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VIDEO POKER
 Bob Dancer writes a video poker column for beginners to experts. He also writes a column each week with Jeffrey Compton titled Player's Edge, which features information on promotions at various Las Vegas Hotel. Player's Edge is published each Friday in the Las Vegas Review-Journal. Click here to send Bob Dancer an e-mail.
June 25, 2002
Comparing the worth of 10/7/80 combinations to 10/7/50 Combinations
10/7 Double Bonus is one game where knowledgeable players have the advantage --- so the game has been studied extensively by several top players, including me. The IGT version of the game, by far the most common, returns 50 coins per coin bet for a straight flush.
The 10/7 game found on Bally GameMakers returns 400 for a straight flush when you bet five coins --- which averages out to 80 coins per coin bet, although you don't get that amount unless you bet max coins. Players who wish to differentiate between the two games usually refer to the IGT version as 10/7/50 and the Bally GameMaker version as 10/7/80.
For players who know the worth of various combinations in the 10/7/50 game, it is not difficult to determine how much the value of each combination changes when you are playing the 10/7/80 game.
Assume you are playing for dollars. (If you play for quarters, simply divide all dollar figures presented here by 4.) So getting a straight flush on the 10/7/80 game is $150 more valuable than getting it on the 10/7/50 game. If we knew the value of a 7h8h9hTh combination in 10/7/50, what would its value be in the 10/7/80 game?
There are 47 cards you can draw to any dealt 5-card hand. Two of those cards (the 6h and the Jh) complete a straight flush worth an extra $150. So the value of this combination is worth an extra 2 * $150 / 47 = $6.38 in the 10/7/80 game. A one-way straight flush draw (like 6c7c9cTc) would be worth an extra amount equal to half that, or $3.19.
Three card straight flush combinations need to draw two cards, and there are 1,081 combinations of two cards you can draw to each 3-card starting point. Open-ended straight flush draws (like 6s7s8s) have 3 different combinations to complete the draw (namely Ts9s, 9s5s, and 5s4s). So these will be worth an extra 3*$150/1,081 = 42¢. 3-card straight flush draws with one inside (like 3d 4d 6d) have two combinations which will yield the straight flush (namely 7d5d and 5d2d), so they are worth an extra 2*$150/1,081 = 28¢. 3-card straight flush draws with two insides (such as 2c5c6c) have only one combination that will complete it (namely 3c4c) so that is worth an extra 1*$150/1,081=14¢.
Sometimes it is not immediately obvious which category to place a 3-card straight flush draw in. For example, consider Kh Qh Jh, which happens to be a 3-card royal. The value of the royal (i.e. $4,000) hasn't changed between the two games. And the only straight flush this combination may be part of is KQJT9, so this is treated as a straight flush combination with two insides (for straight flush purposes) and its value increases by 14¢.
Two card straight flushes aren't held in the 10/7/50 game, but occasionally a suited 45, 89 or 9T are held in the 10/7/80 game. Two-card royals are frequently held in both games. How much these combinations increase in value depends on how many straight flushes may result. The only straight flush a king-high 2-card royal may be part of is KQJT9. Since there are 16,215 possible combinations when you draw three cards, the value of each king-high 2-card royal will increase by 1*$150/16,215 = 0.9¢. Queen-high 2-card royals may be part of a KQJT9 or QJT98 straight flush, so their value will increase by twice this much, i.e. 1.8¢. Finally, a suited JT may be part of three different straight flushes, so its value increases by 2.8¢.
The value of holding single cards only increases by an infinitesimal amount. A single jack, for example, may be part of 3 straight flushes, each of which have one chance in 178,365 of coming home. So the increase in value of a J is 4*$150/178,365 = about a quarter of a cent. A single ace, king or queen increase in value by even less than that.
So what does this all mean? If you know, for example, that on a hand such as 4h 6h 8h Js 7d that it is correct in the 10/7/50 game to hold the J by about a penny, then with the new pay schedule the value of the suited 468 goes up by 14¢, so we know that we should hold 468 in the 10/7/80 game.
Next week, I'll provide a list of plays that are different between the two games. To make a complete list, we need to talk about straight penalties, flush penalties and straight flush penalties. Players who do not wish to concern themselves with such matters may use the same strategy for both games. The differences are only worth .03% or so in expected value. For a dollar player, this would be about $1 per hour.
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