Behavior Design

Just read this pdf that David Ngo came out with called learn behavior design. Here are some notes/thoughts:

• fog behavior model
• to do anything (eg: pick up phone), you need all three of (1) trigger, (2) ability, (3) motivation
• hot triggers- something u can do right now- vs billboards
• ability vs motivation tradeoff-
  ​ doing something hard requires high motivation; if your motivation ever drops, then you break your habit​
• ​​tiny habits + celebrations
• ​LT behavior chg can come from chging environment​
• ​LT behavior chg cannot come from just motivation​ (because it is too unstable and so you will break habit)
• ​u want to ​
  get to the "blue path"
  ​ from the behavior grid​
  ​ at behaviorgrid.org​. ie. how to start doing familiar behavior, and then slowly increase/build from there
• ​ design many many beneficial behaviors that get to ​​good outcomes (eg: a bunch of behaviors that make you healthy)​ and then wait for the tiny habits to take hold and grow naturally
• ​easy to do in beginning and end of day​
• http://www.behaviorwizard.org
• ​motivation wave
• natural to have ​peaks where you can temporarily do hard things and troughs/normal periods
• ​​
  ​help people succeed on the most desirable behavior that matches their current motivation
• ​
  ​should somehow measure how motivated u r and then do the hardest work possible (any higher == not enough motivation and give up)
• when you are at peak motivation, do hard things that will 
1. ​​
   structure future behavior
2. ​reduce barriers to behavior
3. increase skill/capability so it's easier to do activity in the future
• these all move future activities further down the motivation/ability curve towards easier to do --> less motivation required later​
• ​do your tiny habits, prestructured behavior, and easy one time behaviors, baby steps during trough
• ​you cannot "motivate" behavior change; artificially boosting motivation doesn't work​

Setting up podcast alarms for your mac

Quick notes on how to configure your mac so that you can wake up to podcasts/get podcasts to play every hr etc.

1. make a podcast playlist on itunes
1.  create a smart playlist from your musics tab as follows (I called mine "New Podcasts") 
2. you probably want to configure the podcast settings so that you only keep the most recent episode (otherwise say for NPR hourly podcasts, your playlist will include multiple podcasts from NPR hourly)
2. create an application with automator
1. create a new application and save it somewhere
2. search for itunes and put "get specified itunes times" into the right side (then add your playlist u just made)
3. search for itunes and put "play itunes playlist" into the right side
4. this is how it should look at the end.
3. system preferences -> users & groups -> login items: add your automator application to get it to run on login
1. to get computer to automatically turn on, system preferences -> energy saver -> schedule -> startup/wakeup every day at xyz time
4. go to calendar and add repeating items for daily/hourly runs
1. create a new event, make it repeat
2. go to the alerts -> custom -> open file. and instead of opening calendar, open the application
5. to automatically download/get the most recent podcasts, the easiest would probably be to write an applescript, then export it as an application (and then schedule to run it right before your podcast alarm)
   
   

Poker: running cards multiple times

Consider the following a quick exercise in combinatorics. We are investigating the effects of running cards twice. You can see a real life example here. It is known that the EV doesn't change when you run multiple times (but you lower your variance). Let us check this claim.

Let's take the case of KK vs AA allin after a blank flop. After the flop, there are 45 cards left. If we run it once:

EV for KK = Pr(K on turn and no A on river) + Pr(no A on turn and K on river) + Pr(K's on turn and river) = 2/45 * 41/44 + 41/45 * 2/44 + 2/45 * 1/44 = 8.383838...%

Notice that the first two terms are the same because turn/river is interchangeable. Double checking this on pokerstove and using a flop with 0 chances of runner runner flush/straights, we get 8.384%. Nice. Exact.

Let's say we run it the second time. A couple possibilities in the first run:

• one A came out (2/45 * 41/44 * 2 = 8.2828%)
• then EV for second run is 2/43 * 40/42 * 2 + 2/43 * 1/42 = 8.9701%
• two A's came out (2/45 * 1/44 = 0.1010%)
• then EV for second run is 2/43 * 2 - 2/43 * 1/42 == 2/43 * 41/42 * 2 + 2/43*1/42 == 9.1915%
• one K and one A came out (2/45 * 2/44 *2 = 0.4040%)
• then EV for second run is 1/43 * 41/42 * 2 = 4.5404%
• one K came out and no A's came out (2/45 * 41/44 *2 = 8.2828%)
• then EV for second run is 1/43 * 40/42 * 2 = 4.4297%
• two K's came out (2/45 * 1/44 = 0.1010%)
• then EV for second run is 0%
• no A/K came out (41/45 * 40/44 * 2 )
• then EV for second run is 2/43 * 39/42 * 2 + 2/43 * 1/42 = 8.7486%

The above EVs were also double checked with pokerstove using dead cards (A, K and blanks) and should be the exact probabilities. Adding these all up, the EV over all cases for the second run is 8.3838%- same as the first run.

Poker: Pot Odds 2

Some follow up thoughts on the first post about odds. To get the most precise numbers for your hand's equity/odds, you should compare pot odds with your hand's odds of hitting its outs.

So using the same scenario from the first post, the third/most precise method is as follows:

Method 3 == Pot Odds vs Odds of Hitting Outs
Pot odds == 1:5
Your hand has 8 outs. On the turn, there is 52 - 5 = 47 cards left. Your odds of hitting  outs is 8 : (47-8) == 8:39 == 1:4.875
Since pot odds > odds of hitting outs, you should call.

