Effective bankroll with pending bets?
October 13th, 2018 at 1:21:30 AM
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How would you calculate your effective bankroll (for kelly betting, or rather 1/2 kelly) if you have futures bets and/or other investments that should return money later? For instance, let's say the following is true:
Your bankroll consists of $3,000 cash on hand.
$500 bet at +200 that has a 40% chance to win.
$200 bet at +100 that has a 55% chance to win.
$300 bet at -150 that has a 50% chance to win (this one is -EV).
So you have $3k cash + $1k pending. I know how to calculate the expected value....but what would you consider your effective bankroll at this point? I don't think you can just add in your expected return to your COH to get an effective bankroll number -- since for example, you could have a $100 bet at +1,000,000 with a 1% chance to win, you can't consider that to be worth $10k for kelly betting purposes. Also, you can't discount the $1k pending and say it's worth nothing. It's gotta be somewhere in between.
Yes, I know that you could just treat it as having a $3k roll for this example, but that's not what I want to do, especially if/when a huge % of BR is tied up in futures bets. Also, I'm working on figuring out how "worth it" futures bets are, because that money will be tied up for a good length of time -- EG: Putting in $10k worth of futures at 1% edge that resolves in 12 months isn't worth it, because that's hogging up $10k worth of capital for only $100 in EV. Of course, that being "worth it" is subjective, since it may be worth it for someone with a huge bankroll and money just sitting idly by, while someone else with a smaller bankroll, it's not going to be worth it because that money can be used now and rolled over several times, generating more EV.
Your bankroll consists of $3,000 cash on hand.
$500 bet at +200 that has a 40% chance to win.
$200 bet at +100 that has a 55% chance to win.
$300 bet at -150 that has a 50% chance to win (this one is -EV).
So you have $3k cash + $1k pending. I know how to calculate the expected value....but what would you consider your effective bankroll at this point? I don't think you can just add in your expected return to your COH to get an effective bankroll number -- since for example, you could have a $100 bet at +1,000,000 with a 1% chance to win, you can't consider that to be worth $10k for kelly betting purposes. Also, you can't discount the $1k pending and say it's worth nothing. It's gotta be somewhere in between.
Yes, I know that you could just treat it as having a $3k roll for this example, but that's not what I want to do, especially if/when a huge % of BR is tied up in futures bets. Also, I'm working on figuring out how "worth it" futures bets are, because that money will be tied up for a good length of time -- EG: Putting in $10k worth of futures at 1% edge that resolves in 12 months isn't worth it, because that's hogging up $10k worth of capital for only $100 in EV. Of course, that being "worth it" is subjective, since it may be worth it for someone with a huge bankroll and money just sitting idly by, while someone else with a smaller bankroll, it's not going to be worth it because that money can be used now and rolled over several times, generating more EV.
October 13th, 2018 at 7:27:45 AM
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Deciding if the futures bet is worth it is the easiest one to answer. Look at the formulas that have applied Kelly to long term stock market investing.
You can even use these formulas to help when multiple bets are pending. When making a sports wager there generally only two or three results (win, lose, or push). With stocks, there is a seemingly endless possible results (the company goes bankrupt, turns into the next Amazon, or anywhere in between). When multiple bets are pending, the number of possible results grows exponentially. Have 10 bets pending and there are over 1,000 different possibilities, most of which will give a different ending bankroll (assuming no pushes). If pushes are possible (and even probable like paigow or hockey 1p), it's like 60,000 different possibilities
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My intuition is that $4,000 *should* be close enough, and better than $4,070 because of the extreme example you gave*
The reason I like bankroll + cost of pending wagers over bankroll + value of pending wagers is because the bank roll is the result of resolved wagers. The number of resolved wagers completely dwarfs the number of pending wagers. So the 'value' of wagers is already accounted for in the bankroll side of the equation.
*with a $4,000 bankroll and an offer of +1,000,000 with a 1% chance, $100 is way over Kelly. So at the time of the bet it must have been worth even more than $10,000 or made when the bankroll was much higher
You can even use these formulas to help when multiple bets are pending. When making a sports wager there generally only two or three results (win, lose, or push). With stocks, there is a seemingly endless possible results (the company goes bankrupt, turns into the next Amazon, or anywhere in between). When multiple bets are pending, the number of possible results grows exponentially. Have 10 bets pending and there are over 1,000 different possibilities, most of which will give a different ending bankroll (assuming no pushes). If pushes are possible (and even probable like paigow or hockey 1p), it's like 60,000 different possibilities
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My intuition is that $4,000 *should* be close enough, and better than $4,070 because of the extreme example you gave*
The reason I like bankroll + cost of pending wagers over bankroll + value of pending wagers is because the bank roll is the result of resolved wagers. The number of resolved wagers completely dwarfs the number of pending wagers. So the 'value' of wagers is already accounted for in the bankroll side of the equation.
