Video Poker Odds of flush holding 4 cards

A 240,000 hand royal drought is about twice as unlikely as the OPs orginal question. These things occasionally happen and the more you play, the more likely you'll experience a drought at some point. I play mostly single line somewhat infrequently, so my own ~120,000 hand drought felt endless (took about 35 months). But then I got 5 royals in less than half the time/hands! So there also will be times you'll get multiple royals in 40,000 hands. Hopefully that will happen to you sooner than later.

 

This is the correct way to calculate the probability, and as noted above, works out to about 0.5%. I have a seen a variety of meanings for the term odds, but I usually think of it as expected return on investment, although it's so often used interchangeably with probability that that could be another of its meanings now. With respect to EROI, That's mostly relevant before you bet, not after you have bet and been dealt a hand, since the bet has become a sunk cost after the deal.

- A self-aware nitpicker

 

Why are you assuming it’s not rigged? Is that not possible, do machines not malfunction?

I understand that is extremely unlikely, but so is 0/25.

 

Why should I assume they were rigged just because a 1 in 200 event happened? If they were rigged, why do these machines offer garbage games like 7/5 DDB (House edge of 4.29%)? If all the games were rigged, you should seeing games like 9/6 DDB (House edge of 1.02%) all over instead. In class II games (where the games are electronic bingo and the standard probabilities of poker don't apply), that's EXACTLY what you see.

I can't completely rule out that IGT is in a major conspiracy theory with casinos, completely risking their gaming licenses in the process, but I'd say the odds are much less than 1 in 200. Also those who tend to keep meticulous play records and divulge them on forums, they sound like they fall within expectation.

 

Lots of good discussion on my original experience and question. Just to clarify this scenario happened during a practice session on Wizard of Odds web-site. Wife and I are going to Vegas in a couple weeks and I was just trying to polish up on my play. Though the most hands I ever play for "real" money is 5, I like to practice using 25, 50 or even 100, (1), it's more fun if your just practicing and (2), it really helps me understand variance and the effect it can have on any one session at the casino. Helps keep my blood pressure and stress level down when I hit the inevitable horrible session.

 

When I leave the casino with the same amount of money as I brought I feel like I won
overall I do agree with you but there is a small amount of rewards credits or comps that do in fact mean that a getting your money is actually getting more then your money back on that individual hand/spin. congrats you netted 1/2 a penny profit in this case

 

While it sucks to be on the short end of a 200-1 event, it happens all the time in a casino. I would be shocked if a casino would risk their license/fines on a VP machine.

 

Define, all the time. In what instance does a %.05 non volitile (i.e. CORRECT PLAY) instance happen all the time. I’ll wait.

 

I’m not going to create another nonsense thread, but to those who have already responded to the OP, and anyone new for that matter who and how many have gone 0/25 on a 4 to the flush draw?

I will start. Never.

I also believe I have never played a malfunctioning machine, but to this point... I’ll never really know, will I?

 

Look at any slot machine, lets go with WoF, what are the odds of even getting a spin bonus? Lets just say for fun that it is 200-1, walk through the casino and you will hear the bonus going all the time because of the sheer number of times it is played. Just because the "correct" draw was taken doesn't mean luck doesn't play a part in what gets drawn. What are the odds in the same number being rolled in roulette back to back? Probably pretty high, but I am pretty sure if you get the wheel data from any casino it happens on a daily basis.

Edit: Let us all remember the difference between improbable and impossible.

 

38-to-1 after the first spin....and for each and every spin thereafter.
Separate, independent events, people! C'mon!
Spin the wheel, roll the dice, take a draw in VP... doesn't matter - each hand/number/color is a single by-itself event.
Just because they let you play multiple starting hands in VP makes absolutely no difference than playing a single game multiple times.

Let's look at the 4-flush. By drawing one card to this on a 25-play, the OP is simply speeding up what would happen (eventually) if he were playing single-play.
Eventually, he'll get 25 four-to-a-flush hands... and each time he does, he has a 20% chance of filling it...and an 80% chance of NOT filling it.
Hand #17 does not give a damn whether or not he filled it during the 16 previous times over the past 2 days. There remains an 80% chance that this one will fail too.
(PS - Hand numbers 18 through 25? Same thing!)

 

How about a different way to look at this, and still acknowledge the math.

If you were to draw to the flush 20% of the time, then how about this.

Out of 10,000 hands, that means you get your card 2,000 times and miss it 8,000 times.

So, you could actually go 8,000 hands in a ROW without getting a good card.

25 in a row in that scenario is not bad. LOL!

 

@tringlomane you May as well stop. Some aren’t going to follow no matter how you explain. But as a fellow realist mathematician....good explanations sir.

 

The probability of a single number is 1/38. The odds in favor are 1 to 37 and the odds against are 37 to 1.

 

Please forgive me but the math nerd in me is about to be released. It's nice to see someone correctly use the term "probability". Most people do not realize that "odds" and "probability" are not the same thing but they are related. When they say "odds", they usually mean "probability". The terms "chance" and "probability" are usually the same thing when spoken by most folks. Odds is broken up into two categories which is "odds in favor" and "odds against". Odds in favor is the number of ways an event can happen vs. the number of ways it cannot happen. Probability is the number of ways an event can occur divided by the total number of outcomes. Odds in favor reverses those numbers. Usually, it's written as 1 to 3 or 3 to 1. A colon may be used to show 1:3 or 3:1. I don't like books that use fractions since that confuses odds with probability. I'll use a single number on a 00 roulette wheel as an example. The probability, or chance, of picking the correct number is 1/38. The odds in favor are 1 to 37 and the odds against are 37 to 1. For roulette to be a fair game (EV = 0), you should be paid at a scale of 37 to 1 which is the odds against it happening. Obviously, a single number is paid at 35 to 1 which gives the casino a 5.26% house advantage.

 

Yes.
Furthermore, if you happen to pick the right number, the probability of it coming up on the next spin? It's still 1/38. It does not go up or down based on the fact that it just came up on the previous spin. The previous spin is now completely meaningless.
This is what some seem to keep forgetting - that the same holds true when drawing 1 card to a 4-card flush... whether it's one such hand or 1000 - whether it's one at a time or a 25-play all happening at the same time.
The probability of failure is 80% (roughly)....9/47 of the remaining cards are the winning suit...38/47 of the remaining cards are losers. You are FOUR times more likely to lose each hand as you are to win. True for ALL 25 hands....or 1000 hands.

As for predicting an outcome in advance, the prediction would be that 5 of his 25-play would be flushes, based on the probability multiplied by the number of upcoming events. (25 x 20%).

I know - here's an easier way to express this:
I play blackjack, double-deck.
Math says I should be dealt about 3 or 4 blackjacks per hour of play... or one per 20 hands dealt.
Now, suppose that I've played 100 hands without getting a blackjack (yes, it's happened to me...more than once). Does that indicate, somehow, that over the next 100 hands I'll be dealt 10 blackjacks so that the result is equal to the advanced expectation? (10 out of 200, or 1-in-20).
Of course not! Nobody would think that!
They would (correctly) observe that my failing to get a blackjack in those first 100 hands makes no difference to the next 100 hands... & that I should not expect more than 5 over the next 100.
This is EXACTLY the same as the 25-hand one-card draw to a flush. Just because the first 20 of them failed does NOT mean that last 5 will be flushes.

 

I think the Powerball is rigged. I never win it.

 

You likely will win it someday, as long as you play every week for the next 3.9 million years.

Best of luck!