Taxes

They say the only two sure things in life are death and taxes. I don't want to think about the former, so I'll talk about the latter. Specifically, how to treat all this money that has been flowing in from poker and blackjack from a tax perspective?

This is the point where poker1eh starts laughing as he has none of these problems - as a Canadian citizen, all gambling winnings are tax free. Jerk - stop laughing. Now. I mean it.

Anyway, if it wasn't apparent by the fact I'm writing this article in the first place, I will be paying taxes on all my winnings. This even includes the $10 and $20 gift certificates from GamesGifts, etc. Everything on the up-and-up. So how is this done?

First of all, let's define how the IRS taxes gambling. The core concept is that the IRS treats each session as a taxable event and treats each of them differently. From publication 529:

You must report the full amount of your gambling winnings for the year on Form 1040, line 21. You deduct your gambling losses for the year on Schedule A (Form 1040), line 27. You cannot deduct gambling losses that are more than your winnings.

You cannot reduce your gambling winnings by your gambling losses and report the difference. You must report the full amount of your winnings as income and claim your losses (up to the amount ofwinnings) as an itemized deduction. Therefore, your records should show your winnings separately from your losses.

This (already) has a few important implications:

• You need to keep records on a session-by-session basis
• If you do not itemize your deductions on Schedule A (e.g. you take the standard deduction) the you cannot deduct your losing sessions, and will pay taxes only on your wins.
• If you have more losses than wins, you cannot offset any "regular" income from your gambling losses - you can only deduct losses to the extent of your wins.

In terms of the records needed for the first item above, there is more guidance in the same publication:

Diary of winnings and losses. You must keep an accurate diary or similar record of your losses and winnings. Your diary should contain at least the following information:

1. The date and type of your specific wager or wagering activity.
2. The name and address or location of the gambling establishment.
3. The names of other persons present with you at the gambling establishment.
4. The amount(s) you won or lost.

The four pieces of information above define a "session". However these were designed for brick and mortar type games - the concept of a "session" is rather murky online where I can multitable. For example, if I sit down one evening, have anywhere between one and four tables of poker open at any one time over the course of the night, and play $0.50/$1 tables as well as $1/$2 tables, leave some "bad" tables and join others, how do I measure how many sessions have I played when I stop for the night? Is each table its own session? Is each limit its own session? Is the entire night a session? Unfortunately, there have been no court cases or IRS Revenue Rulings on this point.

Let's look at how each of these scenarios would look from an export I did from my Poker Tracker database in mid-July, when my total net wins were $242.37

1. If each table where I got dealt at least one hand was its own session, I have a total of 395 sessions
• 197 winning sessions totaling $1,426.23
• 198 losing sessions totaling $1,183.86
2. If each limit (per night) was its own session, I have a total of 117 sessions
   • 58 winning sessions totaling $952.01
   • 59 losing sessions totaling $709.64
3. If each night was its own session, I have a total of 97 sessions
• 48 winning sessions totaling $893.52
• 49 losing sessions totaling $651.15

And, for the hell of it, even though we know it isn't correct:

1. If each week was its own session, I have a total of 23 sessions
• 16 winning sessions totaling $539.52
• 7 losing sessions totaling $297.15
2. If each month was its own session, I have a total of 6 sessions
   • 5 winning sessions totaling $261.22
   • 1 losing session totaling $18.85

Note that each one of these results in me having a net win of $242.37, as required.

This is an interesting example of "the long run" in that things that appear random on a very short timescale actually are not when viewed over enough samples to make a difference. In other words, if I told you I had played a game and had won 197 times and lost 198 times, you'd likely think that I must not be very good at the game, or at most about average. But if I told you I had played a game over a series of months and that I'd had five winning months and one losing month, you'd draw a different conclusion. This is a phenomena not limited to poker - for example, budgeting falls into this category. I have no earthly idea how much I'll spend on groceries today or even this week, but over the span of a month or year I can take a pretty good guess. Budgeting (or specifically, tracking against budget) on too short a timeframe is a useless exercise, but much more predictable and useful when viewed over a longer term.

OK, OK, but back to taxes - which one of these is the correct method for filing taxes?

