Flush on the board

what are the odds of all 5 cards on the hold em board being the same suit. assuming the cards go to the river how many hands would have to be played for the board to "flush"?

this is similar to the question I asked a week or so ago about flopping trips, I just wondered out of how many hands will the entire 5 cards all be the same suit?

the answer to the trips flopping question was one in 425 hands should the flop be trips, this is the same type question.

thank you
KM

0.197%, or 1 in 507.8 hands, not counting straight flushes.

the straight flushes add another 0.00154%

Thank you for all the great info. I have an observation and I would appreciate any feedback- I will try to keep this short.

I have played at an online poker site off and on for the past few years. I won't name the poker site- lets just say it rhymes with jokerstars.

I kept track of a few things after getting some information from this site, and a few other places as well.

Here is what I found after a little over 25000 hands played in about a month. I play Heads up tables only and I play 3-4 hands a minute (15 second hands are the average-sometimes less, depends on the other person). I typically play about 3 hours a day, more on the weekends. So in an average month I will play about 22000-ish hands. I did this research during some time off, and it was about 5 weeks, so the 25000 makes it a little more realistic.

1. Trips flop on average every 120-130 hands (every 20-25 min). Granted I will play at sometimes 2 or 3 tables in an hour, depending on the other person. I strived to stay at the same table, but I really don't think that has much bearing on the outcome. The odds say trips flop every 425 hands.

2. The table will be flush (all 5 cards to the river the same suite) every 150-200 hands (every 30-35 min). This one is more difficult obviously because it is tough to get to the river even with 4 of the same suit out there, but I purposefully had to play some hands differently to get this statistic. The odds say the table will flush every 508 hands.

I have sent this data to the web administrator and asked for some type of explanation, but they don't really address my question. Instead they try to teach me how to play poker. I am convinced that the dealing is somehow altered.

your thoughts-
Thank you in advance

While some would say that your sample is too small (I might be one of them), I find it easier to say that your math is flawed, so how can we evaluate anything you state?

For example:

Quote: strikeu

...3-4 hands a minute...

...flop trips on average every 120-130 hands (every 20-25 min)...

3 x 20 = 60. 4 x 25 = 100. Therefore, according to your 'agerages', you're actually seeing trips about every 60 to 100 hands. Not only is that a big spread, but it is far more frequent that even your math suggests!

Could it be that you're actually seeing more hands per minute that you suggest, and/or that there is more time between seeing trips flop?

Maybe, you're seeing the trips on different tables and forgot to multiply the above hands-per-hour by the table count.

Yes I am seeing more hands per minute than that, especially at a good table with a fast thinking opponent. Here is what happens- I used 3.5 hands per minute, 210 hands an hour as a baseline (I had to use a number). However, I can measure clock time better and more accurately than I can measure hands played per hour, so the less accurate of the 2 measurement tools is the number of hands played. However, I HAVE to use the number of hands played, because the odds are based on number of hands dealt, not time. In my numerical analysis, I’m using time as the known quantity, and interpolating the number of hands as best I can (my function will not go through all my points on the curve LOL). There may be a way to get just the number of hands I have played, but if there is, then I don't know how to get it.

The “flopping trips” is MUCH easier to measure then the flush board. When you dissect it, 2 things affect my experiment;

1. Every time one of these 2 things happen (trips flop or the board flushes), I take time to document it, (basically cut and paste the info from the hand history add it to my existing record keeping) this takes maybe 30-40 seconds to do. This will often make the other person leave the table if they see me "sitting out" or taking too long to play the next hand. So when that happens, I have to stop the clock, and restart counting when another player sits down. The more accurate measure for me is clock time. I can write down the time it happened, and subtract the dead time when no one was playing at the table with me, so Yes in fact it would be more often (measured in the number of hands played) than I said, but in trying to keep the story short, I didn't go into all that and instead tried to make the more important point that trips flop somewhere between 4-6 times more often than the odds dictate, and the board flushes at least that often if not more so.

