Gaussian distribution model doesn't fit poker? (long)

[Cosimo]

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I'm writing a sim at the moment to see what it spits out for number of negative swings, how big they are, etc. I'll definitely review the links you've posted (I remember ROR stuff from BJ days) for an answer to what I'm looking for.

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OK, simulated 100 million hands about 40 times. I'm currently off to bed and running 10 billion. Edit: took about 20 minutes. Biggest downswing was -1492 BB, EV was within 0.3% of expectation, -100 downswings every 14k hands, 73 downswings over 1000 BB.

A downswing is considered the movement from the last peak (current maxima) down to lowest minima that occurs after that peak and prior to the next new maxima. Say you run up to +100BB, fall to +50, up to +101BB. At that point, the downswing is added to the list of downswings and marked as -50. Say you run up to +100BB, fall to 50, back up to 90, then down to 30, then up to +101. This is a -70 downswing: 100 to 30.

75% of all hands have a return of 0, the remaining 25% are clustered around [-2,6] with a few outliers, representing big hands, sufficient to give the SD. Player folds SB 75% of the time, and wins 7% of hands over-all.

EV: 3
SD: 1.75/h
Most common biggest downswing: -1000 BB
Occurrence of -100 downswings: once every 12k hands
Occurrence of -300: once every 120k hands
Occurrence of -500: once every 1M hands

Occurrence of -100 downswings at +4BB/100: 1/11k hands
Occurrence of -100 downswings at +2BB/100: 1/16k hands

Almost nothing I did to tweak the payout schedule (as long as it remained at 7% wins, the same SD, and same EV) signifigantly changed the swings. I ran about thirty different schedules, and the occurrence of -100, -300, and -500 downswings remained remarkably stable. Rare big losses (turn and river capped, hand lost) and rare big wins (3-way capped turn/river) did not drastically change how often big downswings occurred.

The biggest factor affecting how often downswings occurred -- cutting the worst downswing in half, reducing the rate of 500+ downswings by a factor of 50, etc -- were accomplished by increasing winrate. Likewise, decreasing winrate signifigantly increased the number of big downswings. Also, when I tweaked the payout schedule such that the most negative of the losses was smaller (less negative), the once-in-a-million-hands big downswings got smaller.

Strangely, the number of 100BB+ downswings was inversely proportional to winrate. That is, the higher your winrate, the more likely to see small downward blips. This bit I don't yet understand. Edit: this is because a less successful player will stay in a downswing for a longer time, taking more hands before he passes his previous maxima. The more successful player will constantly set new maxima, and hence have more little down-ward bilps. This is an artifact of when I consider a downswing to be over.

Conclusion: in the long long run, the rarity of big pots and their size didn't have a signifigant effect on the frequency or size of downswings.

The main thing I got out of this exercise is that -100BB downswings will occur on the order of once every 10k hands. Although very unlikely (1%) for precisely 3000 hands, the "expectation" seems to be more like 30% for any given set of 3000 hands.