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Best of Alan Krigman

Gaming Guru

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Hey, Buddy! Wanna Buy Some Match Play Tokens? Cheap?

9 August 2004

Casinos occasionally give solid citizens free match play tokens as table game rewards and incentives. In case you're unsure how they work, you can augment your wager with match play tokens up to the value of your cash bet on most even-money propositions. Win, and you're paid based on the sum of the two components, but the casino returns only the cash part of your bet and keeps the match play portion. Lose, and both elements get swept away. You have an edge on rounds using match play. And the advantage extends over later wagering because your expected profit on coups with match play exceeds the bosses' projected earnings on ordinary rounds for equal money at risk. The house accordingly needs more action to catch up than you had with the tokens.

What if you could buy match play tokens from the casino or a third party? They may be a sweet deal. Or, a bad bargain.

At over $0.50 per dollar of "face value," you'd be wasting money. For instance, pretend a $10-denominated match play token cost $6. This and $10 in cash chips could gain you $20 minus $6 for the match play token the casino will keep -- a net of $14. But a loss would set you back $16. So you're putting up $16 for a $14 profit on a bet where $16 at risk should earn you $16.

At exactly $0.50 per dollar of face value, buy-your-own match play would be a wash. At this price, you might bet $10 in cash and a $10 match play token that set you back $5. A win brings $20 but the house keeps the token, netting you $15. A loss costs you $10 in real money plus the match play token, also $15. It's just like risking $15 to win $15. You reach the same conclusion betting less than the maximum match play with your cash.

As another possibility, the casino or some third party might offer match play tokens at under $0.50 per dollar of face value. For example, at 25 percent discount, a $10 match play token would cost not $5 but $3.75. Betting $10 in cash with one such token, you'd collect $20 on a win but give up the match play, netting you $20 - $3.75 or $16.25. You have $10 + $3.75 or $13.75 at risk. The even-money proposition gets you $16.25 for $13.75.

Edge under various circumstances depends on the specific wager. Bets on Player at baccarat illustrate the effect. With match play costing $0.375 per dollar of face value, you have a 10.5 percent edge as opposed the casino getting 1.3 percent. You expect to make eight times as much per dollar as the bosses would with a pure cash bet. You can therefore go eight rounds betting $10 in cash for every round at $10 in real money plus $10 in match play tokens that you bought for $3.75 each, before the house regains the edge. That's nine rounds you enjoy as a favorite for every match play token bought at 25 percent off $0.50 on the dollar.

Here are three formulas you can punch out on any calculator to figure how many total rounds you can gamble at an advantage over the house, per match play token you buy, in other situations. The formulas give rounds for arbitrary values of discount (D percent) and house edge under standard conditions (e percent), for three different ways of betting after your match play tokens are gone.

    1) Bet at the previous nominal level (e.g., if you were risking $10 cash and $10 match play, continue at $20)
    R=0.25*[(D/e) + 1].

    2) Bet at the previous cash level (e.g., if you were risking $25 cash and $25 match play, continue at $25)
    R=0.5*[(D/e) - 1].

    3) Bet at half the previous cash level (e.g., if you were risking $100 cash and $100 match play, continue at $50)
    R=[(D/e) - 2].

Trying a few typical values will quickly show you that the deeper the discount and the lower the "official" edge, the more action you can obtain with positive expectation. And, of course, more discounted tokens let you play longer at an advantage overall. In a game with low normal house edge, like blackjack with good Basic Strategy (e=0.004), as few as 10 tokens discounted by 25 percent (D=0.25) can get you an entire casino visit in the catbird seat. Demonstrating the ditty penned by the poet, Sumner A Ingmark:

In resolving an impasse you may find it effective,
To consider the problem from a whole new perspective.

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.