The way these rules have been interpreted in the online realm is that a player can net his results in two (or more) different games/tables if they were the same game played at the same limit, continuously, as part of the same session. This implies that in hypothetical example above, no matter how much table hopping I do and no matter how long I do it, I actually have 2 sessions - a session of $0.50/$1.00 and a session of $1/2. In addition, for my actual play it means that for my particular situation I take the second example above: 58 winning sessions of $952.01 and 59 losing sessions of $709.64

Likewise, every single day of blackjack would need to be recorded with what your balance was at the beginning of the session and the end. Since there is (as far as I know) no PT equivalent to automatically track these items, I have been doing this by hand in an Excel spreadsheet.

OK, that was a pain. Why do I even care that I have to declare more income if I'm only going to subtract it as a deduction later? Sure, the IRS makes me jump through hoops, but this method shouldn't hurt me, right? Not so fast.....

• This method increases your AGI and if you are in a high enough income bracket, you start to lose the ability to claim your full exemptions, claim your full deductions, contribute to Roth IRAs, etc. It may also subject you to the AMT. All bad stuff, although for the amount I'm throwing around, not that big a deal. But you can see that adding $950-ish to my AGI is a lot different than just adding my net win of $240-ish. But in general, unless your AGI passes one of these levels this method does not result in increased taxes - I'll pay the equivalent taxes on my $240-ish, regardless of how it lays out on the tax forms.


• At present, nine states (including Michigan!) do NOT allow the full deduction of gambling losses when calculating state taxes. Yes, this means that I am taxed on the $950+ of winning sessions, but I cannot deduct my $700+ in losses (actually Michigan law seems to be kind of screwy in that I can actually deduct my first $300 of losses, but no more). At the Michigan tax rate of 4%, this increases my tax bill by $16 over what I would have paid if I could have deducted all the losses. That doesn't sound like much, but it is actually almost 7% of my actual earn! In fact, assuming this ratio holds for my entire year (that my winning sessions will be about 4x my net profit and my losing sessions will be about 3x), my effective state tax rate could be up to 16% on my winnings! Ouch, ouch, OUCH.

One last things before wrapping up this long article. How are bonuses / rakeback / other prizes treated from a tax perspective? I haven't looked this up in detail, but I would be very surprised if they couldn't just be treated as just another winning session. I will be going on this assumption until my research tells me otherwise.

Yes, and I can still hear you laughing, poker1eh.......

Example of increasing your EV by betting appropriately

The EV of the bonus discussed in the previous posts ($100 + $100 / $2500) with a House Advantage of 0.5% is $187.50. The way in which we can calculate this is to assume your bet size is very small - say, 1 cent. This is important because with a bet size that small you will (almost) never bust out, and your EV just becomes your initial bankroll minus the amount the house will take out of all of your bets:

EV = Initial Bankroll - (HA * WR)

In this case, EV = $200 - 0.5% * $2500 = $187.50. QED.

I have previously mentioned that there are ways you can slightly increase your EV by wagering in a certain manner, but only by taking on a ton of risk. For example, take the following strategy:

1) Bet $200 (your entire stack) on the first hand
2) If you win, bet $400 on the second hand
3) If you win, bet $800 on the third hand
4) If you win, bet $1100 (exactly enough to meet your $2500 WR)

I think it is pretty obvious that this strategy is highly variant. What is the EV, though? There are 3 cases:

1) You win all bets and end with $2700. Your EV is the probability this happens times the amount you have at the end. In this case, the probability is (0.4975)^4 = 6.1%. This works out to an EV of $165.40

2) You win the first three bets and lose the fourth. EV = (0.4975)^3 * (0.5025) * $500 = $30.94

3) You lose at some point. EV = $0.

Thus the overall EV of this strategy is $165.40 + $30.94 = $196.34 !!! So, by taking on the risk of going bust 88% of the time, making $500 6% of the time, and making $2700 6% of the time, I've managed to increase my EV by a whopping $8.84 - although in terms of percentage, that is a 10% increase in EV. On the other hand, I'm sure the hourly rate is through the roof since you took (at most) a minute to play those hands. :-)

The reason that EV increases is that most of the time in this strategy you don't have to meet the WR - you've gone bust before the House Advantage can act on all $2,500 of your bets. This seems counterintuitive that the more you go bust the higher your EV, but this is exactly what happens with all betting strategies, not just this one. The EV doesn't increase by much (as shown), but it does indeed increase. This also explains why I had to choose a bet size so small that you would never bust out to truly calculate the initial EV - as soon as you have some non-zero chance of going bust, you may not need to wager the full $2500 and your EV goes up a little bit.

