# Five 1st places in a row?

• Bronze
Joined: 02.07.2007
Hello, dear Sit & Go players.

I'm a cash game player, who doesn't play SNGs that much. Still, there's one thing about them that called my attention. Sometimes, you can get a jackpot if you win a certain number of SNG's in a row under special promotional circumstances. PartyPoker's currently running "Jackpot Hunter" promotion is one of them. You can win, for example, as much as \$10.000 out of 5 tiny \$3 SNGs, and that's just the lower jackpot.

That's a lot for a casual player indeed. Sometimes I play low buy-in SNGs just for fun, and I remember I once opened two of them and ended up getting 1st place on both. And yesterday, I played a \$1 one after being eliminated from the pokerstrategy tournament, to "try to get my dollar back", and I won it, too.

Getting these jackpots doesn't look like a common achievement, though, I don't recall reading any news about people managing to get them, ever. My question is for real SNG pros, who play a lot of SNGs a day, and play them well.

Is winning five SNGs in a row really that unlikely? Have you ever managed to do this, even if there was no jackpot involved? Did boku ever accomplish this during his famous mega-challenge? Would you rather try this, or try to get 1st place in a multi-table tournament of, let's say, 12000 people?

Thanks!
• 27 replies
• Bronze
Joined: 15.10.2008
If we take 12% as probability of 1st place in 9 player SNG then:
12%^5 = 0,00248832% is probability of having 5 x 1st place in row, or
on average every 200.939 games we have one.

Don't know what is probability of 1st place in 12000 players MTT but good players should be 1st more then 1 time in 12.000 games.
• Bronze
Joined: 22.06.2009
am I ask, what rake is there ?
• Bronze
Joined: 02.07.2007
Hi Riddlah. Entry fees at the lowest buyin PartyPoker SNGs are very high as far as I know, I believe if you buy-in for a \$3 SNG, only \$2,40 of them go to the prize pool. The jackpot money has to come from somewhere, that's true. If we find another poker site where the fee for these games is \$0,40 instead of \$0,60, after 100.000 games we would save \$20.000 in fees, two times the jackpot Party offers in this promotion. That makes the thing look bad indeed, but I'm still interested in getting more input.

Hi ChoChiKun. These SNGs at Party have 10 seats instead of 9, for your information. Still, if we give our hero enough of an edge over the other players to say his probability of achieving 1st place is still 12%, and 12%^5 = 0,00248832% (or roughly 1/40188 or 1:40187) how do we use this to say we need 200.939 games on average to have the happy streak? Are you counting every set of 5 separately? Remember that Lose-Lose-Lose-Win-Win one day, and then Win-Win-Win-Lose-Lose the next day would also be valid, too.

It would be cool if some hot SNG players with thousands of games of theirs in their database would tell us what his real 1st place frequency is.

Thanks for your replies so far.
• Bronze
Joined: 15.10.2008
Originally posted by LMOJ
Are you counting every set of 5 separately? Remember that Lose-Lose-Lose-Win-Win one day, and then Win-Win-Win-Lose-Lose the next day would also be valid, too.
Yes, I count every set separately so I made mistake. We need on average less than 200.000 games.
• Bronze
Joined: 22.06.2009
@LMOJ

I have just around 400 sngs from diferent sites in my databse. I reached max 3 first places in row.

it is very small amount , so just if you are inetersting
• Bronze
Joined: 11.04.2009
Think that you're no longer competing against other players, you're practically playing against the casino.

And as usual that means the casino wins.

You can make the calculation of how much extra rake you generate (real rake- normal rake at that stakes) over how many hands you have to do it as described in the other posts, and how big is the prize.

I can bet you'll recieve significantly less. Basically if you play normal games with normal rake you'll have over time more money than that prize is worth.

It's a kind of "sounds good" idea, but do the math and you'll see.
• Bronze
Joined: 02.07.2007
The prize is \$10.000.

