Hold em odds, but not the normal ones.... Recurring odds

Hi everyone,
this is my first post here so I'm sorry if this has been discussed somewhere else.

We should all know in Hold Em that odds like AA vs any other 2 random cards are at 85%
What I found particularly interesting is when AA goes heads up more than once, in a recurring sense the odds work out increasingly worse.

Round Percentage
1 85%
2 72.25%
3 61.41%
4 52.20%
5 44.37%
6 37.71%
7 32.05%
8 27.24%
9 23.16%
10 19.68%

Ok, so my percentages aren't completely right but the reason I'm running this is because I'm trying to mathematically, probability wise, show how poker in the long term, even if a decent player can have massive down swings. I'm writing a book on the dark side of poker and too often the info we have is all about saying in the long run, things will balance out.

Ideas like in cash games 22 vs AK not suited, the 2s are better off. 55% vs 45%. I've heard many times how in a cash game this should always be played because of the slight edge. While this may be the case, in the real world over time the odds are bad too.

Round 22vsAK (Chances the 22 will win)
1 55%
2 30%
3 16%
4 9%
5 5%

What I'm getting at is, particularly with tournaments, in the long run, even better cards lose often. What I'm saying is, playing right still can have really poor returns. Ok, these examples don't include multiway pots, which of course decrease the odds total, but then the pot is bigger so ROI risk and all that. Also, I've not included stack size yet. That's another variable.

Let's put this hand forward which I lost, and was where I decided to stop playing poker.

Me 10 10
Villain 3 7

Here I'm 85% preflop. I raised a lot and he called (this guy was a total fool needless to say, I expected to get paid off - who wouldn't at 85%?)

Flop came out with a gutshot straight draw for him.
I'm now 80% 20%. I bet hard and he still called. Gambler.

Turn, up and down for him. I'm still ahead. Despite his hand improving his odds are 18% vs 82% I went all in, even though I couldn't know what he had from being too lose. He called of course and I thought I had a good chance.

You know he got there on the river. This isn't about a bad beat story, it's about recurring play. If I'm always playing right, and betting hard on hands when I'm a massive favourite, I'm supposed to win, particularly when I get called and I'm in front.

But, as I've shown above with recurring play, when you're smashing into stacks of almost equal size of better, it's really a question of time until I bust. I know the goal would be to have the biggest stack, but assuming that I'm a decent player playing some better some worse players, over time, doesn't luck influence more and more? A bit like betting against the house, even if the odds are in the hero's favour, if all is on the line, it will go.

If that's the case, unless I get a stack bigger than others, aren't I'm destined to lose even if I always play right?

I hope this question makes sense to the maths people out there.

Thanks for your answers,
Alisdair.

"
Let's put this hand forward which I lost, and was where I decided to stop playing poker."

Worse reason I ever heard of for stopping. Sounds like the rocks who always complain when their Aces get cracked. Or the players who always have to tell a fish how lucky he was to draw out on them. I always congratulate the winner, telling him " That's why I raised. I was hoping to chase you out before you caught a winner". Or anything to reinforce their style of play.

Quote: Formerplayer

We should all know in Hold Em that odds like AA vs any other 2 random cards are at 85%
What I found particularly interesting is when AA goes heads up more than once, in a recurring sense the odds work out increasingly worse.

Round         Percentage
  1              85%
  2              72.25%
  3              61.41%
  4              52.20%
  5              44.37%
  6              37.71%
  7              32.05%
  8              27.24%
  9              23.16%
 10              19.68%

This math is inaccurate for the discussion.

What you've calculated are the odds that the aces will win EVERY TIME.

They have an 85% chance EACH time. The chances they will win twice in a row is 72%.

I.E. The chance that the second aces will win is still 85%, regardless of whether the prior aces won or lost.

all in with a pair of tens...you got what you deserved

No no I stopped cuz I lost too much and couldn't turn it around over 3 years. What I realised was even when favourite going all in eventually when AT equal stacks I'd lose

Perhaps you misread my hand. I was the same as AA. Wouldn't you go all in AA? Particularly against loose bad player who obviously was on a lucky draw? Why not? I had him. Got what I deserved? I deserved to win 80% of the time. And I'm no rock.

