1 00:00:00,399 --> 00:00:05,200 the year of the cyber athlete electric boogaloo edition here we go where we 2 00:00:05,200 --> 00:00:09,040 droppin so to start off we're going to be doing um 3 00:00:09,040 --> 00:00:12,240 going over just basic setup, problem, and definitions so our task here is to 4 00:00:12,240 --> 00:00:14,799 program three different online blackjack casinos 5 00:00:14,799 --> 00:00:18,160 all of which use perfect shuffles as the base of their probability so 6 00:00:18,160 --> 00:00:21,199 all the dealers gonna be using only perfect shuffles to shuffle their decks 7 00:00:21,199 --> 00:00:23,840 if you don't know a lot about perfect shuffles you can go check out the paper 8 00:00:23,840 --> 00:00:27,119 uh the problem here is that you only have 10 hours not necessarily to make 9 00:00:27,119 --> 00:00:29,279 them but just to bleed them dry you want to 10 00:00:29,279 --> 00:00:32,079 since since you know everything there is to know about perfect shuffles you 11 00:00:32,079 --> 00:00:35,840 should be able to go in there and mop up um so i'm going to go over a few of the 12 00:00:35,840 --> 00:00:37,680 definitions i'm going to be using in this video 13 00:00:37,680 --> 00:00:40,640 so for bots these are computer players who play with you you'll be playing with 14 00:00:40,640 --> 00:00:43,520 between one and four bots depending on what casino you're in 15 00:00:43,520 --> 00:00:46,800 there's three types of casinos there's high stakes standard and rapid fire 16 00:00:46,800 --> 00:00:50,079 i'll get more into the differences in a little bit um 17 00:00:50,079 --> 00:00:53,680 so behaviors the bots are dealt to first then the player than the dealer that 18 00:00:53,680 --> 00:00:56,399 happens twice second time dealer putting his card face 19 00:00:56,399 --> 00:00:59,760 down since we know all about perfect shuffles we know what card that is and 20 00:00:59,760 --> 00:01:03,359 the next card's coming up in the deck uh the dealer and the bots hit until 17 21 00:01:03,359 --> 00:01:06,560 then they stand the player goes last after all the bots then the dealer so 22 00:01:06,560 --> 00:01:09,840 for an example so bots are dealt to then the player 23 00:01:09,840 --> 00:01:14,479 then the dealer bots are dealt to player dealer 24 00:01:14,479 --> 00:01:17,600 bot one always already has 21 so he stands 25 00:01:17,600 --> 00:01:22,080 bot two has 15 so he has to draw this card but he's gonna bust himself 26 00:01:22,080 --> 00:01:27,680 um so now it's our turn um we have 17 so if we take this eight 27 00:01:27,680 --> 00:01:30,880 right here then we bust so we can't take it um we 28 00:01:30,880 --> 00:01:34,079 have to stand but then the dealer is gonna he has seven he's gonna draw 29 00:01:34,079 --> 00:01:39,360 the eight and then draw the four again giving him um 19 so we don't win every 30 00:01:39,360 --> 00:01:41,840 time um this is a more complicated example 31 00:01:41,840 --> 00:01:45,439 but same same thing bots are dealt to player dealer bots are dealt to 32 00:01:45,439 --> 00:01:47,759 player dealer i don't really care i'm not going to go 33 00:01:47,759 --> 00:01:50,560 over the bots just know that they're picking up their cards based on their 34 00:01:50,560 --> 00:01:55,040 programmed behaviors so we have nine or 19 35 00:01:55,040 --> 00:01:58,960 um depending on what what we count our ace as cause aces are either 36 00:01:58,960 --> 00:02:05,040 one or eleven um so with 19 this eight would bust us uh the 37 00:02:05,040 --> 00:02:07,600 dealer has 20 so he won't be picking up anything 38 00:02:07,600 --> 00:02:11,200 now with nine we could pick up the eight giving us 17 and then pick up 39 00:02:11,200 --> 00:02:15,840 the three giving us 20. um the two will bust us here so we stand at 20. so the 40 00:02:15,840 --> 00:02:19,360 best case scenario here um is the tie so these are all the 41 00:02:19,360 --> 00:02:22,400 outcomes possible i'm not going to go through every single example like i did 42 00:02:22,400 --> 00:02:25,360 there so for the center casino you're playing 43 00:02:25,360 --> 00:02:28,959 between