5 ms·
How to play continuous blackjack
- texaslonghorn5 4y agoInteresting problem statement and good analysis. If I am understanding correctly then this is continuous space discrete time. How might the problem change if time was also continuous, meaning card-draw would be integration of some random continuous function, rather than discrete samples?
- kqr 4y agoI can't seem to access the server with the article right now, but generally the easiest way to get there is as the limit of the discrete case as the timestep δ -> 0 and the payoff scaled down so they still add up to the same macro conditions. I suspect it would be the same but less interesting, though. The smaller you make the increments, the closer the optimal stopping point is to 21. At the limit, the stopping point would be 21, and -- I think -- all N players plus dealer would have an 1/(N+1) chance of reaching it. Basically, without jumps, it just becomes a situation with all players waiting for a continuous counter to reach 21, and then stopping precisely as it does. The one who was lucky to have the fastest counter (on average) wins. (With jumps as in discrete Blackjack, the fastest counter not necessarily the best!) What might make it more interesting is if you did introduce discontinuities in the otherwise continuous process. So basically each player is fed with what looks like the absolute values of stock price movements, and has to stand somewhere. That should be easy to simulate and maybe even fun to play!
- Someone 4y agoIf there wouldn’t be a delay between observing the current value and stopping (assuming a reasonably well-behaved distribution P), that problem is trivial: stop when you reach the threshold. So, you would have to add some time delay between observation of a value and actual stopping. Intuitively, I can think of two stopping strategies that might be optimal: call ‘stop’ when the expected value at stop is that ≈ 0.5706 or call stop when the probability of overshooting it is 50%. I’m fairly sure that intuition is wrong in general, though.
- hnhuhn 4y agohttps://archive.ph/HqOvu https://archive.ph/HqOvu
- roninghost 4y agoHi Alex, did I get my Tipler back from you? Just kiding, nice article.
- alexmolas 4y agois that you AJT??
- SilasX 4y agoWhat is going on? I remember seeing this several days ago, which the search feature confirms[1], but now, it appears again with the same story URL but is now only two hours old? With all comments forward-dated too? [1] https://hn.algolia.com/?q=continuous+blackjack https://hn.algolia.com/?q=continuous+blackjack
- jtokoph 4y agoHN admins/mods are able to give posts that they deem interesting a second chance.
- AreYouSirius 4y agoCasinos shuffle cards after every 1-5 draws, online casinos shuffle cards after every draw, so COUNTING CARD IS DEAD. AND WAS VERY LONG TIME AGO 99.99% of youtube channels dealing with counting cards are SCAM.
- AreYouSirius 4y agoso even if everything in that paper is VALID mathematically, in reality it will not work because blackjack in casinos is DIFFERENT game then one that is played in this paper.
- hot_gril 4y agoThe paper isn't claiming anywhere to tell you how to play in casinos.
- whiterock 4y agoit‘s a mathematical excursion… it‘s not meant to be a real life applicable thing. read the article before posting please :)
- alexmolas 4y agoyou're right! The article is not about the usual blackjack but a continuous version of the game, however I find interesting to understand this kind of problems. And maybe some day the casinos will start playing this version of the game ;)
- coopreme 4y agoThere are still many Vegas casinos where you get 3/2 odds on blackjack and play with a six deck shoe. Don’t give business to the strip CSM and 6/5 games if you don’t like it.
- evandale 4y agoThere's still single and double deck blackjack too. Treasure Island on the strip has double deck and a lot of casinos on Fremont, with El Cortez being my favorite, has single deck. Both are 3/2.