2. Documentation is even more difficult when I examine the flush board. Getting to the river with 5 cards of the same suit is extremely difficult, especially with a loose opponent. I play very tight (that’s just my playing style), so I have to find another player that is also tight in order to see the river more than once every 8-10 hands. I used averages here also, but the number of hands played versus the number of times I see the river is not as accurate as I wanted as a measurement tool. So, again I use clock time. I am seeing a flush board about every 40 minutes of steady playing (regardless of how many times I get to see the river-which in and of itself that statistic is staggering). Working backwards with my 210 hands per hour, 40 min is about 70% of an hour so I used 150 hands JUST AS A COMPARISON to the 507 hands that the odds dictate (yes this assumes I see the river every hand which is NOT the case). However, It is almost impossible to keep a game going and only used the times I see the river as my baseline.

Bottom line, my point only gets made more clearly if we distill the information any further. If I was seeing these happen maybe twice as often…no big deal, especially based on 25000 hands, but 4-6 times more often??

Both of these examples are probably +/- 10%, which doesn't change my observations that much.

Using observed frequencies of 1/130 for flopping trips, and 1/200 for the board being suited, I show the following, assuming every hand was played to the river.

Trips
Expected = 58.82
Observed = 192.31
Std dev = 7.66

Flush
Expected = 49.52
Observed = 125
Std dev = 7.03

So there trips are 17.4 standard deviations over expectations, and the flushes are 10.7 over.

However, it makes for terrible statistics to make estimates at both the number of observations and sample size, as well as formulating the hypothesis to fit the data.

What this calls for is to make a clean start making EXACT records of how often:

1. Trips are flopped.
2. Board is suited after the river.
3. Flops seen.
4. Rivers seen.

OK, great thank you for the info.

Here is an aside note and a couple of last questions-

I have played this site for a couple of years (off and on for several months at a time when my schedule allows) and have seen this type of dealing since I started playing this particular site. I decided to try a semi-mathematical approach just in the last couple of months, as I seem to have been playing quite regularly since late summer. My point is, I'm not a newcomer to the game, and definately not a newcomer to that particular site. I have played other (MANY other) online sites and never have I seen such instigating, provocative and "hyped" type dealing at any other site. (just an aside note)

my questions are these--
1. the site administrators say they have some company that verified their dealing. I can't seem to find whatever company they mentioned (they gave me the name), but they say a sample size should be 50000 hands. thats about 2 months playing for me..maybe a bit more, but do you agree with 50000 as a legitimate sample size, why or why not? and if so, does that mean for the flush board, do I have to see 50000 rivers?

2. Have you heard of anything like this before?

thanks again

Quote: strikeu

my questions are these--
1. the site administrators say they have some company that verified their dealing. I can't seem to find whatever company they mentioned (they gave me the name), but they say a sample size should be 50000 hands. thats about 2 months playing for me..maybe a bit more, but do you agree with 50000 as a legitimate sample size, why or why not? and if so, does that mean for the flush board, do I have to see 50000 rivers?

2. Have you heard of anything like this before?

You're welcome.

1. The more egregious the cheating is, and the more probable the event, the small the sample size it would take to prove your case. My case against Casino Bar rested with only 332 hands. To just say anything, I'd suggest starting with 1,000 hands. Post the results, and based on how they look a better estimate could be made.

2. All the time. Players make accusations of unfair play against every casino, including the vast majority that play fairly. I think it is due to selective memory and a misunderstanding about the laws of probability. This goes for electronic gaming here in Vegas too. Pick up any issue of Gaming Today and you'll read quacks ranting about how video poker or video keno isn't fair, with no statistics to back up the case.

Thank you again for all your insight and information.

What I think I will do, is simply stop playing on the site that rhymes with jokerstars. I have sent them my information, and they reply EVERY time with a poker lesson for me, and PAGES of rebuttal, citing bad beats and sour grapes on my part.

Just as an aside note, this is all play money I got my info from. I have not (and with my suspects and my facts-will not) deposit real money into their site again. as a matter of fact, the hands I saw on the real money tables (almost 7000 hands) was what prompted me to move over to the play money tables to gather the information for my experiment.

I play on a LOT of the online poker sites (brick and mortar also), pretty much every online site I can download to my computer and run. Probably 8 or more decent sites, and by FAR I have not seen the provocative, enticing, and instigating dealing on any other site. Of course I've seen some bad beats, but that’s different. I can accept bad beats as part of the game- that’s not bad dealing that’s bad playing.

By the way, I loaded up BODOG (recommended from this site, and a new one for me). I have played for the last week or so, seen trips flop 3 times, and one flush board- a little more in line with the odds.

Thanks again, K