Number Crunching (3 of 4)

After whimpering about losing to two-outers last post, I caught one of my own today (again on Absolute). Had kings and was up against a pair of eights. Flop came 844 and my adversary pushed hard, making me think overpair. The turn was a Q and I slowed down, figuring QQ or AA real possibilities. I had to stay, though. Had to find out. Then, like the conclusion of Tartuffe, the king stepped in at the end and improbably saved the day. (And helped make that particular sequence of 100 hands end in the black.)

Last post I wondered whether these numbers -- win rate, standard deviation, and number of hands played -- might also help in the effort to determine bankroll requirements. Seems like they should. In Simon’s original post (the one that got me on this train of cogitatin’), he linked to a site that includes a “bankroll calculator” that uses win rate, standard deviation, and “risk of ruin” (i.e., the chance one is willing to take of busting one’s entire roll) to compute bankroll requirements. The calculator follows a forumla created by BruceZ, a frequent poster over on the 2+2 Forums whose posts about math and probability are very well received over there. (Here’s the original thread where BruceZ’s formula was posted.)

When I enter my win rate (2.5 BB/100) and standard deviation (18 BB/100), I get the following bankroll requirements according to various levels of “risk of ruin”:

I’m playing $0.50/$1.00 limit, so one BB or “big bet” equals one dollar. According to the site on which this calculator can be found, BruceZ’s formula is on the conservative side (e.g., compared to one created by Mason Malmuth). In any event, we can see here that -- according to BruceZ’s calcuations -- I really need something in the neighborhood of $200-$300 to be reasonably comfortable I won’t tap out my funds playing at this limit. By the way, reading around I see most saying that 5% is about the highest risk of ruin most players can stand -- only maniacal thrillseekers go higher -- while less than 1% is probably much too low.

Kind of an interesting chart, I suppose. Notice that if I tried to play at my usual limit with only $44.92 as a bankroll, I’d face a 50-50 chance I might go bust. Back at the beginning of October I actually got to test this idea (in a way) when -- overreacting to the UIGEA passing & all of the predictions of armageddon that quickly followed -- I cashed out all my moneys except for $50 over on PokerStars. However, I continued to play my regular $0.50/$1.00 game. I managed all right for a few days, then had a downturn and at one point found myself literally down to my last chip (on Stars, anyway).

This was no doubt one of the goofier poker experiments I’ve ever tried. When the slide began, I decided to see if I could survive it without redepositing. Late one Sunday night I went to a table with my last $19.80 and proceeded to slip down into single digits. Before long I found myself sitting in the big blind with just $2.40 left having been dealt . Woe is me. Only the small blind called, and the flop came . The SB checked. Having caught a tiny part of the flop (and feeling not a little desperate), I most certainly bet, and the SB called. The turn was the . Again -- check, bet, call. The river was the , giving me two pair but also perhaps completing a back door straight or flush. The SB checked, I crossed my fingers and chunked in my last 40 cents, and the SB called. Luckily for me, my opponent only had a pair of deuces, and I was still in the game (with $4.60).

I actually made it back up to $16.35 before leaving that table. And, eventually, I kicked it back up over $50 and on up to the more comfortable range I’m at right now. (I performed similar experiments on the other two sites I play as well -- Full Tilt Poker & Absolute -- though in neither case did I come so close to being “felted” as happened at Stars.) I knew it was harebrained to try to play without a roll like that . . . even if it were just an experiment. Not having chips did cause me to play differently -- and incorrectly, I am certain. Still, I think I did learn a modest lesson about bankroll management during my brief impersonation of a real, live degenerate gambler.

Getting back to the subject at hand, the bankroll calculator does echo what most suggest regarding bankrolls for limit games where one often hears 300 big bets as a standard recommendation. Some say 500 BB for online players (since they often multitable). And, of course, playing short-handed games (as I generally do) also tends to increase one’s variance, thus making it even more imperative to have a sufficient roll.

Ever since I began playing $0.50/$1.00 games, I have kept around $300-$400 available for use at the tables. Anytime I rise above that range I cash out a hundred, and so my “bankroll” per se is not identical to my overall winnings. In any event, it is good to know that the strategy I have intuitively followed (mostly) is supported by this here analysis of the numbers.

The next question, of course, concerns whether I might seriously consider moving up in stakes. Do these numbers I’ve established at one level offer any indication whatsoever about my chances for success at the next? Or am I tracing one long (albeit diverting) non sequitur here?

Well, either way, I have to play this one out. Have to find out.