So there is a house game where one of the players/dealers has hit the straight flush 4x in the last 6 weeks.

I haven't been there to see it hit, but I receive a mass text when it does get hit since the SF is progressive it will reset back to something in the 2k range

The rake is usually $5 or $10 max depending on how much action there has been.

My question is, what are the odds of hitting a straight flush 4 times over that time frame?

Straight Flush 1 in 72,193 hands

lets assume 20-25 hands an hour and 40 hours of play a week for this particular player

so that's 800-1000 hands a week
for 6 weeks that would be 4,800-6,000 hands


***This is where my math might break down. Please HELP.****
So i assume 6000/72193 = 8% to hit it once during that span
So i assume to hit it 4x it would be 0.005%

that would be equal to 5 in 100,000 ?
1 in 20,000 over the course of that time frame


Any Help would be appreciated!

That's about right (not mathematically precise, but a pretty good approximation) for the chance that one specific player will hit a 1 in 72,000 hand 4 times if he only plays 6000 hands ever. If you have a 10-handed table, it's about 10 times as likely that someone will hit 4 straight flushes in the same time.

If someone plays 60,000 hands, it's also much more likely (10x again? more?) that he'll hit 4 straight flushes over some 6000-hand span somewhere along the way.

Now say it's 10 players playing for 60 weeks, but we also count getting quads 4 times in 4 weeks, or 2 royals in 2 months... Play enough hands and you are guaranteed to see some "unlikely" results once in a while.

This effect has some sort of name, where you retroactively see a pattern and go looking for the odds. It's sort of like saying "what are the odds that I'd have 79 and the board would run out 34K 4 A?" after that exact thing just happened. Looking backwards, the odds are pretty much 1.

[/killjoy]

thank you sir

what if i said i noticed a similar thing happen last year

would you then think maybe some collusion is going on?

collusion? outright cheating? of course.

That depends entirely on how similar the thing is and in what ways the thing is similar.

Is "house game" here = home game? Or, is this an underground card room that has paid dealers who also play... and may be insuring that the house doesn't have to pay the bonus?


As briefly described in your OP...... my hackles are raised, a bit. Is it the SAME player/dealer, or are the 'winners' rotating?

We definitely need more details (with a clear identification about what you think, vs what is fact) about the structure of the game and the personnel... but I don't like the implied idea much.

You say progressive in the title -- is there some sort of jackpot being paid for these straight flushes?

Following through a bit farther on my math above: Say it's 1/20,000 that this one guy will hit 4 SF's in 6 weeks. For 10 players, it's 1/2000. For 60 weeks it's 1/200. If there are 20 things that would make you go "wow, what are the chances?", it's down to ~1 in 10 that you'll be here posting a thread. If there are >10 guys out there watching for things, it's virtually guaranteed that someone will come along and say "wow, what are the chances". And people regularly do.

The question often is "this seems unlikely, does that mean I was cheated", but it's absolutely impossible to deduce cheating from an unlikely result. A LOT of poker hands get played in a given day, week, or year. Somewhere out there, there are some insane longshots coming in. Unlikely results happen all the time in honest games.

If you're worried about cheating, look at procedures. Who is shuffling the deck? Who is cutting it? Are all the cards visible 100% of the time? It gets quite difficult in practice to cheat if basic procedures are in place.

its not a home game but an underground poker game, illegal poker house

straight flush gets bigger after each session

the player who has won it is a dealer there and a player. He won the last 4 straight flushes in the past 6 weeks.

hahahaha. at least they could try to make it less obvious.

First, unless this is a 5-card stud game, the frequency is considerably higher. 72,193 is the correct number for 5-card hands, and it excludes royal flushes. The correct frequency for a 7-card hand for any straight flush including ace-high is once every ~3,217 hands.

At a quick glance, one would estimate that over 6,000 hands, an individual player "should" hit a straight flush almost twice. But to be precise, the probability of hitting 4 straight flushes in 6,000 hands would be:

Probability of hitting on one hand = ~0.00031.
Probability of hitting once in 6,000 hands = 1 - (1-0.00031)^6000 = 0.845. So there's about an 84.5% chance you'll get at least one straight flush every 6,000 hands.

You use the probability mass function to calculate the probability of getting at least 4 straight flushes in 6,000 hands, and the math works out to about 11.9%.

That of course is assuming that a player sees every one of those 6,000 hands to the river, since it's based on 7-card hand frequencies. It also doesn't account for any restrictions on hitting the HHJ, such as using both hole cards, which would further reduce the probabilities.

Now, what are the odds that this dealer has dealt 6k to-the-river hands in the last 6 weeks, or 1k hands per week? Perhaps if he's dealing every day... And do we calculate the odds that one person gets 4 SFs before 5-9 other players get a SF... in 6 weeks?

OP, the red flag is getting bigger, and darker....

Either the estimate of hands dealt per hour and hours played per day is correct, or it isn't. For the sake of discussion I'm just assuming it's correct and that the hands counted were all dealt to the river. If it is an overestimate, then it reduces the likelihood that the player hit his 4 straight flushes, but it also increases the likelihood that no other players hit any.

I'm also assuming that the usual HHJ requirements are in place, i.e. that both hole cards must play in order to make the best hand. With this requirement, a player will make a straight flush once every ~6,746 hands. This excludes hands that would be counterfeited, such as a player holding Ah5h on a board with 2h3h4h6h, since it would result in a 6-high straight flush and the Ah hole card wouldn't play. The probability of one player making four straight flushes in 6,000 hands goes from 0.119 using any 7 cards down to 0.0129 (~1.3%).

Basically, you want to know what the probability is that one player will make 4 straight flushes in 6,000 hands, while the other 8 (assuming every hand had 9 players dealt in) make a total of 0.

The probability of 0 straight flushes occurring in the other 48,000 hands dealt is 0.0008 (0.08%). In practice, this would happen more frequently because players would fold some hands that would have made a straight flush if it were played out to the river. But with a jackpot in play I think it's reasonable to work off the assumption that players are likely to see flops with qualifying hands and chase down the draw if they hit the flop.

Anyway, the probability of both events occurring (one player hitting 4 times and the other 8 players hitting 0 times) is just 0.0129 * 0.0008 = 0.0000105 = ~0.001%.

is OP really saying nobody else had a SF during this 6 weeks? I find it hard to imagine a cheating scenario where this could be arranged. How big is the room?

Again, it's usually fruitless to use probabilites to discover cheating (much as I appreciate your input GutshotJeff! will be reading about probability mass functions soon ). Unlikely things happen all the time in perfectly honest games.

Who dealt the hands? who shuffled? who cut? is the deck kept in view 100% of the time? Are burn cards used correctly?

I was wondering that too and scrolled through the posts before doing the math.

Certainly doesn't prove anything but might be enough to convince a player to steer clear. But if the probability alone of the one guy hitting 4 times is enough to convince you that there are shenanigans going on, you'd really have to believe that every deal is stacked. It's 16 times more likely that any one player would hit 4 straight flushes than it is that no one else would.