*with a $4,000 bankroll and an offer of +1,000,000 with a 1% chance, $100 is way over Kelly. So at the time of the bet it must have been worth even more than $10,000 or made when the bankroll was much higher
October 14th, 2018 at 5:49:45 AM
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Quote: TomGDeciding if the futures bet is worth it is the easiest one to answer. Look at the formulas that have applied Kelly to long term stock market investing.
You can even use these formulas to help when multiple bets are pending. When making a sports wager there generally only two or three results (win, lose, or push). With stocks, there is a seemingly endless possible results (the company goes bankrupt, turns into the next Amazon, or anywhere in between). When multiple bets are pending, the number of possible results grows exponentially. Have 10 bets pending and there are over 1,000 different possibilities, most of which will give a different ending bankroll (assuming no pushes). If pushes are possible (and even probable like paigow or hockey 1p), it's like 60,000 different possibilities
I'll have to check that out. Thanks. I started a bit of searching and haven't found anything on that....I'm assuming this is different than the regular Kelly criterion?
Quote: tomg-----
My intuition is that $4,000 *should* be close enough, and better than $4,070 because of the extreme example you gave*
The reason I like bankroll + cost of pending wagers over bankroll + value of pending wagers is because the bank roll is the result of resolved wagers. The number of resolved wagers completely dwarfs the number of pending wagers. So the 'value' of wagers is already accounted for in the bankroll side of the equation.
I'm not really looking for an answer for the specific example I put out, but more of how to calculate the effective bankroll. The use of the extreme example was to show you can't just use the expected return ... and the opposite is true too, where you can't discount it at all if it is near certain to win.
Not sure what you mean by the number of resolved wagers completely dwarfs the number of pending. I don't know how many futures are in action, but likely several dozen and may consist of somewhere between 10% and 50% of the bankroll.
I was confused by your last sentence there and thought about it some earlier today. I thought I could prove you wrong there by estimating numbers (poorly) in my head, but after doing some math just now, think I can prove "bankroll + pending = effective bankroll" and that you're right in that regard.
Let's say you have an opportunity where you have a 2% chance to win and the payout is 100-for-1 (where fair odds would be 50-for-1). You'd have a 100% advantage and since the payout is 99-to-1, your kelly bet would be 1/99 of your bankroll. I use 1/2 kelly, so my optimal bet would be 1/198 of my bankroll. Say I have a $198 BR. Either way works going forward.
If you were to make 198 bets all at the same time, where each has a 98% chance to lose, then your ROR is going to be (0.98^198) = 0.01831314723, which is pretty darn close to 1/2 kelly at 0.018225. For the full kelly player, it'd be (0.98^99) = 0.13532607744, which again is very close to a full kelly ROR at 0.135.
Only thing I'm not sure about is if that's by mere coincidence or if that's actually what it is? I doubt it's a coincidence, since I'd have to make 3 wrongs to make a right in this case. But then....why aren't the numbers exactly the same?
Also, I believe the ROR %'s attached to kelly aren't really fair to attribute to it, because if you're using the kelly criterion properly, your ROR is going to be 0%...it just means that your sizing of bets, if never altered, would result in 13.5% or 1.8225% or whatever ROR for life. So in that sense, you wouldn't use the "bankroll + pending = effective bankroll" methodology if you ascribe to kelly betting....since you want 0% ROR, but betting it all would give you a >0% ROR.
NOTE: You could view it as either making the 198 bets of $1 each all at the same time OR view it as already having -- say -- $150 in action already down, with $48 remaining. It's going to be the same thing....would you still bet $1 on that proposition just because your cash+pending=$198?
Quote: tomg*with a $4,000 bankroll and an offer of +1,000,000 with a 1% chance, $100 is way over Kelly. So at the time of the bet it must have been worth even more than $10,000 or made when the bankroll was much higher