Thanks dj for the most intelligent reply yet which addresses my question instead of criticise my thoughts or style.

What I'm saying is the chances of winning in the long run are low if always reinvesting the same stack like in a tournament. Like if you played Phil hellmuth style tight it's bound to have issues when playing hands out comPletely. Sure if you bluff right points and get someone to fold they are edges. But even with a favourite advantage the likelihood of winning each hand played correctly decreases significantly.

with TT you had no idea you were an 80% favorite during the hand.
you only know that subsequently. TT is not a very strong hand.
sorry, but going all in with TT with a possible strait on the board...
you asked us to assume you were a decent player, i cant make that assumption

Quote: Formerplayer

Perhaps you misread my hand. I was the same as AA. Wouldn't you go all in AA? Particularly against loose bad player who obviously was on a lucky draw? Why not? I had him. Got what I deserved? I deserved to win 80% of the time. And I'm no rock.

Any thought this was one of those 20% times ?? 80% is just that. Lose an 80% chance and decide to quit. DUMB !!!!!

You're not listening to my point so dont worry. If you ain't got the guts to play 1010 against the hugest gambler at the table or fold qq to the tightest player youre not playing the player. My instinct was right.

If you lost too much over 3 years, you lost becuase you were playing against better plays or stupid. Heer this same whine from players. I should have won, how could he call me with A7, etc. Same as saying if only my opponents were smarter I could win. ROFLMAO

This board seems to have non readers. I didn't quit because I lost just this hand. I quit for reasons above. It happened to be my last hand which was the icing in the cake. And no thanks for not answering my real question. Help with the Maths not the opinion on what I want to do. Seems poker players cant accept others who quit this far.

Can someone talk about recurring Maths please?

" assuming that I'm a decent player playing some better some worse players, over time, doesn't luck influence more and more? "

Don't need to be a mathematician to answer this NO !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Quote: Formerplayer

Can someone talk about recurring Maths please?

I think I understand where you're coming from with the recurring odds but it doesn't work that way. If we played an even money coin flipping game you should win 50% of the time.

Round 1: 50%
Round 2: 25%
Round 3: 12.5%
Round 4: 6.25%

Using your logic you may think that by round 4 you're destined to lose. However, that 6.25% is the chances you'll win 4 in a row. If you've already won 3 (or lost 3 or any other combination) the chances of winning on round 4 are 50%. Likewise, when you say round 10 your AA wins 19.6% of the time you should actually be saying "the chances of winning 10 times IN A ROW with AA is 19.6%." Regardless of how you've done on the previous 9 AA hands, your chances of winning on the 10th occurrence is 85%.

Yes thats what I mean.
But, imagine you're all in each time and against equal stacks or reasonable stacks. Then you run into trouble.

First off, poker is not solely based on math. It's based on so many variables, and that's why so many people play it.

If it was solely based on math, and everyone played based on the percentages, then getting draws out of the pot would be as simple as an overbet.

POPCAN! THANKS.

That's what I mean. Obviously there are many variables, the most important here is stack size.

If I'm playing a tournament on and on, the chances of winning every hand that I "ought" to win, and going all in, I have a very slim chance of winning "in any given tournament" unless my stack size is big enough to take the hits. Basically, for better odds I need to lose to small stacks and get lucky some times and outdraw other players (hopefully bigger stacks) sometimes.

I understand that AA vs 2 cards at $100 a shot means I'll win $850 in the long run, everyone should. The part that interests me and I think many people miss is that double or nothing approach is much more complicated and risky.

