What percentage of blackjack hands should you win?

Let's look at the winning probability — from multiple runs, the range is always between 42% to 43% and the losing probability is always between 47% to 49% , the losing probability is always higher than winning, which indicates the casino will end up making money than any one of us if we play a significant number of ...

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Make Your Bookie Cry And Pull The Hair By Generating $23,187

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How much will 100,000$ win you at Blackjack?

Isn’t there something magical about a casino? in a theatrical sense, you walk into a casino, all the bright lights shining at you, there is a strong, soothing and sensuous smell and you hear people celebrating their wins! now you’re ecstatic, you cant wait to feel the chips in your hands, you think to yourself that this is the night, the night you always dreamed of , you’re going to make the winning of your lifetime! You begin to play Blackjack, you make significant wins, you’re feeling like you’re on cloud nine and then comes the boom. How long has the winning streak lasted? not much, Well, does this scenario look familiar to you? (Or is it just me who goes through this!)

After my recent visit to a casino I came out thinking that there must be a strategy to win and I’ve to find out the probability of winning this game. I googled Blackjack strategies and almost all websites pointed me to the Basic Blackjack chart of betting, I got my head around it pretty quickly and now it was time to put it to test, what other way than simulating allot of random hands of Blackjack between players and dealer right?

Well, that’s exactly what I did, Let’s assume we have 100,000$ to bet(I so wish!), each bet will cost us 10$ and we play 10,000 hands. Let’s think of the questions we can try to answer through our simulation;

How much do I win after playing 10,000 hands?

What are the win & loss percentages?

How many Blackjack's do I hit? (1,000 atleast, one in ten hands?)

How much does the Dealer make?

Which hands are the luckiest?

Can we create a matrix of — player cards win percentage against the dealers cards? (I’ll use this in my next casino visit and make the moolah!)

Simulation Setup

To simulate the casino game, let’s have 6 players playing — each with a pot of 100,000$(High rollers, man!) and a dealer. Each bet will be of 10$, a blackjack win will give a return of 3 : 2, that is a 10$ bet will return 25$ (inclusive of your 10$ bet) and a normal high win or dealer bust will give a return of 1 :1, that is a 10$ bet will return 20$. For simulation purposes, let’s ignore insurance, splits,double down and any other bonus plays. As all the casino’s now usually deal with 6 set of cards in a deck, we’ll use the same, that is a total of 312 cards during each round — we’ll shuffle all cards each round to mimic the continuous shuffling machines(bye bye card counting!). The dealer begins dealing cards with player 1 to player 6 and ending the deal with himself. He also has his first card face up. The players will make a decision to hit for more cards or stand based on the sum of their first two cards dealt and the dealer’s face up card, again based on Basic Blackjack Strategy(refer here). Alright, now let’s run the simulation and look at the results, shall we?

Game Results

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Let’s look at the Total statistics of all hands played by all the players together first and then move on individual player stats: After playing a total of 60,000 hands and betting a total of 600,000$ the players together win only 586,625$ that is a drop of 2%. The $Amt won to Bet ratio is 0.98, only a factor above 1 will ever give you a profit from the betting. Let’s look at the winning probability — from multiple runs, the range is always between 42% to 43% and the losing probability is always between 47% to 49% , the losing probability is always higher than winning, which indicates the casino will end up making money than any one of us if we play a significant number of hands. Let’s us look at the blackjack hit ratio — our initial aim was to hit a 1000 Blackjacks out of 10,000 hands, that is a 1 in 10 or 10%, we have hit 2845 hands out of 60,000 total hands, which is a hit percent of only~5%. Which has been our luckiest hands ? — no surprises here, they are a pair of 10 (10,J,K,Q — all have same value in Blackjack). Let’s move on individual player stats.

Player Statistics

An interesting observation is that each player statistics are similar to each other and to the overall combined statistics. All the inferences from the above section can be applied here as well. How about we look at some losing statistics?

From multiple runs, we see that a Players Bust out (sum of their cards goes over 21) ~ 17% to 19% whereas they get beaten(Dealer sum of cards is higher than theirs) around 28% to 30%. This clearly suggests that the Basic blackjack strategy makes one very conservative in hitting more cards. While the dealer bust outs 24% to 25% times, lesser than the player beat%. Maybe we should look at the winning and losing matrices and make few tweaks to better the losing stats. Any surprises here with lucky hands? not really, as expected 20 and 21 gives you the most number of wins. Interestingly, 17 & 18 has a very high probability of losing ~60% to 70%. While 13,14,15 & 16 — the probability is losing is >50% to 60%. This could potentially be our area of strategy which we can improve our losses.

Winning % Matrix,Player Sum of Cards against Dealer Face up Card

Highlighted(Boxed) areas have bad winning percentages, which could be our focus of improvement, the strategy at the moment for 14,15,16 &17 against a dealer face up card of 8,9,10 & 11- is to hit for more cards to get the edge over a dealer, if we can look closer into how exactly did we loose these hands- whether if we busted the cards or if we were beaten by the dealer’s high cards, we could then improvise the strategy as needed.

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Inference

Speaking in terms of strategy, the % of wins are decent with player sum of 12,13 and very high win % with 20 and 21. The Basic strategy looks certain to give us a 42% win rate for significant hands(~50 Hands), but this win rate is not sufficient to make any profit at all. If we can increase this win rate to about 50% or 55%, we could be certain of a profit. So, how do we increase the win rate? — wait for it, drum roll — part two of this article will give you those details. For now, remember my friend, if you’re at the blackjack table and your current win rate(hands won to hands played)is above 55% and greater I suggest you get of the table and collect your winnings! I hope this article has shed some light into betting patterns and given you an insight on the odds of you winning.

Try the Simulation?

For all the folks who would like to see the code and try the simulations — https://github.com/Mojocolors/Blackjack-Odds . Until part two — Happy Reading, Happy Playing!

towardsdatascience.com - How much will 100000$ win you at Blackjack? - Towards Data Science

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