1/7/2023 0 Comments Python card game simulatorPS The expected win is about $1.756 per game with the "48" or "50" strategy. I'll look at simulating playing on trying to get 3 cards ahead now. With probability #\frac 2 3# you are level after 50 cards, so with probability #\frac 1 3# you win $1.īoth strategies win $1 on average in this key case. Consider a playing card game in which the outcome is completely reliant on the initial distribution of the playing cards. All other cases being equal.įinally, it's just as good to play on if you are one card ahead after 49 cards from the "48" to the "50" strategy as your expected winning would be: A player gets two points for a payer consisting of two cards with rank 10 or greater. A player gets one point for a pair consisting of two cards with rank less than 10 (with an ace counting as greater than 10). For each player, all pairs in their hand are put down. That all adds up to an expected win of $1.2 dollars for the "48" strategy against $1 for the "46" strategy in these key cases. At the start of each hand, each player is dealt four cards. With probability #\frac 3 # of winning $1 after 51 cards. With probability #\frac 3 5# be level after 48 cards. With the "48" strategy, you would play on and: With the "46" strategy, you would quit now and take the $1 whenever this happens. The test case is where you are # 1# after 47 cards. You can confirm analytically that it's better to play on from 46 to 48 as follows. My first simulation gives an average win of #0.963# for the first strategy #1.200# if you try to get two cards ahead only until the second card (then quit whenever you are one card ahead after that) #1.318# if you try to get two cards ahead until the 4th card etc.Īnd, in fact, the optimum strategy is to keep playing until the 48th (or 50th) card looking to get two cards ahead. That's an average win of almost the same as above, but you can still win $1 on most of the remaining games. If your strategy is to play on to the second card, then you win $2 almost 50% of the time and are back to even about 50% of the time. If your strategy is to quit, then you win $1 every time this happens. You should stop when your current advantage is greater or equal to the expected maximum advantage if you continue the game. If there is a high enough variance so that you can expect some greater advantage at some point later on, then it is better to play for that.
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