I don't know if this is of any interest to others, but I personally found it quite informative:

Based on a sharkscope graph of winnings at SNG it seemed like my winning/losing streaks seemed to go in spells of either running very good or very bad in a way that was counter-intuitive:



What I did was plot my actual distribution of winning/losing streaks and compare with one I generated from a Monte-Carlo using a win frequency of 20%:



The 2 graphs come up extremely close. So the lesson I learnt is that while it may seem that you are being doom/boom switched, or that your style of play somehow changes to reinforce streaks, the reality is pretty much as expected in terms of statistics.

Note that even though I am only winning 20% of SNG's on average I am still in profit due to the fact that these are predominantly 5 seaters and quite often I come second, the prize from which more than pays for the rake yielding a net ROI of 1-2%.

What I do find interesting though are those graphs which just seem to go monotonically in one direction. That would be very hard to model since any monte-carlo is bound to show a distribution similar to that above. Could it be that they are the result of some kind of chip-dumping or cheating?

Do you have any examples of straight-line graphs that are played for sngs similar to yours, with x-scales so small? Usually these straight-graphs are really plenty chunky, but they're over a lot more games so the deviance is hidden by the scale.

If you send me the prize structure and your "expected" distribution of results, I can produce all sorts of simulations for you so that you can see what your graphs "could" look like. You will see that they can be all over the place...even over some pretty large samples.

Thanks for the offer but no need really. The spreadsheet I used to do the Monte-Carlo can also be used to generate a winnings chart and I can well believe these could be all over the place. For truly awful or brilliant players there should be quite a close match to the expected line after enough samples, but for break-even players it will just meander about the x axis as per a random walk.

Incidentally my greatest number of successive losses out of the 1450 samples was 40 (for the simulation displayed it was 30).

To Rusty: I take your point about scale. I have seen quite a few though from SNG's that follow an almost exactly straight line for 2000 games, which is about my own scale. I don't like to post anyone else's stats on here in case I get someone on my back over it. But it does seem a bit suspicious.

Here is a distribution of winnings for the following scenario:

$5 SNG with 5 players. You win $25 if you win but otherwise lose $5. You play 1300 games. Your chance of winning is 20%.

The x axis is your winnings, y is frequency:



Your expectation is obviously zero but you could end up either up $1000 or down $1000 or somewhere in-between depending on your luck.

This was based on simulating the 1300 games 10,000 times.

I'm assuming you meant you won $20 if you won the SnG... But this is a good example that variance is definitely a bitch.

Oh Sorry yes. You win $25 but you paid the $5 entry fee upfront so your net win is $20.

I observe that this is happening to many SnG players graphs that I see.

Inluding this guy: http://forumserver.twoplustwo.com/54...6/index52.html

Who played very many SnGs with payouts of 50-50. The payout structure is so that half the field lose and the other half get their buyins back + money after host many chips they have. So the result will be close to the same as when playing DoNs.

If you play a game where you win $20 20% of the time and lose $5 80% of the time, your expected profit (as you say) is zero and your standard deviation is $10. If you play N games, your expected profit remains zero and your standard deviation is $10 times the square root of N. For N > 30, the distribution will look much like a Normal distribution with zero mean and $10*N^0.5 standard deviation. For 1,300 games that's a standard deviation of $361, so you should only lose more than $100 about one time in 361 (it's a coincidence that the numbers are the same) using the Normal approximation, or 1 in 472 with an exact binomial distribution.

On the other hand, you expect to get one downswing of $5*ln(1,300)/ln(0.8) = $160 during the 1,300 games. A drawdown of over $250 without a win is unlikely (less than 2% chance to happen at any point in the 1,300 games).

The chance of being down more than $1,000 at any point during the 1,300 games is twice the probability of finishing more than $1,000 down, or 2/472. The chance of a drawdown from peak of more than $1,000 is just under 1%.

Thanks for your input Aaron.

It is of course the case too that your variance is much less severe if you play D2N's rather than a winner-takes-all game. Shown below is a 10K game simulation for D2N's where you have a 50% chance to double your money (ie a coin toss):