one and four bots so this is what you're expected to win 44 00:02:28,959 --> 00:02:31,920 um lose and tie for high stakes you're only playing 45 00:02:31,920 --> 00:02:35,519 between three and four bars so it changes these numbers a little bit 46 00:02:35,519 --> 00:02:38,720 uh rapid fire only between one and two so 47 00:02:38,720 --> 00:02:42,080 uh these will be um a little different as well 48 00:02:42,080 --> 00:02:45,840 um so for more outcomes specifically hands for hours this is gonna be very 49 00:02:45,840 --> 00:02:48,560 important uh so i i calculated the hands for hour 50 00:02:48,560 --> 00:02:52,400 looking at typical casino hands per hour for blackjack and then 51 00:02:52,400 --> 00:02:56,400 averaging them based on the amount of bots you'll be playing with over the 52 00:02:56,400 --> 00:03:00,319 three different casinos so for an example in the santa casino 53 00:03:00,319 --> 00:03:05,360 you should win 30 out of 56 um different uh 54 00:03:05,360 --> 00:03:09,360 outcomes um and so we can just multiply that times 100 55 00:03:09,360 --> 00:03:13,519 to get approximately 54. since you're going to be averaging 100 hands per hour 56 00:03:13,519 --> 00:03:18,480 you should win a pro about 54 hands now getting into betting 57 00:03:18,480 --> 00:03:23,920 so these are the minimum and maximum and max earnings amounts per each casino 58 00:03:23,920 --> 00:03:27,360 it's it's different based on what what casino you're in our goal is here we 59 00:03:27,360 --> 00:03:31,120 want to we want to get all three of these maxes all right is it 60 00:03:31,120 --> 00:03:33,920 possible and if not what's the maximum earning that we can 61 00:03:33,920 --> 00:03:39,120 maximum um amount of earnings we can get um so for example let's do 100 wager in 62 00:03:39,120 --> 00:03:42,879 the um standard casino each hand for an hour so you have 100 63 00:03:42,879 --> 00:03:47,440 hands you should win 54 times making 5400 you should lose about 32 times 64 00:03:47,440 --> 00:03:52,159 going off for a previous table losing 3200 so you'll make 2200. the 65 00:03:52,159 --> 00:03:55,840 cool thing here is that if you look at this using one two and three dollar bets 66 00:03:55,840 --> 00:03:59,840 you see a pattern you see it goes up by the same amount every every dollar 67 00:03:59,840 --> 00:04:03,120 bet so that i'm calling this the difference 68 00:04:03,120 --> 00:04:07,200 and what this means is that earnings per hour say at the standard casino 69 00:04:07,200 --> 00:04:10,640 is equal to 22n where n is your bet amount 70 00:04:10,640 --> 00:04:14,720 so um that's that's important you're betting the same amount over and over 71 00:04:14,720 --> 00:04:18,639 and over again for an hour so i made a program that uses random bet 72 00:04:18,639 --> 00:04:23,680 amounts between um a range and then over um x hours of play 73 00:04:23,680 --> 00:04:27,680 what this shows is that um betting randomly in a range is the same as as 74 00:04:27,680 --> 00:04:30,400 betting um the min max plus two so like the 75 00:04:30,400 --> 00:04:34,639 average of your range or the the meat median of your range um 76 00:04:34,639 --> 00:04:38,639 consistently consistently for an hour um so i'm going to use this program to show 77 00:04:38,639 --> 00:04:42,320 this example we're going to bet between 10 and 90 in the rapid fire casino for 78 00:04:42,320 --> 00:04:44,960 six hours and these are expected outputs we 79 00:04:44,960 --> 00:04:49,280 should have an average bet per hand of about 50 and then average 80 00:04:49,280 --> 00:04:53,840 earnings per hour of about 450. so let's go ahead and check this out 81 00:04:53,840 --> 00:04:57,520 right here so you put in uh your difference and the average hands per 82 00:04:57,520 --> 00:05:01,360 hour from the previous tables put in your betting range how many hours 83 00:05:01,360 --> 00:05:04,160 you're playing what this does it's it's first of all 84 00:05:04,160 --> 00:05:08,400 this is just a random number function it is all this is just a 85 00:05:08,400 --> 00:05:12,000 nested for loop um it gives you your random