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the year of the cyber athlete electric
boogaloo edition here we go where we

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droppin so
to start off we're going to be doing um

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going over just basic setup, problem,
and definitions so our task here is to

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program
three different online blackjack casinos

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all of which use perfect shuffles
as the base of their probability so

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all the dealers gonna be using only
perfect shuffles to shuffle their decks

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if you don't know a lot about perfect
shuffles you can go check out the paper

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uh the problem here is that you only
have 10 hours not necessarily to make

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them
but just to bleed them dry you want to

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since since you know everything there is
to know about perfect shuffles you

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should be able to go in there and mop up
um so i'm going to go over a few of the

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definitions i'm going to be using in this
video

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so for bots these are computer players
who play with you you'll be playing with

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between one and four bots depending on
what casino you're in

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there's three types of casinos there's
high stakes standard and rapid fire

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i'll get more into the differences in a
little bit um

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so behaviors the bots are dealt to first
then the player than the dealer that

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happens twice
second time dealer putting his card face

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down since we know all about perfect
shuffles we know what card that is and

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the next card's coming up in the deck
uh the dealer and the bots hit until 17

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then they stand the player goes last
after all the bots then the dealer so

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for an example
so bots are dealt to then the player

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then the dealer
bots are dealt to player dealer

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bot one always already has 21 so he
stands

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bot two has 15 so he has to draw this
card but he's gonna bust himself

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um so now it's our turn um
we have 17 so if we take this eight

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right here
then we bust so we can't take it um we

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have to stand but then the dealer
is gonna he has seven he's gonna draw

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the eight and then draw the four again
giving him um 19 so we don't win every

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time
um this is a more complicated example

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but same same thing
bots are dealt to player dealer bots are dealt to

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player dealer
i don't really care i'm not going to go

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over the bots just know that they're
picking up their cards based on their

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programmed behaviors so we have nine or
19

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um depending on what what we count our
ace as cause aces are either

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one or eleven um so
with 19 this eight would bust us uh the

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dealer has 20 so he won't be picking up
anything

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now with nine we could pick up the eight
giving us 17 and then pick up

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the three giving us 20. um the two will
bust us here so we stand at 20. so the

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best case scenario here
um is the tie so these are all the

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outcomes possible i'm not going to go
through every single example like i did

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there
so for the center casino you're playing

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between one and four bots
so this is what you're expected to win

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um lose and tie
for high stakes you're only playing

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between three and four bars so it
changes these numbers a little bit

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uh rapid fire only between one and two
so

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uh these will be um a little different
as well

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um so for more outcomes specifically
hands for hours this is gonna be very

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important
uh so i i calculated the hands for hour

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looking at typical casino
hands per hour for blackjack and then

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averaging them based on the amount of
bots you'll be playing with over the

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three different casinos
so for an example in the santa casino

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you should win 30 out of 56
um different uh

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outcomes um and so we can just multiply
that times 100

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to get approximately 54. since you're
going to be averaging 100 hands per hour

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you should win a pro
about 54 hands now getting into betting

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so these are the minimum and maximum and
max earnings amounts per each casino

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it's it's different based on what what
casino you're in our goal is here we

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want to we want to get
all three of these maxes all right is it

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possible and if not
what's the maximum earning that we can

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maximum um amount of earnings we can get
um so for example let's do 100 wager in

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the um standard casino
each hand for an hour so you have 100

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hands you should win 54 times making
5400 you should lose about 32 times

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going off for a previous table
losing 3200 so you'll make 2200. the

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cool thing here is that if you look at
this using one two and three dollar bets

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you see a pattern you see it goes up by
the same amount every every dollar

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bet so that i'm calling this the
difference

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and what this means is that earnings per
hour say at the standard casino

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is equal to 22n where n is your bet
amount

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so um that's that's important you're
betting the same amount over and over

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and over again for an hour
so i made a program that uses random bet

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amounts between um
a range and then over um x hours of play

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what this shows is that um betting
randomly in a range is the same as as

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betting
um the min max plus two so like the

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average of your range
or the the meat median of your range um

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consistently consistently for an hour um
so i'm going to use this program to show

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this example we're going to bet between
10 and 90 in the rapid fire casino for

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six
hours and these are expected outputs we

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should have an average bet per
hand of about 50 and then average

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earnings per hour of about 450. so let's
go ahead and check this out

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right here so you put in uh your
difference and the average hands per

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hour from the previous tables
put in your betting range how many hours

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you're playing
what this does it's it's first of all

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this is just a random
number function it is all this is just a

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nested for loop
um it gives you your random bet amount

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and then this is kind of the meat of it
it

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it multiplies it um pi by the difference
kind of going back to that times

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n um uh function or that that we found
and then dividing it by your average

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hands per hour
so typically um you would make your bet

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times a difference for one hour you just
divide it by your average hands per hour

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to see
like how much money you would make off

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of that one hand if you were to do it
for a full hour

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um it adds that up and then it does it
for

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in this case um 122 hands
and then repeats that six times since

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you're playing for six hours
so we should get around 450 right down

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here for average earnings per hour
since we're using random numbers we're

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not going to get it exact every time
but on average you can see we're hitting

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it um sometimes a little less sometimes
a little more but on average that's what

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you can expect same with the average bet
per hand or sitting right around 50.

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all right going back here

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so banning you can actually get banned
um

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just like you can in real life if you
get banned from um

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say the uh high stakes you get banned
from all three so all them below it

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however if you get banned from let's say
rapid fire on the bottom with

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the lower max earnings um you're fine so
that's where we're going to want to

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start
so ways to get banned um hitting the max

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earnings at that casino
consistently betting the max

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quote-unquote suspicious betting that's
why we're gonna be

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using random bats and then that's why i
made that program um

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so we're gonna bet randomly within
roughly ten percent of the max minus one

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so if we can't bet the max we'll just
bet the max minus one

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and then bet within about um ten percent
there because we want we want money

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um so for example so for the santa
casino the max bet

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um the max bed is 1 000
and then 10 of that is 100 um 1 minus

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max 999 so we're going to be betting
between

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899 and 999 so we sh
what this means going off of the program

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is it it basically is
um equal to 949 over and over betting

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that over and over
so we should expect this much money 20

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um to make that every hour we can check
that using our

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program and sure enough
yep right around twenty thousand eight

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hundred and nine hundred fifty average
bet

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all right so to wrap up um we have our
average earnings per hour

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for each casino and how long it'll take
to reach the max that casino the problem

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is that this doesn't add to 10
so we're gonna have to spend um a little

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bit of time in the rapid fire
since you can't make that much anyway so

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spend a little bit of time there
and then max out standard max out um

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high stakes getting you about 1.1 mil
it's not everything but it's

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99.2 percent there thanks for watching