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| By | Variance swings and the law of large numbers | |
| jeff 8/16/2013 11:18:06 PM | There's a recent thread at Paceadvantage where the topic is Blackjack. For those of you who might not know, back in the early 1980's, before I took up betting on horses in a serious way, I used to spend many a weekend in Vegas counting cards. The rules and conditions for the serious 21 player were better back then than they are today... Single and double deck games were widely available. Dealers of those games dealt deeper into the deck than they do today. Players were afforded more liberal spreading of bet size and spreading out to multiple hands on the fly (before drawing heat from the pit.) Blackjack paid 3/2 everywhere instead of the 6/5 that's become commonplace today. Players could double after splitting pairs, resplit pairs (and in some casinos) double on pairs that had been split multiple times. I recall one such hand where I had about $300 riding on the whole thing when it was all said and done - after an initial bet of just $25. Luckily, the dealer broke. Afterwards I recall telling a buddy of mine about the hand. Naturally he asked "Would you have played it the same way had the initial bet been 5 green chips instead of red?" I remember telling him there was no other choice: "There's a mathematically correct way to play every possible hand. You HAVE to make the correct play every time!" In many casinos the dealer was forced to stand on soft 17 instead of hitting soft 17 so widespread today. That rule was the first of many where I began to notice that rules changes were making the game incrementally tougher to beat. Back then, many casinos offered surrender (half your bet) on the first 2 cards dealt. (That rule wasn't widely advertised but it was available at many places if you bothered to ask.) Also, there was the occasional dealer willing to deal a 2 deck game down to virtually the final few cards (provided I was generous with the tips.) As the game of 21 in Nevada became less and less player friendly - and as I became more cognizant that I was breathing in insane amounts of second hand smoke - I gradually lost interest in 21 and gravitated towards horses. The second hand smoke issue was a biggie for me. Very early on, one of the things I LIKED about betting horses was the idea that I could "work" outside - with past performances spread out on a picnic table... in the sunshine no less! One of the better 21 books (my opinion) in my "library" is Million Dollar Blackjack by Ken Uston. One of the things that has always stuck with me were Uston's accounts of his teams playing hundreds of thousands of hands under ideal conditions - and sometimes ending up in the hole even after months of play. Uston's approach to handling this (again my opinion) bordered on genius. Uston constantly drilled the players on his teams to make sure they were sharp and playing the hands in a manner that was as mistake free as was humanly possible. It is clear (to me) from what Uston wrote that he understood and accepted the idea that this was hardly enough. It is also clear to me that Uston used bet sizing to account for short term swings and variance - as well as the law of large numbers. The stated objective of Uston's bet sizing was to realize profitable play (accentuated through compounding) and double the starting bank in 95% of the team's extended sessions - with an (acceptable) percentage chance of losing the starting bank (tapping out) in 5% of the extended sessions. (A topic worthy of another write up.) Uston believed that no matter how well the players on his teams might play the hands, and no matter how accurately they might keep the count, and no matter how good they were at finding games with favorable conditions vs. staying out of games with poor conditions - think efficiency... And despite the fact that it was (and still is) widely accepted that computer simulations by Braun, Thorpe, and others have shown that counting while varying bet size with the count, and playing the hands perfectly in accordance with the count is capable of producing a long term edge for the player over the house of better than 2 percent when the hands are played (again perfectly) during R&D by computer... Whereas the records kept by Uston and his teams indicated that their long term edge over the house averaged about 1 and 1/2 percent... Despite ALL OF THAT, it is clear (again to me) based on what he wrote that Uston believed even the best players playing as mistake free as possible under ideal conditions were still subject to short term variance and swings completely outside their control. However, given enough hands played accurately with an edge: Uston also believed the law of large numbers would assert itself in the long run. Q. How does any of this relate to betting on horses? Last December I traveled to AZ to spend time with family over the Holidays. FYI, AZ is the only state in the US where betting on horses over the web or by phone is a felony. (So no betting on horses for me during such visits!) However, I did bring a laptop along - and whenever free time presented itself I did some Data Window R&D... and came up with a handful of (what looked to be) decent UDMs based on new ideas... one of which I am going to use here in this post to (hopefully) get the point across that we as horseplayers do in fact struggle with the same swings and variance faced by Uston and his teams while playing hundreds of thousands of hands under seemingly ideal conditions. Without giving my UDM Defintion away (I may want to do more R&D and eventually work it back into my lineup for live play) here is what one of my UDMs looked like in the Data Window during the development sample which was essentially the first 11 months of calendar year 2012: http://www.jcapper.com/messageboard/reports/Paint_A.txt I validated the UDM with a 1 month sample that was essentially all tracks everywhere during the month of December 2012: http://www.jcapper.com/messageboard/reports/Paint_B.txt Note: The UDM header displayed in the Data Window shows a "Tag Date" of 12/12/2012. The last mod I made to the UDM def on that date was something I considered to be really minor and therefore didn't let it impact the time frame of my development and validation samples. In retrospect (given the outcome) that was probably a mistake. Also, in retrospect (again given the outcome) 30 days and the 200 odd plays in that time period was probably too small a validation sample. Shortly upon my return from AZ, based on the performance in the validation sample (and unable to contain myself) I decided to promote the UDM to live play. At the time I gave the UDM the following name: P_A_I_N_T and color coded it in such a way that it was highly visible on my reports (thus the UDM name.) Maybe you can guess where I am going with this... Here is the performance of the UDM during the first 3 months of 2013: http://www.jcapper.com/messageboard/reports/Paint_C.txt As you might well guess, I decided to stop using the UDM for live play towards the end of Feb 2013. I recall a phone conversation one Sunday morning shortly after that when my brother called to catch up and ask how I was doing. I recall telling him I was pissed at myself for flushing several thousand dollars worth of "PAINT" down the drain. Imagine my surprise a few days ago when I ran PAINT through the Data Window for 2013 ytd... http://www.jcapper.com/messageboard/reports/Paint_D.txt Please don't feel sorry for me. This wasn't the only new UDM I promoted to live play during the year. (But it was one of the few that didn't work out for me.) My point? (Which hopefully isn't lost on you.) Variance and the law of large numbers applies to horseplayers too. -jp . ~Edited by: jeff on: 8/16/2013 at: 11:18:06 PM~
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| Cole 8/17/2013 7:24:22 AM | Thanks for sharing Jeff--very interesting.
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| Charli125 8/17/2013 3:21:10 PM | This is one of the times when I would look at it by track. It's possible that this UDM is deadly at certain tracks, that run at certain times, and not at others. I assume you already did this and didn't see a correlation, but that's why i almost always end up excluding certain tracks from my UDM's. Certainly proves that past results are not indicative of future results!
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