So note that this is much more precise, and only deals with the turn card (ie. if you had read the second post about bet sizing, this assumes that you will bet optimally on the turn again and that effective stack size is large enough for optimal bet)

However, the disadvantage of pot odds is that when the probability is small, the odds change very rapidly to any small change in probability. ie. 1:49 vs 1:99 is actually only 1% apart. So whereas for equity calculation, you are "safe" if you have say a 5% buffer between required equity vs hand equity, here there is no similar rule and you might be easily mislead as to how much edge you have.

Let's look at what a 5% equity edge means for different pot odds.

Bet Size	Pot Odds	Required # of Turn Outs Without Buffer	Equity + 5% Buffer	Required Hand Odds With Buffer	Required # of Turn Outs With Buffer
1/4x pot	1:5	7.8	21.7%	1:3.6	10.2
1/2x pot	1:3	11.8	30.0%	1:2.3	14.2
1x pot	1:2	15.7	38.3%	1:1.6	18.1
2x pot	1:1.5	18.8	45%	1:1.2	21.4

Without the 5% buffer, the Required Hand Odds should equal pot odds. Instead, as you can see, 1:5 -> 1:3.6, while 1:1.5 -> 1:1.2. Hence there is no easy way to build in some buffer with pot odds. However, you may have noticed that the required outs actually increases by a constant (2.4 outs) when you build in a 5% buffer. This makes perfect sense- 2.4 outs --> an extra 5% chance of drawing out.

Thus the optimal way to give yourself a buffer is to calculate the odds as is, but then require a couple extra outs to be conservative.

Interestingly, if you look at the # of outs required for 1x pot and 2x pot bets on the flop, they are actually "ahead" (> 50% chance of drawing out by the river). So it seems as though any drawing hand that could call a > pot sized bet could also just raise or push all-in. More on this next.

Poker: Bet Sizing

Following the last introductory post to poker, here is an example on how to determine bet sizing based on the texture of the flop.

Let's say effective stack size is 200 BB, we are in button/cutoff, it was limp/folded to us, and we raised to 4-6 BB and one player called. So the pot is ~10 BB (8.5-13.5 BB depending on dead money/size of raise) and effective stack size is 195 BB.

Let's say the flop comes with two flush cards (two cards of same suit) and you have top pair top kicker and you are committed to calling the all-in even if the another flush card comes because you have a weird hunch/you are tilting etc. Let's look at what you need to bet taking into account the implied pot to push a flush draw opponent out of the pot.

The flush draw opponent has 36% equity -> you want to lay 1.8:1 odds for optimal play -> with an implied pot of 10 BB + 195BB, that is a bet of 205/1.8 = 114 BB. This sounds ridiculously huge and incorrect. There are two reasons for this. 

1. Being willing to commit 200 BB on a flush board with top pair is an incorrect play. 
2. The existence of a turn bet means that the true "correct bet" amt is much lower. 

We will look at these two lines of thought below and examine what the "correct bet" should be if we take such factors into account..

How much you would typically/normally commit with top pair top kicker
Generally, with top pair or worse, you want to control the pot to be medium sized. Let's look at what that means for the flop/turn/river betting rounds:

1. if betting sizes were pot sized, I would say two bets would already be really pushing it. (ie. you would control the size by either bet/check/bet or bet/bet/check etc). In this case the pot would be 90 BB by showdown and you and your opponent would have each put in another 40 BB.
2. if betting sizes were 1/2 pot, it is probably feasible to bet on all three rounds. In this case the pot would just be 80 BB (35BB each since flop). But betting like this might be stupid with the flush draw on the board.

From these rough estimates, it seems that we should be willing to commit another 35-40 BB to this 10 BB pot. Let's say that the implied pot size is 10 + 35 BB. Then the optimal bet is 25BB, or 2.5x the pre-money pot. This certainly seems more reasonable but from what we know empirically about poker betting, it still seems to be on the high end. Let's move on to consider the fact that there can still be betting on the turn/river.

Betting on the turn

From the conclusion of last post, remember that by betting optimally against a dog, each time you bet, you are effectively causing them to loose money equivalent to them folding to the bet in the long run. I would thus make the following statement:

By betting optimally on the turn, it is as though we have cut off the opponent's chances to draw on the river. ie. it is as though the opponent loses the pot right here on the turn.

Now, we can see that perhaps our opponent doesn't have 36% equity, since after they see one card on the turn, we can bet again, which is equivalent to cutting them out right there. So they have 9 outs out of 47 possible turn cards. So we could lay 38:9 ~= 4.2:1 odds to price them out. With a 45BB implied pot, this means betting 10.7 BB ~= 1.1x the pre-money pot. This is more inline with what we know as "normal" betting. 

What is interesting is that if you follow this line of reasoning/betting on the flop, you are committed to betting the turn 100% of the time if no flush cards come out- otherwise you are actually giving your opponent 36% equity and good odds to call on the flop.

So it turns out that maybe our flop bet sizing could vary depending on our game plan on the turn.

As a matter of exercise, let's look at what our proper bet on the turn is. Let's say we just bet another 1x pot on the flop- so the turn pot is 30BB (and we are ready to commit another 25-30BB). What is the optimal bet on the turn if no flush cards come? They have 9 outs out of 46 river cards, so we lay 37:9 ~= 4.1:1 odds. With an implied pot of 60BB, this means that betting 15xBB = 1/2 the pre-money pot.

So either you bet [1.1x pot on flop AND 0.5x pot on turn], or maybe you need to overbet on the flop by betting (at most?) 2.5x pot if you intend to (sometimes? check the turn.