We can use one more example just to prove that I'm not playing tricks: the next bonus I will likely do is a $100 + $125 /$4500 bonus. The strategy of betting very small has an EV of

$225 - 0.5% * $4500 = $202.50.

The strategy of betting $225, $450, $900, $1800, $1125 will satisfy your $4500 WR, with the following EV:

1) Win them all: (0.4975)^5 * $4725 = $144.00
2) Win first 4, lose last one: (0.4975)^4 * (0.5025) * $2475 = $76.19
3) Lose at some point = $0

EV = $144.00 + $76.19 = $220.19

Again, the EV doesn't increase by much in dollar terms, but is almost 17% greater. If you (somehow) have the bankroll to withstand the wild swings this strategy would have, a 17% increase in EV may be significant.

For what it is worth, I have plugged the numbers for this new bonus into my spreadsheet and also used an updated "equivalent hands per hour" number of 375 based on the speed of my last bonus. If I choose to continue to flat-bet $3 it should take me 4 hours with a RoR of 6.4% and a RoL of 22.1%. If I bump it down to $2 the numbers become 6 hours, RoR of 3.1%, RoL of 17.3%.

But, really, I just hope a good poker reload comes along. :-)

Blackjack Variance

As promised, some math backing up the variance talk in the last blog post. It seems obvious that increasing your bet size will increase your variance, and (amazingly enough) the math supports that! Adding two columns to my previous table for the $100+$100/$2500 WR at 300 hands/hr:


where RoR is your Risk of Ruin (losing your entire $200 bankroll) and RoL is your Risk of Loss (losing more than your $100 bonus, leaving you in the red for the bonus, but not broke). Some of the RoR numbers for the very large bet sizes are likely incorrect due to the model I used, but the $1-$5 bets should be fine.

To perhaps better visualize these numbers, I present the following graph:

• The green line is at $200, your initial bankroll.
  
• The black line is at $187.50, your EV. Note that this is at the center of these curves, and thus your most likely result.
  
• The red line is at $100, the amount of money you deposited.

The way to interpret this graph is that the area under the curve is proportional to your probability of winning that much money.

For example, take the lowest (purple) curve, gotten by flat-betting $1 over the whole bonus. The area of under the curve to the left of the $100 line is your probability of finishing your bonus with under $100. You can see that area is small compared to the entire area under the curve, thus your chance of finishing in the state is also small. From our table above, that "small number" is actually the 6.4% RoL from the $1 line.

Likewise, there is virtually none of the curve that would appear to the left of $0 (none of it looks "chopped off" by the left hand side of the chart, thus your chance of finishing below $0 is vanishingly small. From our table, that chance is 0.1%.

Note several things about this chart:

• Our EV never changes regardless of how much we bet - it is always $187.50. While not strictly correct, it is correct enough for our purposes.
  
• The larger bet sizes have a much larger variance - note for example the amount of the $5 or $10 curve that is to the left of the $100 line, and the amount that looks chopped off. However, this variance is also manifest on the right side of the chart - the only way your will ever end a bonus with $450+ is to bet $10 or more.
  

As you can see, there is some very wide variance, even for very small bet sizes. Even flat-betting $3/hand will have you losing money almost 20% of the time and going broke entirely about 3% of the time, but will also have you making over $30/hr in the long run. I am personally comfortable with this level of risk, and may even step it up to the $5 level, but I am not comfortable with more than that variance.

Actually, if I ever decided to step up my betting amount, I would likely multi-hand instead of increasing my one-spot bet. For example, 3-spotting $2 has about the same variance of single-spot betting about $3.50. The only issue is whether I can play more (or a similar number) of hands per hour 3-spotting. Maybe I'll try that on my next bonus and see how it goes.

My spreadsheet can also show me how lucky I was to be up $250 on my first bonus. As it turns out, there is a 5% chance the way I played that bonus that I would be up $250 (or more). Always nice to hit the 20-1 shot on my first try. :-)

My next post may be about how the EV of differing betting strategies is not quite the same, but will also so how little EV can be gained by them, at the expense of generating insane amounts of risk.