Monday, February 6, 2006

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Lottery: Do they make sense of the martingale?

I told him a friend and all of a sudden I smiled incredulously.

Then I gave a couple of laps. I thought, finally, after all, in lotteries bet a number, there is a chance to win a lot, and probability of losing.

In the lottery, when double bet, it makes sense to bet on different numbers, while the martingale betting is always the same. For this reason, you can win the lottery but have no reason to retrieve the bet, while the wheel itself is recovered every dollar.

The advantage of the lottery is not betting limit, unlike the casino, which is a martingale always winners, but need a lot of dough if you have very bad luck.

I'll put an example with the Euromillions, so popular with both boat and has been. I'm assuming that if hits 2 +1 (minimum accuracy) need to earn 9 euros. The probability of touching 2 +1 is 1 / 38 = 2.63% (I have not calculated what I got from here ). The probability that you touch is NOT 37/38. The minimum bet, as you know, is 2 €.

The minimal martingale goes like this:
7 3 694
2 2 9 97.37%
2 4 9 94.81 % 5
2 6 9 92.31%
2 8 9 89,88% 1
4 12 18 87,52% 6
4 16 18 85,21% 2
6 22 27 82,97% 5
8 30 36 80,79% 6
10 40 45 78,66% 5
12 52 54 76,59% 2
16 68 72 74,58% 4
20 88 90 72,61% 2
26 114 117 70,70% 3
34 148 153 68,84% 5
44 192 198 67,03% 6
56 248 252 65,27% 4
72 320 324 63,55% 4
92 412 414 61,88% 2
120 532 540 60,25% 8
154 686 693 58,66% 7
198 884 891 57,12% 7
254 1138 1143 55,62% 5
326 1464 1467 54,15% 3
420 1884 1890 52,73% 6
540 2424 2430 51,34% 6
3118 3123 49.99% 5

The columns are:
1 .- The amount to bet to win
2 .- The cumulative amount lost if you lose
3 .- The amount to be won, if winning
4 .- The probability of losing
5 .- Net income

As you see, so that the probability of loss is less than 50% have to play for 36 consecutive weeks to the same combination of numbers displayed in the first column.

In case you are curious, so that the probability of losing less than 1% have to play for 173 weeks in a row, this is 40 months, almost 4 years. You can imagine the payout.

mathematically possible, is physically absurd?

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