In theory, if you are playing a game where the odds are in your favor, and you play long enough, eventually you will come out a winner. In practice, though, you have a finite stake, and you are going to quit if you run out of money. Thus you could very possibly walk away a loser from a game that is actually in your favor. This phenomenon goes by the evocative name of gambler's ruin.
In video poker, gambler's ruin is especially relevant because about 2% of your total payout (it varies from game to game) is due to the royal flush jackpot, which occurs on average once every 40,000 hands or so. Thus, even if the machine has a fraction of a per cent bias in your favor when you play them optimally (and some do, see my strategy article), the game will still be in the casino's favor as long as you do not hit a royal flush. And, of course, if you do hit a royal flush, it is really hard to walk away a loser.
The calculator tells you what your probability is of being in each winnings range (including "retired" and "busted"), for the number of hands shown. You enter your initial stake, and at what point you will be willing to walk away a winner. (I hope this is not a completely foreign concept for you.) You can run it for any number of hands.
The estimated elapsed time in the calculator is based on the rule of thumb that you play about 10 hands a minute; 600 hands an hour. This is fast, but not blindingly fast. You may play slower or faster and you should adjust the estimate accordingly. The calculator assumes you are playing 5 quarters with every hand.
The percentage returns used by the calculator assume you play the
optimal
strategy and make no mistakes. The returns are:
|
Machine Name |
Return |
|
Jacks-or-better |
99.5% |
|
Jacks-or-better (4700 royal) |
99.9% |
|
Jacks-or-better (8/5) |
97.3% |
|
Tens-or-better |
99.5% |
|
Bonus Poker |
99.3% |
|
Double Bonus |
100.2% |
|
Deuces wild |
100.8% |
|
Joker wild |
100.6% |
|
Joker wild (4700 royal) |
101.0% |
|
Five wild cards |
99.0% |
Many casinos give you a very good way to measure how much you have played, that is, how much money you have put through the machine. Their slot machine club’s cards displays the “points” you have earned. For example, at the various Station casinos in Vegas, you get one point for each $1 you play. At the Venetian in Vegas, you get one point for every $35 of play. (It used to be $25, but they changed to disadvantage video poker players.) Of course, this does not necessarily mean that the Station casinos are a better deal; it depends on how much the points are worth in terms of perks. But regardless, by looking at your points, you can see how much you have played.
If you’ve played with the Gambler’s Ruin calculator above, you would have seen, even with a game in your favor such as full-pay Deuces Wild, if you start $100, most of the time you are going to lose it. This is to be expected. But recently I had five $100 sessions in a row in which I not just lost, but, it seemed to me, lost exceptionally fast. So I used the calculator above to determine whether my experience was really that unusual. The table below has the results:
|
Chance of Losing $100 |
Points ($) |
|
1% |
328 |
|
2.5% |
388 |
|
5% |
460 |
|
10% |
568 |
|
25% |
881 |
|
50% |
1710 |
This table shows the probability of losing $100 after a certain number of points. In this case, one point was $1 of play, but you can convert it to your favorite slot club’s point value. The table shows, for example, that only 1% of the time would players lose $100 in 328 points or less. On the other hand, half of the time a player should lose $100 in 1710 points or less. This table is only valid for a $0.25 full-pay Deuces Wild machines. For other denominations, convert the points to hands. (328 points = $328 / $1.25 = 262 hands).
So how bad were my five bad sessions? The probability I could have lost that fast for was 1.5%, 25%, 20%, 20%, 15%. I was very unlucky. The chance that five sessions in a row would yield results that bad is 0.015*0.25*0.20*0.20*0.15 or less than 2 chances in 100,000! It was enough to make me question whether the machines at that particular casino were on the up-and-up. The next session, however, I hit a royal flush. Of course, that proves nothing, but it made me feel better, and I still play there.
By the way, here is the table giving the probabilities for losing $50:
|
Chance of Losing $50 |
Points ($) |
|
1% |
113 |
|
2.5% |
132 |
|
5% |
155 |
|
10% |
193 |
|
25% |
303 |
|
50% |
596 |
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