Saturday, August 25, 2012

Wheaties, Aces & Probabilities


Let's say that someone asked you to tell them what President Franklin Roosevelt ate for breakfast on some particular Sunday morning in the year 1942. You probably couldn't answer this, right?

Well, that depends on what you mean by "answer." Unless there was a specific news item or event he was attending for breakfast that day, in which the foods were specifically mentioned by a reporter, we couldn't definitively state what the man ate....

...ah, but we could do some logical deduction to narrow the possibilities. We know for instance which foods were not available in those days, such as many of the modern commercial cereals. We also know that most people of that period tended to eat traditional "breakfast"-type foods, and not things like soups, pastas, and other "lunch" or "dinner" foods. We also know that FDR was in relatively poor health during this period, afflicted with polio, advancing age, and the stress of World War II, so we might rule out some of the heavier types of foods that might have been uncomfortable for him to consume, such as steak with eggs. We also know that his wife, Eleanor, looked closely after his health, and would probably have a say in what foods the President's chef did and did not serve her husband.

We could also look at FDR's schedule, and see whether he was at the White House that day, or whether he was on a trip, and what meetings he had scheduled for that morning, etcetera. We might also note that this was a Sunday, and people tend to eat "special" breakfasts on weekends. Perhaps he reportedly loved pancakes, but knew that they made him drowsy by noon. He might also have disliked waffles, tolerated french toast, and couldn't stand English muffins... and so on.

In other words, we could narrow down FDR's food choices by looking at all the seemingly unrelated things we know or could discern about the man and the situation he was in at that specific moment of his life. This could help us fine tune our information, and if pressed we could actually come up with a probabilistic guess at what he ate for breakfast on that specific day. This might look something like: 55% probability he had eggs, bacon, and toast, 30% probability that he had oatmeal, 10% chance he ate pancakes, and 5% probability he skipped breakfast altogether and just had a cup of coffee. In other words, we could put FDR on a "range" of breakfasts using deduction and logic.

This is the same type of reduction process you need to go through when trying to put your poker opponents on hand ranges. You need to pull in all the information you know about the player and the current situation to rule out cards, and narrow down the range of hands they hold. What type of player are they? Are they loose or tight? Aggressive or passive? Bluffy or ABC? What is their current mental state? Have they won or lost a big pot recently? What types of hands have we seen them play previously? What position are they in? Are they positionally aware? Are they playing L1, L2, or Level 3 poker? Are they betting, raising, or just calling in this particular hand? How are they reacting to the board texture? Are there any tells we can discern? Betting patterns? What other players are involved in the hand? What are those people doing, and how is this player reacting to them? What is the pot size? What cards do we know he can't have, such as those in our own hand or ones that were accidentally turned upright? And so on...

Putting players on a range of hands isn't rocket science, but it does take active, logical, deductive work. A solid, mid-position ABC player cold calls an UTG player's preflop raise? Well, we probably can remove AA-QQ, AK, AQ, and KQ from his range, as he would probably reraise with these to isolate. We can also probably remove many of the trap hands from his range, small suited connectors and gappers, and of course all the usual garbage hand, as we said he as a solid ABC player. This might leave small and medium pairs, some bigger suited aces, and medium suited connectors in his range. He might also be getting tricky with some bigger suited connectors, as we just saw him drag a big pot, and we know that he tends to open up his game if he feels he's free-rolling. The downstream players from him are all loose and passive, and we know that he knows this, so we can further eliminate hands that he would limp-reraise with. Etcetera. When the board comes out and we see what he does, we can further narrow the range based on how wet the flop is.

By the time we get to the river, we should be able to put this player on a fairly tight handful of possible cards. We can then estimate our own equity against this range and make good decisions based on seemingly sparse and unrelated information. Wheaties or Captain Crunch? Aces or a bluff? Poker is all about deductive reasoning to figure out what your opponent has in his hand... and that starts primarily with what he most likely doesn't hold, eliminating those from his range....

...and in doing so, we might just also be able to tell them what they ate for breakfast, too.

All-in for now...
-Bug
PS. While fishing was FDR’s favorite outdoor social activity, poker was one his favorite sources of indoor relaxation with friends and staff. Gives a whole new meaning to the term "New Deal," eh?

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