Why A Bankroll Matters: A Practical Example

On Saturday Night Live Chevy Chase was playing the role of Gerald Ford when he was asked a question during a presidential debate.  In response to a budget question, "Ford" said, "I wasn't told there would be math involved."

Warning: There will be math involved!

What follows will, I hope, be instructive.

Most people don't understand randomness.  If a flipped coin will be "heads" 50% of the time, that doesn't mean that if it has been tails 10 times in a row, it is any more likely to be heads on the 11th try.  A coin doesn't have a memory, and evey trial is independent of the others.

Randomness can by messy, which is why very good poker players can have long winning streaks, but also long losing streaks.  Those long losing streaks are the reason that poker players need a bankroll of many times their tournament buy-in.  The numbers that I usually see tossed around* for a sufficient bankroll are something like this: 25 buy-ins to play cash games, 50 buy-ins to play SNGs (single-table tournaments), and between 100 and 300 to play multi-table tournaments.

Here is a practical example from my play on 3/15 and 3/17 (I didn't play on the 16th.)  It's a small sample size that mathematically proves nothing, but it shows how important a bankroll is.

Starting on 3/15 at 1845 and ending at 0317 on 3/17, I played 15 SNGs.  In general one has to cash in about 50% of SNGs played to make money.  I did not cash in the first ten, so I lost 15 buy-ins at $1.65 each.  Then I cashed in 3 of the last 5, including one 1st place cash (which is worth about 4 buy-ins.)

So, I need to cash (finish 1st, 2nd or 3rd) about 50 % of the time, but I failed to cash 10 times in a row, so I must be really bad, right?  No, that's just randomness.

If I'm capable of cashing 55% of the time, that doesn't mean that I'll necessarily cash more than 5 times out of 10, or more than 25 times out of 50.  But if play 1,000 SNGs, I should cash pretty close to 550 times.

Remember, I said earlier that a good SNG bankroll amount is about 50 buy ins.  The use of a proper risk or ruin formula would mean that while I'm dealing with those downswings, my risk of ruin (the chance that I will go broke and lose all of my bankroll due to variance) is probably something like 3%.  All other things being equal, the bigger the bankroll, the more cushion one has against variance, and the smaller the risk of ruin.  If I kept increasing my bankroll without moving up to more expensive tournaments, the risk of ruin would eventually be close to zero.

So, let's look at the numbers for those 15 SNGs.

My SNG buy-in was $1.65, and I lost 10 straight, so that cost me (1.65)(10) = $16.50.

In the last 5 SNGs I placed 3 times:  one 1st place, one 2nd, and one 3rd.  First place paid $6.75, 2nd place paid $4.05, and 3rd place paid $2.70, for a total of $13.50 in cashes.

For SNGs 11 through 15, I paid 5 buy-ins and cashed 3 times, so my profit for those 5 SNGs is:

(total of 3 cashes) - (5 buy-ins)
= (6.75+4.05+2.70) - (1.65*5)
= 13.50 - 8.25 = 5.25

Now, bringing it all together, I no-cashed 10 SNGs, then made a profit in the last 5, which comes to:

-16.50 + 5.25 = -$11.25.

I lost $11.25 overall playing those 15 SNGs  But lets look at the numbers a little more closely:

$11.25 is 6.8 buy-ins, so my bankroll covered that loss.  I'm not in any danger of going broke.

The 1st 10 SNGs, of course, cost me 10 buy-ins before I finally cashed.  Again, not a problem, because I have the bankroll to handle streaks like that.

Also keep in mind that in any poker tournament, including SNGs, a cash is always worth more than the buy-in.  In this case, my 3 cashes were worth a total of $13.50.  The 15 buy-ins cost me:

(15)(1.65) = $24.75

So I paid $24.75 in buy-ins and my total cashes were $13.50.  Just three cashes covered 54.5% of my buy-ins. ( It helps a lot if at least 1/3 of your cashes are for 1st place.)

Since I have a decent bankroll, losing might be frustrating, but it's not scary.  I know that there will be downswings.  I know that there will be upswings.  I've had times when I played 10 SNGs and cashed in 7 or 8 of them.  That's positive variance, just as failing to cash 10 straight times is negative variance.

Someone who doesn't understand these concepts will never be good at poker.  There are players who won millions of dollars on national television and are now broke.  I hear about a new one about once a month.  You have to be able to manage your money, both when you're playing poker and when you're not.

As long as I keep studying and improving, and as long as I keep a decent bankroll, I'll be fine.  I lost one of those 10 SNGS with my pair of queens against a pair of jacks, and my opponent got a third jack on the river.  Queens beat jacks 82 % of the time--but not every time.  When I lose as big favorite, and it seems to happen over and over, I know that it's just variance.  I take a few seconds to shake it off, then I open another SNG.

I know that I'm smarter than most of my opponents.  I know that I study more than just about all of them.  I'm learning to fix my mistakes and weaknesses, and I'm constantly learning how to better manage my ADD.  That's a winning formula, and it will pay off.

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*There is a lot of math involved in coming up with buy-in numbers, using mathematical concepts like standard deviation and risk of ruin forumlae.  I could study the math and do my own risk of ruin calculations if I wanted to spend the time (I took two college statistics courses) but since those buy-in numbers are generally accepted and they tell me what my bankroll should be, I haven't bothered to investigate the math behind the concept.  I might at some point.