Longshots
  • In a recent post, someone remarked that it doesn't pay to play Carribean Poker until the jackpot gets to $250k. This seems very similar in thought to me to those that don't play the lottery until the jackpot gets to X amount.

    For me, it seems silly. The chances of you hitting the jackpot are so remote that it doesn't seem as if it would ever be worth it. If you have a 1 in a million chance of hitting a jackpot that is $10 million dollars, statistically you might say you should go for it because your expected value is high, but realistically you can't count on being the one in a million.

    Is there a statistically equivalent measure for this phenomenon? That is, basically subtracting longshots from the picture to get not an expected value, but say a realistic value?

    Now, for blackjack it may not really come into play since there are not these kinds of longshots are work, I don't think -- but maybe I'm wrong.
  • Here's why that works, and it does work.

    What you look at is risk and reward. If you have to risk a $10 min bet every time, you look at the odds of your winning. Say you come up with 1/10000. Clearly, if you make more than 100,000 bucks when you win, and you win once every 10,000 times, then you ought to play that game, correct?

    Lotteries follow the same rule, but the jackpot _never_ reaches anywhere close to the odds of you winning causing you to come out ahead. But the progressive jackpots in various games can and do reach beyond that point. And when it does, you just make the bet and play the odds. You won't win very often, obviously, but over time, you should win enough to more than break even. But only when you can compute the actual odds, as a fraction like 1/10000. Invert the fraction and multiply by the min bet you have to make to qualify for the jackpot. If the jackpot is larger than that number, go for it. If it is about the same, you are playing a coin toss.. If it is lower, you are playing a losing game. :)
  • I think you misunderstand. I know how to get the expected value. My point is that I will never play enough to reach the number of trials you need to be under the curve such that it is more likely than not that within those trials you will have one win (i.e. with n=1, the p-value with a 1 to 1,000,000 chance of winning 10M is not going to be good enough; n has to get pretty big). It seems like enough people don't focus on that aspect.
  • The probabilities are the same however, whether you play 1 hand or N thousand hands. This is the same idea as jumping on progressive slot machines when they are nearly into the "bonus" situations.

    But for the bonus progressive carnival game options, the idea is that in general, they are lousy bets period. But on rare occasions, while they are still lousy in their probability of your winning on a single hand, they are still a +EV bet, which is what advantage play is all about. 3-card poker can be beaten with a flashing dealer, but you won't win every hand, you just end up with a big edge, but not a certain win.
  • If by "probabilities" you mean EV, then you are right. However, I'm talking about p-values, where the N, if I'm remembering my statistics correctly, does matter.

    As a simple example, if you flip a coin three times, the chances that the results will equal the EV are much less than if you flip it 10,000 times. My point is that with odds of winning the jackpot so low, the N has to be fairly large to get a confidence interval where you can say you are probably going to be winning some money. Thus, the "odds" for the casual player who will go to the casino once a year and play Carribean Stud should be different than the "odds" for the professional who goes every single day. The EV doesn't change, but the degree of confidence of coming out a winner does.
  • Of course that is true. Remember that the "break-even" point is simply that point at which the probability of your winning the bet inverted (which is the number of rounds you need to play to expect to win one time) times your bet size, gives a value that is right about the value of the progressive pay-off. If the odds are 1/250000, and you are betting $10 a pop, when the progressive payoff is 2.5M you expect to exactly break-even. As the payoff continues to rise, the probability stays the same, so you begin to expect to do better than break-even. It depends on the jackpot you are after. If it is 2,500,010 bucks in the above game, you expect to win 10 bucks for every 250,000 rounds played. Not particularly good. But if it is up to $5,000,000 bucks, then you expect to win 2,500,000 for every 250,000 rounds played, or about 10 bucks per round played, which is a 100% payoff.

    You get to pick the jump-in point based on break-even and how far over that the actual payoff goes.

    Just remember that _any_ bet has some payoff amount that will turn it into a +EV game, assuming the bet is not an exactly zero probability bet.

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