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    "def one_ace(n):  # Compute the probability of one ace in each hand using n samples\n",
    "    import numpy as np\n",
    "    rng = np.random.default_rng()  # defaul numpy random number generator\n",
    "    \n",
    "    deck = np.arange(52)  # cards will be numbered from 0 to 51\n",
    "    aces_ok = 0  # number of successes will be stored here\n",
    "\n",
    "    # To fix values, we will atribute 0, 13, 26 and 39 to the four aces\n",
    "    # Could be any four distinct numbers in 0 .. 51.\n",
    "    \n",
    "    for k in range(n):  # sample n times\n",
    "        hands = rng.choice(deck, size=(4,13), replace=False) # Choose randomly the four hands without replacement\n",
    "        \n",
    "        # construct a four components array with the number of aces in each hand\n",
    "        naces = np.sum(hands==0, axis=1) + np.sum(hands==13, axis=1) \\\n",
    "               + np.sum(hands==26, axis=1) + np.sum(hands==39, axis=1)\n",
    "        \n",
    "        aces_ok += np.product(naces)  # if there is one ace in each hand, the product is one, otherwise is zero\n",
    "    \n",
    "    return aces_ok / n  # frequency of successes"
   ]
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   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "one_ace(100000)"
   ]
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   "execution_count": null,
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   "source": []
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