The most similar thing at PokerStars are the \$3 + \$0,40 SNGs. You'd pay \$0,20 less in fees for every game, for a significantly higher prize pool I must add.

So the PartyPoker player will pay \$10.000 extra in fees after 50.000 games.

How do you calculate the "expected" number of times you will have five 1st places in a row over a course of 50.000 games given a specific hero's 1st place frequency?

I am no mathematician, but I'm sure knowing how to do this would be an important step forward in our calculations, since counting each set of 5 games separately doesn't account for all the favorable cases. We could even make a graph with hero's 1st place frequency as horizontal (x) axis and expected amount of happy streaks over 50.000 games as vertical (y) axis.
Any mathematicians out there?

• Silver
Joined: 31.01.2009
my math:

x^5 = chances of getting 5 1st places in a row.

Where x is the frequency that a player gets 1st place.

[img]http://www2.wolframalpha.com/Calculate/MSP/MSP4919903h63da1ff58200005i9d77bhf9hfg8b1?MSPStoreType=image/gif&s=3[/img]

Consider only the positive side
1 is 100% and 0 is 0%

I think if you use mathplot you get accurate graphs. But the math itself is pretty simple. But you can see that if you reach 1st place less than 50% of the time, the chances are pretty close to 0%.
• Bronze
Joined: 17.10.2008
and people will not rig them?
• Bronze
Joined: 06.10.2008
Yea, just get 8 other people to enter the same SNG, they let you win 5 times in a row and you split the 10k?
• Bronze
Joined: 02.07.2007
Hi Alverine.

In that case, if the hero can get 1st place 16% of the time, the chance of doing it five times in a row is 0,16^5 = 0,0001048576.

Looks pretty close to 0%, but, remember the prize is \$10.000. So with the above mentioned chance, his equity for that prize is almost \$1,05.
For each 5 games he will pay exactly \$0,20 x 5 = \$1 extra in fees compared to a site with cheaper fees. And \$1,05 - \$1 = \$0,05.

So a player who can win one of these SNGs 16% of the time can play five of these SNGs during a promotion like that one, and, comparing extra rake paid and prize equity, he gets almost 5 cents of positive expected value!!

If he could win 50% of the time, the EV in terms of extra rake vs jackpot of playing five \$3 SNGs during the promotion would be brutal: +\$311,50

This is still a simplified and not quite accurate way of looking at it. Some of the things we have not considered and that make EV better include:

- The fact that if the hero doesn't get 1st place on his 1st, 2nd, 3rd, or 4th SNG he doesn't pay the full \$1 of extra rake, because the "succession of 5" ends prematurely. And that happens way more often than winning 4 SNGs in a row and then failing to win the 5th one.

OR

- In case we "force" our hero to play a set of 5 every day regardless of the result, if he gets a result like lose-lose-win-win-win on a set, on his next set he will only have to win his first and second SNGs, and he gets the jackpot. This is why I asked for a formula that would calculate the "expected/average number of happy streaks" given an "x" hero's 1st place frequency and a succession of 50.000 games by the way.

Rigging them is not supposed to be possible by the way (hi excelgeo and Octhellior), the handing of the jackpot is not automatic, you have to send an email to support after accomplishing it, and they check for any signs of cheating before awarding the prize.

The promotion was for December 2009 only, though. It's over, but maybe it will be back.
• Bronze
Joined: 11.09.2008
I once won 6 short handed SnG's on fulltilt followed by a 90KO tourney. Good runs do happen.
• Bronze
Joined: 04.12.2009
I've been reading this thread for a while and it got me searching for an appropriate solution. I stumbled upon http://www.mathforum.org/library/drmath/view/56637.html

. . . . . (1 - px) . . . . . 1
q(n) = --------- . ------------
. . . . . (r+1-rx)q . x^(n+1)

using the formula here and using the Hero's chance of a first place at 10% I came up with a probability of a run of 5 NOT occurring in a trial of 50000 at 0.607

so.... the probability of such a run occurring is 0.393

That is that 39.3% of the time you play 50000 games you can expect a run of 5 straight wins.