AA vs any 2 cards
$100 at 85%
$200 at 72.25%
etc

It starts getting to a point where it's a lot like playing the house on a system that will be bound to lose. I know this isn't what poker players want to hear so I'm not surprised by any backlash. In my mind, to win a big tournament you have to play right and still get a bit lucky. While everyone criticises me, I've won many many many STT, and small MTT, I've many times made the money when full tilt was going well in the $22 45 player MTT. It was one of the best pay out games for me. Problem was playing big MTT like 5000 players or so, being sucked out by A6 against my AK or having other worse cards like trip Q with A kicker and someone calling with pocket 3s and hitting their 2 outer. It's happened to us all. The fact that it happens means there are more variables that are likely to influence our likelihood of winning a tournament, when I do the maths, the longer the tournament the bigger the chance luck will come into it

Popcan you're right, by round 4 in a row when I should lose there is still a 6.25% chance of winning. In my mind I was adding up how many times I'd clashed with a certain hand like AA, by the 3rd time I knew it was at risk of not holding up probability wise. Sometimes it did, others it didn't and I didn't sook like people are suggesting. It was calculated. But, when I had a stack 150% the average and against someone who had the same stack, even if I played right and they turned over KK and hit their set, then so be it, is there any other play I should have made? Mathematically, I really don't think so. If that is the case, then aren't we all, even when ahead, at the risk of luck trumping and knocking us out of a tournament? The only issue I can find that keeps bad beats vs good play buoyant is stack size, it's the only way I can see that a good player can survive. Does this sound right?

Yes of course, that's why I was drawn to it too. Love tells and all that too.

What I'm saying is even if a player could see through cards and make the right play every single time. Recurring probabilities determine a much higher chance of failing that I think people realise.

Quote: Formerplayer

Popcan you're right, by round 4 in a row when I should lose there is still a 6.25% chance of winning. In my mind I was adding up how many times I'd clashed with a certain hand like AA, by the 3rd time I knew it was at risk of not holding up probability wise.

I'm not sure if you missed my logic or perhaps phrased that statement wrong. When you've just won you last 3 AA opportunities in a row and you're presented with AA a fourth time you have an 85% chance of winning that hand, not a 6.25% chance. The chances of winning four in a row BEFORE you're dealt your first AA is 52.2% (as you can see in your round percentage chart). In other words, say your goal is to win 4 AA hands in a row:

The first time you're dealt AA you have an 85% chance of winning THAT hand and a 52.2% chance of winning your four in a row.

The second time you're dealt AA you, again, have an 85% chance of winning that hand and a 61.4% chance of winning your four in row as you've already won one and only need to win this plus two more hands.

The third time you're dealt AA you, again, have an 85% chance of winning that hand and a 72.2% chance of winning your four in a row as you've already won two and only need to win this plus one more hand.

On your fourth and final AA you, again, have an 85% chance of winning that hand AND an 85% chance of winning your four in a row as you've already won three and only need to win this hand.

That said, I do somewhat see where you're coming from if you get pushed all-in by someone with a larger stack every single hand. If we're talking tournament play then you do need to win every single time you're pushed all-in in order to continue. However, if everyone at the table is even with you and you win the first hand then you have a sizable chip lead which means that next person who goes all-in won't knock you out of the tournament. Another factor to take into account is that you most likely don't have an 85% chance to win against an all-in raise pre-flop. This is because you need to assume that someone pushing all-in probably doesn't have a horrible hand. A game where everyone is always going all-in does require a lot more luck but a skilled player can also take advantage of that situation.

Quote: Formerplayer

If that is the case, then aren't we all, even when ahead, at the risk of luck trumping and knocking us out of a tournament?

Absolutely, but a skilled player will be knocked out less often and will win these tournaments more often. A player constantly chase bad draws is going to be knocked out early and often.

Quote: Formerplayer

The only issue I can find that keeps bad beats vs good play buoyant is stack size, it's the only way I can see that a good player can survive.

People who play idiotic draws (I hate that term that rhymes with "honk") will be knocked out fairly quickly. Meanwhile the skilled player is waiting for a very strong hand that he will play aggressively in order to extract the most money out of the bad players & calling stations. Going back to the percentages, if a skilled player gets an 85% hand early on against poor players then around 85% of the time he will most likely pick up a sizable chip lead early on that protects him against future lucky draws.