Two Plus Two Older Archives - Closer look at Variance, Real ROI (After Tax)

I simulated 1000 SNGs to see how real the variance can be. Using assumptions of 42% ITM, 16.8% 1st, 8.4% 2nd, and 16.8% 3rd (based on 2/1/2 for ITM finishes), the following ROIs were simulated.

42.5% 26.5% 28.2% 28.6% 24.2% 40.5% 38.3% 28.6% 38.2% 30.6%21.6% 32.0% 30.5% 27.6% 21.6% 33.8% 30.8% 29.2% 18.2% 32.1%

These just show the variance involved, and pointlessness of bragging about 1000 SNGs (or usually much much less). The real variance would take into account your opponents, your own good/bad play, etc., and the variance would be even higher. It also shows that 1000 shows generally that you can be a winner, but not that you're crushing the game, or that you can barely beat it. (Results were calculated using a random number generator in excel, where if that random # was < .168 (1st), if the random # was .168<#<.252 (2nd), if the random # was .252<#<.42 (3rd). This was simulated 1000 times, and ROI was calculated from that. Slightly different ITM and 1st-2nd-3rd breakdowns have similiar variances.)

TAX included in ROI's:
The ROIs people throw around aren't real. They are pre-tax, much like the paycheck before it takes the big hit. If I play 1000 $20+$2 SNGs and my stats are:
1st: 168
2nd: 84
3rd: 168

My (pre-tax) ROI is: 29.8%
My (pre-tax) profit is: $6,560
Now the tricky part: Let's say I play in sessions of 4, as in 4 SNGs then take a day off. I simulated the 1000 SNGs and divided the sessions into winning and losing. In the case of blocks of 4 sessions, there were 146 winning sessions and 104 losing sessions. You are required to pay tax on any winning gambling session, and in our 146 winning sessions I won $11,712 (very reasonable based on the simulations). Assuming I'm in the 25% tax bracket, I'll pay 0.25 * $11,712 = $2,928. So my total profit is $6,560 - $2,928 = $3,632 for an after tax ROI of 16.5%.

If I assume I play in sessions of 40 SNGs, then it is reasonable to assume (again, based on simulations) I have 21 sessions where I win $6,960 and 4 sessions where I lose money, I'll post an after tax ROI of 21.6%.

In one very plausible scenario for a part timer doing 4 SNGs per session in 1000 $55+$5 SNGs, we have an ITM% of 38%, a pre-tax ROI of 9.4% and an after tax ROI of -0.4% for a pre-tax profit of $5,150 and a post tax profit of -$197.50, based on winning $21,390 in 138 winning sessions versus 112 losing sessions.

I've recently started to win a little money in the SNGs (<$1000) and once I read all winnings were supposed to be declared, as opposed to net profit, I realized I wasn't doing quite as well as I thought, not to mention the fact that my 180 SNGs are useless as a reliable sample, and I thought I'd share. I couldn't find a thread mentioning tax in calculating ROIs and stats in general, which I imagine is because most small timers just don't pay tax on their winnings. The pros use a Schedule C to report their winnings as their sole employment, this analysis was more for the recreational player. If I'm wrong on the tax stuff, I have no problem being corrected.