This seems too low to me and i'm not wholly convinced that I understand the value of x in this equation but it's a place to start
• Bronze
Joined: 04.12.2009
Just done some more calculations. With a 20% chance of finishing first Hero can expect to have a run of 5 wins 99.99% of the time he plays 50000 tournaments

So more realistically - when the hero's edge is 11% he can expect such a run 51.1% of the time.

The figures can be misleading though, as the % chance of a run of 5 is NOT directly proportionate to the total number of tournaments played.

In other words for 11% first place finishes...

50000 - 51.1%
25000 - 30.1% and not 25.6% as you might expect
12500 - 16.4% and not 12.8%

I can't get my head around the logic to this!! But I've checked and double checked the working and it seems sound.
• Silver
Joined: 18.03.2008
about 50/50 taking everything into consideration
• Bronze
Joined: 05.06.2009
the most ive ever won is 3 in a row howeve ri consider myself a cash game player. i hav never heard of any1 winning 5 in a row and although i believe it is extremely hard i still believe it is possible. however if u r goin to try and win 5 sngs in a row at partypoker 3 dollar then u will find it dat much harder as the blinds are speed and in my opinion with speed blinds it eventually comes down to luck and gambling. prefer 10 min blinds by far.
• Bronze
Joined: 06.05.2008
I seem to remember Blue Square doing something similar - Win 5 S&Gs in a row for a jackpot and the jackpot was won a few times, so it can be and has been done. They were not turbos they were normal speed games.

My gf tried them and managed 3 in a row but never got any further than that.
• Bronze
Joined: 02.07.2007
Originally posted by nibbana
The figures can be misleading though, as the % chance of a run of 5 is NOT directly proportionate to the total number of tournaments played.

In other words for 11% first place finishes...

50000 - 51.1%
25000 - 30.1% and not 25.6% as you might expect
12500 - 16.4% and not 12.8%

I can't get my head around the logic to this!! But I've checked and double checked the working and it seems sound.
Well, it can never be "proportionate" in the way you said I might expect, because that would mean that, if chance after 50000 games given a specific hero's edge exceeds 50%, then after 100.000 games, the chance with the same edge would exceed 100%, and you know that can never be! Hehe.

A games-played-vs-chance-of-hitting-the-jackpot-at-least-once graph, given a fixed hero's edge, would obviously be some kind of curve that gets closer and closer to 1 (or 100%) the more games we have, but never reaches it.

What you found is the biggest step forward made in this thread so far, and I must congratulate you for that. So now we have a formula that lets us know the chance of hitting the jackpot exactly zero times given a specific hero's edge and a specific number of games, which also allows us to know the chance of hitting it once or more, by doing 1 minus that formula. And it's complicated enough.

But we can't stop here! Next step for our EV calculations would be finding a formula to find the chance of hitting it exactly once, and then another one for exactly twice, then the 3-hits one, and so on until 5 or more...

Or, if possible, just one formula that would give the average number of hits directly, like if hero's edge is 20% and the number of games is 50000, then the hero hits the jackpot an average of 3,8 times or whatever the result would be.

Then, the only thing left to get would be some data from regular SNG winners which track their games, and can tell us their 1st place frequency, so we get some realistic heroic edges.

Looks like if the number of wins in a row required was only 3, some of us would've got it at least once already, wouldn't we, Fagin and kb021292? Yes, the \$3 SnGs at Party are speedy, so push & fold stage comes fast. Maybe ICM calculations with "added" value to 1st place which accounted for the chance of getting the jackpot (in effect \$100 extra for the 3rd SnG - like some kind of ticket, \$1000 extra for the 4th SnG, and of course \$10000 extra for the 5th SnG) would be applicable here? I'm not into ICM at all so maybe I'm talking nonsense.

Anyways, thanks for all your replies, guys!
• Bronze
Joined: 17.10.2008