Good day!
I was messing around with simulations in a blackjack-like game whereupon the players (in the case of the simulation it was just two players) try to reach as close as possible to 1000 by multiplying the value of their cards. If one player goes over 1000, the other wins. If both players go over 1000 or have the same score the game is a tie--otherwise the player with the product closest to 1000 wins. For example, if $p_1=[10,11,5]$ and $p_2=[11,11,3]$ player one would win since $550>363$. The deck initially has the following frequencies of {"1":4, "2":4,"3":4,"4":4,"5":4,"6":4,"7":4,"8":4,"9":4,"10":20,"11":4} or more neatly {1-9:4, 10:20, 11:4}. Player one hits (draws a card) unless he has a score above 223. Player two hits as long as the chance of losing is below $p$. The graph of the score of player one (n=50,000 iirc), $S(p)$, when plotted appeared similar to $ciel$ and $floor$ functions 1. Why is this occurring?
Best,
Yan
2026-04-29 17:18:15.1777483095
