i dont put my money into the site because i dont trust the site completely. thats why i use there money to play. and that really speaks to my poker skills, because i use there money to win more money. unlike ppl who put there own money into the site.

Yes. It means you suck at poker. A winning player isn't going to waste time playing at any limit that earns them less than their maximum return for the time invested.

or spelling

This could be right! Like I mentioned, I wasn't sure if my calculations as to the TRUE value were correct, only that the observed value was posted (and seemed to be close to my true value). Thanks for your post!

(NOTE: too long and skip if don't like technical details)

Yes, but if there are two of each suit remaining, then the probability of a suited flop is zero... I think your example has gone extreme in an impractical direction, and is likely missing the point.

Here's another way to think about the situation. A bias in the flop texture will occur if the distribution of the remaining deck cards becomes polarized (its "entropy" is low). This is a conceptual issue, and is non-trivial. On the other hand, a bias caused by having fewer cards is essentially a technical issue, and is simply due to a loss of accuracy when attempting to approximate subsequent distributions of the deck as community cards are dealt by the deck's initial distribution (which by the way is the popular way to mentally calculate odds.)

In any case, suppose we forgo the above notes, and instead, delve further into the issue, and quantify it via examples/calculations.

Generally speaking, bias in the color of the flop caused by playing paired holdings happens on a significantly smaller order of magnitude than the one due to playing suited cards, which is why we can expect it will almost surely be absorbed by the latter. (of course, it's possible there are other more significant biases that will counter the latter, but this is not our concern here!)

Consider two examples.

Ex1. 6-handed, half the players are dealt hearts, the other half
dealt another spades. Then the probability of a suited flop is 6.49%. By contrast, if we assume no a priori knowledge about players' holdings, then the probability of a suited flop is 5.18%. A difference on this scale (6.49% vs. 5.18%) would be felt after running into about 6000 such hands.

Ex2. 6 handed, all players dealt high pairs. The probability of a
suited flop is 4.86%. As before, without a priori knowledge, the
probability of a suited flop is 5.18%. This difference would
be felt after running into about 100,000 such hands.

Note in Ex1., the probability of half the players being dealt a single
suit and the other half being dealt another is about 9*10^(-8) %, and
in Ex2. the probability that all players are dealt pairs is about
3*10^(-8)%. So, the scenario in Ex1. is about 3 times more likely,
which makes it easier to observe empirically (it requires going through about 50 times as many hands to observe the bias in Ex2.; on the other hand, good players may be more likely to see flops with pairs than with generic suited cards. But there are armies of bad players who like nothing better than play cards simply because they're suited.)

More generally, let P denote the probability of a suited flop given no a priori knowledge about the distribution of the remaining deck cards. Let N be the number of players. Suppose roughly half of the players are dealt one suit, while the other half is dealt another. Then the probability of a suited flop becomes about

0.5*P*(1-2N/52)^(-1)*(1-2N/51)^(-1)*(1-2N/50)^(-1)*(1+(1-N/13)*(1-N/12)*(1-N/11) ~~ P*(1-0.0079*N+0.0049*N^2+0.0004*N^3)

(e.g. in Ex1. above, N=6, P=5.18%, so according this calculation the new probability is ~ 6.47%, which is pretty close to 6.49% from before)

On the other hand, given N players, suppose each two players are dealt pairs of the same rank. Then the probability of a suited flop becomes about

P*(1-2N/52)^(-1)*(1-2N/51)^(-1)*(1-2N/50)^(-1)*(1-N/26)*(1-N/24)*(1-N/22) ~~ P*(1-0.0079*N-.0003*N^2-0.00001*N^3)

(e.g. in Ex2. above, N=6, P=5.18%, so according this calculation the new probability is ~ 4.87%, which is pretty close to 4.86% from before)

The thing to note are the coefficients of N^2 and N^3 in both equations, which are clearly much larger in the first equation (about 17 times larger for N^2 and 40 times for N^3). Remember, the first equation corresponds to the suit bias case). This suggests bias in the flop color due to playing paired holdings will be absorbed in the one due to suited holdings (if both occur and induce flops with relatively comparable frequencies, which are plausible assumptions as explained before).

Here is another perspective on the situation. Imagine a generalized deck with R ranks and S suits. So the total number of cards, call it M, satisfies M=R*S. Also assume R~S and both are large (so as to eliminate degenerative cases; e.g. R=1 S=10^10 is not interesting!). Let P denote the probability of a suited flop given no a priori knowledge about players' holdings. Then, given N players, if all of them are dealt the same suit to exhaustion, the chance of a suited flop is approximately

P*(1+1/R)

On the other hand, if all players are dealt the same rank to exhaustion, then the chance of a suited flop becomes approximately

P*(1-1/R^2)

So, the pair bias will decline like 1/R whereas the suit bias will decline like 1/R^2. The latter is a completely different (much faster) order of decline.

