does it matter wheter the houe is benefiting or not? What matters is that you are being cheated. It could be by crooked dealer or players colluding or any number of methods.

A dealers shuffle is not random either, the cards may be marked, the list goes on and on. If people can cheat they will, that's a fact of life.

But the House doesn't play in Hold' um, and if you play a game WITHOUT the house, why would the House cheat?

Does the house tax the players for the use of the table? For example, by taking a certain percentage of your winnings?

Originally Posted by salsaonline

Does the house tax the players for the use of the table? For example, by taking a certain percentage of your winnings?

I don't know how all casinos work, but I have a friend who plays (and wins) fairly regularly. He tells me that the house takes something like $4 per round. In any case it is a fixed fee per hand and not a per centage of the winnings.

A majority of casinos take a fixed rate on a per-game basis, and not from the players, but from the pot, and it's usually less than the buy-in. My Brother goes to Vegas a couple times a year, and always plays Hold um, that's the story I've gotten on it. I, personally, can't wait for my 21st birthday.