Thanks for your comment! I agree that the underlying assumption of opponents you double up against having an equal stack to yours during all phases of the tournament, is not that realistic. If you noticed, I also assumed that half of the chips you accumulate come from making your opponents fold (i.e. no showdown). The model can of course be made better by tweaking the numbers above and including a parameter, which takes care of the fact that your opponents do not always have a same stack size as yours. Still I’m pretty sure the chances of winning a tournament are better than 1/xx. I your model for example, you do not take into account that the opponents you are up against also accumulate chips during the tournament. This greatly reduces the number of all ins in a row you have to win. I guess one way of improving the model would be to investigate how the average number of chips increases during a tournament.

Great article, and research! I really enjoyed reading it. However, I have to agree with some of the other comments that the chances of winning a poker tournament are 1 out of X (X being the number of entrants). That is a far more realistic assumption because you must take into consideration that for a player to double up 10 times in a row (assuming they were dealt pocket aces and they held up every time) their opponents MUST have an equal size stack during every one of those double ups. Otherwise the player could be dealt pocket aces 200 times in a row, and he/she still would NOT have knocked out everyone in the tournament. This probably sounds confusing so allow me to attempt to illustrate it:

Tourney Structure:
——————-

-1,000 entrants
-Buy-in = $100 + $5 rake
-Total prize pool = $100,000
-1st place awarded 20% of pool ($20,000)
-All players start with 3,000 chips
-Total chips in play = 3 million
-Blind levels run for 30 minutes per level
-10 players on table
-Start with 100 tables, and play till one player left on 1 table.

Important note:
—————

The website has rigged the play for you to be dealt pocket aces every hand while one opponent at YOUR (particular) table will always be dealt KK (so they call your all-in) and the board has been rigged so they can never win ;0)

Hand #1
——–
You go all in pre-flop with your AA, and are called by a player holding KK.

Total chips in play during this hand = 3,000 of your chips + 3,000 of your opponent’s chips = 6,000 chips

The board reads: Flop = A K 2, Turn = A, River = 3

Your aces held up, and now you have 6,000 chips; of course if your aces didn’t hold up you would have been knocked out of the tournament.

Hand #2
——-
Same all in by you, and you get called, and win again. Now you have your original 6,000 chips + 3,000 from your opponent = 9,000 chips

Hand #3
——-
Your Aces win again. Now you have 9,000 original chips + 3,000 from opponent = 12,000 chips

Hand #4
——-
Aces win again. 12,000 original + 3,000 = 15,000 chips

Hand #5
——-
Aces hold up. 15,000 + a player who was also lucky and had 7,000 chips = 22,000 chips

Hand #6
——-
Aces hold. 22,000 + 4,000 from another player = 26,000 chips.

Total time elapsed = 6 minutes into the tournament thus far, and 990 players remaining (some knocked out by other players).

Therefore, even after having gone all in with aces, and winning every hand, the tournament would STILL last for hours, and your stack would only increase gradually because no one else would have as many chips as you, and you would only be able to win what they have.

In conclusion, you would have to repeat your all-in for SEVERAL HUNDREDS of hands (not merely 10). Some players would have been busted out by other players, and the tournament would still last a few hours. Therefore, the best answer to the probability of winning a (non-rigged) tournament is still 1 out of 1,000 players, or 0.1%.

I still look forward to reading your other articles =0)

Cheers!

enjoyed your post. nice view.

you should focus on rephrasing the math results in laymens’ terms.

like: this means,for example, that if in a 9 player freezout you play online all-in hands (that you consider, correctly, to be a 80% favourite), you should (in the long run) win 1 in every 2 tournaments. so, if 1st prize payout would be 75$ (for 15$ buy-in) you should get on average around 60$ net every 2 games, leading to a 30$/hour payout :p

what do you do for a living mark? would you be interested in co-authoring a book on poker? (you can write me in private).

Regards,
Lucian

(from Europe)

Mark’s last blog post..Nice try but I’m not that stupid

Mark’s last blog post..Charlie Glynn

Thanks for the comment. Are there any of my variables you find really unrealistic?

Best Regards

Mark

Mark’s last blog post..100$ MLB (Major League Baseball ) fantasy bet freeroll