In any case, the basic point is this: bias in the color of the flop due to playing paired cards happens on a small enough scale that it'll be absorbed by the bias resulting from playing suited cards! In other words, deviations caused by the former will be difficult to measure empirically. This could've been anticipated from the start as pair bias arises for purely technical reasons.

p.s. damn, I didn't intend for this to get that long. I have other **** to do.

me 2, im gonna make an educated guess and say no. the OP was prolly lying to try and get people to feel bad for him and bring bad press to Stars cuz he blames them even though the truth is he sucks at poker. prove me wrong OP, prove me wrong.

I'm not sure I see the relationship between suited holdings necessarily biasing the color of the board and the examples you're using.

I think of it this way - in an N-handed table, 2N cards are dealt to the players before the flop. Having suited holdings is a function of how the suits of the cards that happen to be dealt are distributed relative to specific players, whereas the effect that the suits of the cards that are dealt has on the probability of seeing certain types of flops is a function of the number of cards of each suit in the dealt cards overall.

Your example of having 6 players being dealt suited hearts and 6 suited spades would certainly be one where the remaining cards in the deck would have an uneven distribution, but that is a specific and somewhat extreme case that doesn't I don't think reflects cases where players hold suited cards in general.

As a counterexample that illustrates the distinction I'm describing above, consider a 4 handed table where one player is dealt two spades, one two diamonds, one is dealt two hearts and one two clubs. Then you've also got a situation where all the players have suited cards and the suit distribution of the remaining cards is still exactly even. Then you could take all those suited cards and redistribute them among the players to create a situation in which nobody has suited cards and the same would hold. So it seems to me that players having suited cards alone is not sufficient to necessarily have an large effect on the chances of seeing a suited flop. What really matters is whether the same number of cards of each suit are dealt, regardless of which players get which cards.

***grunch***

it's spelled scame.

This might well be but this isn't really what I was talking about.
Your earlier statement seems to say something quite different (and imo wrong) so I corrected that. Anyways, your calculations seem interesting, maybe I'll have time to look into it anytime soon. I doubt that it's as easy to calculate which bias will be more measurable as there are likely about 312978525716 other things to consider. For example (just to show that things are really unbelievably complicated):
If two or more people each have a pair the likelihood that a flop is dealt is very high. Pairs aren't folded preflop that often. Suited cards don't seem to influence things that much.
So, let's assume that a flop was dealt and we're in a HU pot. The likelihood that both players have pairs is much, much higher than the product of the a priori likelihoods. Granted, the chance that both of them have suited cards is higher than usual, too but I'd expect this effect to be smaller than it is with pairs.

Interesting thread -

I think Daxonovitch got the chance of receiving a paired flop slightly wrong. The way I calculated it was essentially:

chance of a paired flop = 1 - (chance of an unpaired flop)
= 1 - (chance 2nd card is distinct in rank from 1st * chance 3rd card is distinct in rank from both previous cards).
= 1 - (48/51 * 44/50)
= 17.17647%

Looks like I got the same number as 'joka', think this one is correct.

Everyone runs bad sometimes....except Jamie Gold.

Did he win that with a suited flop?

Yes, but he had top top

I think you're still missing the point joka... this part of my previous post might help

"Here's another way to think about the situation. A bias in the flop texture will occur if the distribution of the remaining deck cards becomes polarized (its "entropy" is low). This is a conceptual issue, and is non-trivial. On the other hand, a bias caused by having fewer cards is essentially a technical issue, and is simply due to a loss of accuracy when attempting to approximate subsequent distributions of the deck as community cards are dealt by the deck's initial distribution (which by the way is the popular way to mentally calculate odds.)"

Also, maybe rethink the "1/R" vs. "1/R^2" calculation to see it.

Cheers

Thanks for the post. "suited holdings" refers to situations where the same suit is dealt to many players.

Okay, I was thinking of suited holdings as a pair of suited cards for individual player(s), so perhaps that's not the right term.

-28 EV buyins, obv rigged IMO

Which one of you "Stars is rigged" fish is this? Sounds like youve spent quite some time learning custom stats for your project. LOL. If you just spent that time working on your game... oh the wasted energy.

Why is it so difficult for some people to admit to themselves that they were not born being immediately brilliant at poker? Such that there must be some easily identifiable, yet somehow overlooked, conspiracy that proves their mediocre results are not their fault? How are so many people so desperate and delusional? You really think Stars made it so an ace flops more than it should? LOL? Something so blatant and yet its gone unnoticed by all these people for all this time? LOL. Wow.

IMO the players out there that are intuitive enough to go through the trouble of creating custom stats/reports to backup their "rigged" beliefs like the one in the link are not the ppl i wish to flame.
Like you say above they are blinded by their inadequacies / insufficient poker education causing them to think conspiracy, but i see a big difference in someone who actually tries to prove something before they spout it off and someone who doesnt like JimRob...

ok now please let this thread DIE

mappedout,

That is a fair point. And if everyone just assumed it had been checked, nobody at all would check it. But still. This far down the line... all that energy on something like that... its just amazing to me. I guess kudos to him for staying low profile and doing it on his own though. Each to their own. I was out of line.

I am running so good it's proof stars is rigged... i have been playing like caka but flushes and underpairs hitting trips easily turn me from a losing player to a winning one.. i don't see what the issue is?