LG John

Hi guys, maths isn’t my strong point so can someone check to make sure I’ve got my poker maths correct.

Lets assume (this is texas holdem btw) I have the Ace and 2 of hearts and I find myself in the pot after the turn with just one more card to come. The board is 5h, 6d, 7c, 8h. At the moment I have Ace high (i.e. nothing) but given the amount of people still in the pot its fair to assume that someone has a 4 or 9 giving then a straight thus if I catch an Ace (my overcard) it won’t be enough as I need to make my flush to beat the straight. Under this circumstance I have 9 outs (outs being cards that can turn my hand into a winner). 9 because there are 13 hearts and I’ve seen 4 of them hence 9 left out there. Of the 52 cards in a deck I can see 6 (2 in my hand, 4 on the board) of them so there are 46 unseen cards, 9 of which help me and 37 of which do not. Accordingly a ratio of 9 wins to 37 losses applies so I’m a 9:37 dog. 37/9 is 4.1 so if I draw under the same conditions over the course of many hands I’ll win once to every 4.1 losses or 1:41 (I know this part of the maths is correct as I checked with various sources re: flush drawing at the turn)

I’m last to act (i.e. cap the betting) in the hand and have to pay £2 to call the bet with £14 in the pot. The £14 pot divided by the £2 I must pay to play is 7. In short for every £1 of risk I stand to gain £7 or 1:7. On this basis it is correct to call – yes? The logic being that if I made that same decision every time over say 12 hands I’d win 3 times (rounding to 1:4) gaining me £14x3 = £42 and loose 9 times loosing me £2x9 = £18. Thus £42-18 = £24 profit Is this all correct or have I missed something?

Also can you express it like this (this is that bit I want to be REALLY sure of): I know that my chance of winning is 1:4. If I have to make a £1 to call the pot must be greater than £4, or for a £2 call greater than £8 or for a £3 call greater than £12 and so on?

BTW, this is just one of the examples of how poker is a skill game more than gambling. It’s about quickly calculating if over the long run a call under any particular circumstance will be profitable or not.

Many, many thanks to anyone that takes the time to confirm my maths

Gordo

There's more to it, but your logic looks good so far.....

i.e. there are a number of other outcomes if a heart is not turned:

- you could still win if noone has an Ace, or a 4-9 (a 4 or 9 would complete the straight, any other card 5-8 would give them a pair), or another pair

- even if a heart is turned, there is an outside chance that it could complete a 4 of a kind (if someone, say, held two 6s in hand, and a 6 of hearts is drawn)

Doesn't affect your overall conclusion, just the odds required to calculate it.

Gordo

BOB.T

SNAP! is more my forte

mattstant

hmmmmm after much consultation and head scratching i have come to the conlusion that.















wait for it
























buy a lottery ticket
Its much simpler and you lose less

Blobster

Just a thought, but of those 37 cards that don't help and 9 that do, would you not need to subtract the cards held by the others at the table, and work out the probability that any of these (unobtainable) cards may be hearts - thus lengthening your odds considerably.

Don't play poker myself, but watch CH4 late night poker as often as poss and would love to start playing (for meagre sums initially).

Blobster

Good luck with the hand.

LG John

Gordo I'm very well aware that a heart might not be my only 'out' but for the simplification of checking my maths I assumed in the scenario above that the ONLY cards that could save me is one of the remaining hearts and that if I got it I'd have the nuts. It would take a particularly gifted player to tell if someone had made trips thus discounting some of the hearts I chase as outs (as you say the trip 6s would remove the 6h). The point of the post was to check the maths are correct

Blobster in reality you are correct that theoretically ALL the hearts could be held by other players (with none in the deck) and as such under my scenario you'd be drawings dead. However, for the purpose of 'poker maths' its always done on the basis of what you know V's how many cards are left that you'd don't know about (whether they are in the deck or not). A good player can often spot when another player is acting like they have a card that would normally count as an 'out' and you can thereafter discount it from your conclusions and calculations given that by you hitting and making a great hand he/she makes a monster!

Old_Fart

You should have folded on the first flop. However by playing badly early on you find yourself in this position where you should definitely call as the action indicates no one is representing a strong hand so the 'pot odds' now favour you. Considering there have been 3 rounds of betting how can there only be £14 in there? Everyone has checked hoping to catch a free card? Damn poor poker players for not forcing oponents out earlier.
Have you read Sklansky, Theory of Poker? It rocks
Cman

LG John

Old fart I know exactly what you are saying and to answer your other questions/point I am working my way through several books.

As I said in my most recent post the situation outlined above is just to test the maths and is very unlikely to present itself exactly like that to me. For a start I play poker online so would only play A2s from a late unraised position and unless 10 peeps had come in making it a massive pot (to justify any outs I might have) I wouldn't play beyond the flop to the river so you are quite correct that I wouldn't even be there so to speak.

In hindsite I should have put 'please confirm my maths' to keep poker players out the thread. Its not that I don't enjoy the conversation (I do, so keep it going) but rather that the point was an exercise in maths not poker

Old_Fart

Sklansky deals almost exclusively with the maths behind the game. As you've said it's all about playing 'correctly' and that means playing the odds...but since you never really *know* what the other guy is playing you have to alter the odds based on reading the action..what are they representing? In your example it's pretty safe to assume no-one is holding a pocket pair and has any hope of a full house, in which case your maths looks right.
A more complicated example would have one of the players betting out early on..in which case you have to adjust your odds of catching the heart with the probability that he just got his full house.
Fundementally you always bet when the pot odds are better than your chances..so you are a 1 for 4 dog (3 to 1 in common speak)to catch the heart (which is 99% to be the nuts) and the pot pays 7 for 1 (or 6 to 1) you have to bet.
It's determining your odds which elevates poker beyond pure maths....
C

Rgds
Cman

Fast_Blue_Scooby

Hi Saxo Boy,

How much are you winning from your latest scheme? LOL!!

I've got my game cracked, the one you were trying to get into before, arbing!!

Made over £2500 over the last few weeks and almost £300 today.

I spent ages setting up loads of spreadsheets, calculations etc to cover everything I do. Now it is all at hand.

Is there not something you could download that would analyse your situation and prompt you what to do next? Along with the probabilities etc.

I am sure there should be something, I know I downloaded one for blackjack, to analyse my card counting skills but when I found out that most online casinos (if not all of them), shuffle the pack every single go, I gave that one up.

But if you could get hold of some software or write your own, it would be a great benefit to you in the long run.

elgordano

go 'ALL IN' and bluff your way out of it !!

Gordo

LG John

I'm still up at the moment but there is defo some cracks in my game and I'm trying to improve and sort them. The arb betting just seemed too fast paced for me - i.e. you always had to be ready to pounce and **** knows how you go about spotting them

Fast_Blue_Scooby

Saxo, there are a good 5-10 arbs every day on the horse racing.

You just need to know your horses, which way you think the market will go, what you think the general public will be betting on at the race track and away you go.

Using the exchanges, you can either cover your stake and win if the horse wins or guarantee a sum either way.

Of course you keep the info to yourself, or in my case, I share it with my own syndicate and we all get on within seconds of each other.

I must admit it is fast paced but that is where you get the buzz!!!

I suppose when I am older, I may take up cards!!!! LOL!!!!!

LG John

You have gained a lot of knowledge it would seem to do this well. Its like me inviting you to play poker. I'd mug you for stacks of cash until you pick up the game. That's ultimately why I'm trying to built on something I'm already ok at and have good knowledge of