bet amount 86 00:05:12,000 --> 00:05:13,919 and then this is kind of the meat of it it 87 00:05:13,919 --> 00:05:18,000 it multiplies it um pi by the difference kind of going back to that times 88 00:05:18,000 --> 00:05:24,240 n um uh function or that that we found and then dividing it by your average 89 00:05:24,240 --> 00:05:27,840 hands per hour so typically um you would make your bet 90 00:05:27,840 --> 00:05:31,199 times a difference for one hour you just divide it by your average hands per hour 91 00:05:31,199 --> 00:05:33,280 to see like how much money you would make off 92 00:05:33,280 --> 00:05:36,479 of that one hand if you were to do it for a full hour 93 00:05:36,479 --> 00:05:40,560 um it adds that up and then it does it for 94 00:05:40,560 --> 00:05:45,759 in this case um 122 hands and then repeats that six times since 95 00:05:45,759 --> 00:05:50,240 you're playing for six hours so we should get around 450 right down 96 00:05:50,240 --> 00:05:53,600 here for average earnings per hour since we're using random numbers we're 97 00:05:53,600 --> 00:05:57,280 not going to get it exact every time but on average you can see we're hitting 98 00:05:57,280 --> 00:06:00,400 it um sometimes a little less sometimes a little more but on average that's what 99 00:06:00,400 --> 00:06:05,120 you can expect same with the average bet per hand or sitting right around 50. 100 00:06:05,120 --> 00:06:08,560 all right going back here 101 00:06:09,600 --> 00:06:12,720 so banning you can actually get banned um 102 00:06:12,720 --> 00:06:15,840 just like you can in real life if you get banned from um 103 00:06:15,840 --> 00:06:19,440 say the uh high stakes you get banned from all three so all them below it 104 00:06:19,440 --> 00:06:22,479 however if you get banned from let's say rapid fire on the bottom with 105 00:06:22,479 --> 00:06:26,160 the lower max earnings um you're fine so that's where we're going to want to 106 00:06:26,160 --> 00:06:28,880 start so ways to get banned um hitting the max 107 00:06:28,880 --> 00:06:31,520 earnings at that casino consistently betting the max 108 00:06:31,520 --> 00:06:34,000 quote-unquote suspicious betting that's why we're gonna be 109 00:06:34,000 --> 00:06:37,600 using random bats and then that's why i made that program um 110 00:06:37,600 --> 00:06:40,960 so we're gonna bet randomly within roughly ten percent of the max minus one 111 00:06:40,960 --> 00:06:43,840 so if we can't bet the max we'll just bet the max minus one 112 00:06:43,840 --> 00:06:48,240 and then bet within about um ten percent there because we want we want money 113 00:06:48,240 --> 00:06:51,599 um so for example so for the santa casino the max bet 114 00:06:51,599 --> 00:06:58,319 um the max bed is 1 000 and then 10 of that is 100 um 1 minus 115 00:06:58,319 --> 00:07:01,039 max 999 so we're going to be betting between 116 00:07:01,039 --> 00:07:06,479 899 and 999 so we sh what this means going off of the program 117 00:07:06,479 --> 00:07:11,199 is it it basically is um equal to 949 over and over betting 118 00:07:11,199 --> 00:07:15,840 that over and over so we should expect this much money 20 119 00:07:15,840 --> 00:07:19,360 um to make that every hour we can check that using our 120 00:07:19,360 --> 00:07:23,759 program and sure enough yep right around twenty thousand eight 121 00:07:23,759 --> 00:07:27,840 hundred and nine hundred fifty average bet 122 00:07:29,599 --> 00:07:34,240 all right so to wrap up um we have our average earnings per hour 123 00:07:34,240 --> 00:07:38,560 for each casino and how long it'll take to reach the max that casino the problem 124 00:07:38,560 --> 00:07:42,720 is that this doesn't add to 10 so we're gonna have to spend um a little 125 00:07:42,720 --> 00:07:46,960 bit of time in the rapid fire since you can't make that much anyway so 126 00:07:46,960 --> 00:07:51,599 spend a little bit of time there and then max out standard max out um 127 00:07:51,599 --> 00:07:54,879 high stakes getting you about 1.1 mil it's not everything but it's 128 00:07:54,879 --> 00:08:00,879 99.2 percent there thanks for watching