Figuring out Payback on your wagers

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Payback is the percent of the total wager the player can expect to have returned to him when he plays a particular game. The critical piece here is the total amount wagered. The amount you buy in for is meaningless.

We need to add up every dollar (or nickel or dime or quarter) you put at risk at any point in a game for the entire time you play. If you’re playing video poker and playing the same amount every hand, the calculation of your total wager is very easy. It is the number of hands you played times the amount wagered per hand. So, if you played 700 hands of max-coin quarters, you wagered 700 times $1.25 or $875.

If you’re playing blackjack, the calculation is not so simple. You would have to keep track of how many times you doubled down and split. On average, you wager about 1.14 times the base wager when playing blackjack. So, if wagering $10, you’re really doing about $11.40 per hand. If you were to play 50 hands, we could approximate your total wager at $570.

If you were to play a game like Ultimate Texas Hold’em, you’d have to keep track of how many times you played 4x, 2x, 1x and folded. You would include your ante and blind wagers, but not Trips as this is an independent wager with its own payback.

Ultimate Texas Hold’em also has an average wager per hand associated with it. I believe it is between 4 and 5 units. This means a $5 player is really about a $22 per hand player, assuming Expert Strategy is used. Since we know many players are scared away from betting 4x as often as they should, you’re average wager per hand may be less than this. So, to get a more accurate picture it might be better to keep tabs on your own total wager.

Back to our video poker example. A player wagering $875 at a game with a 99.5% payback will lose 0.5% of the total wager, or about $4.38. This is just a theoretical amount that is more accurate over the long run, which is probably more than an hour or two. The more hands you play, the more likely your actual results will match the expected ones.

Blackjack and Ultimate have similar paybacks to video poker. But, over 50 hands in blackjack (about the same time it takes to play 700 of video poker), the $10 player will wager about $570. With a 0.5% house advantage (100% minus the payback), expect to lose $2.85. A $5 UTH player in for 50 hands would wager something closer to $1,100, which translates to a $5.50 loss or nearly twice as much as a blackjack player wagering twice as much as a “base.” But blackjack has a 1.14 average unit wager as compared to UTH’s 4-plus. As a result, you’ll lose more playing UTH, on average.

There are a variety of methods used to get us to where we need to be, but it comes down to multiplying the payout of each winning possibility by the frequency (probability) of that winning possibility and summing up these values.

Let’s use one of the simplest possible scenarios. You’re playing roulette and just put money on number 22! Assuming a double 00 wheel, if 22 comes up, you’ll win 36 to 1.

So, what is the probability of number 22 coming up? There are 38 numbers on the wheel and each has an equal probability. So 1 of 38 wins and 37 of 38 lose. The probability of winning is 1/38 or 2.6316%. The payout is the total amount returned to the player if he wins. The player will win $36 for each $1 wagered and keep his original wager. Thus the payout is 36 plus 1 (the original wager) for a total payout of 37.

Multiplying the payout of the winning possibility by the frequency of that possibility comes to 97.3684%. That is the payback of wagering on a single number on double 00 roulette wheel. Not every case is that simple.

Next week, I’ll go through more examples, which will include more complex wagers.

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About the Author

Elliot Frome

Elliot Frome’s roots run deep into gaming theory and analysis. His father, Lenny, was a pioneer in developing video poker strategy in the 1980s and is credited with raising its popularity to dizzying heights. Elliot is a second generation gaming author and analyst with nearly 20 years of programming experience.

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